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We describe an optimization-based framework to perform complex locomotion skills for robots with legs and wheels. The generation of complex motions over a long-time horizon often requires offline computation due to current computing constraints and is mostly accomplished through trajectory optimization (TO). In contrast, model predictive control (MPC) focuses on the online computation of trajectories, robust even in the presence of uncertainty, albeit mostly over shorter time horizons and is prone to generating nonoptimal solutions over the horizon of the task's goals. Our article's contributions overcome this trade-off by combining offline motion libraries and online MPC, uniting a complex, long-time horizon plan with reactive, short-time horizon solutions. We start from offline trajectories that can be, for example, generated by TO or sampling-based methods. Also, multiple offline trajectories can be composed out of a motion library into a single maneuver. We then use these offline trajectories as the cost for the online MPC, allowing us to smoothly blend between multiple composed motions even in the presence of discontinuous transitions. The MPC optimizes from the measured state, resulting in feedback control, which robustifies the task's execution by reacting to disturbances and looking ahead at the offline trajectory. With our contribution, motion designers can choose their favorite method to iterate over behavior designs offline without tuning robot experiments, enabling them to author new behaviors rapidly. Our experiments demonstrate complex and dynamic motions on our traditional quadrupedal robot ANYmal and its roller-walking version. Moreover, the article's findings contribute to evaluating five planning algorithms. [ABSTRACT FROM AUTHOR]

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we present an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems. [ABSTRACT FROM AUTHOR]

In this article, we propose deep visual reasoning, which is a convolutional recurrent neural network that predicts discrete action sequences from an initial scene image for sequential manipulation problems that arise, for example, in task and motion planning (TAMP). Typical TAMP problems are formalized by combining reasoning on a symbolic, discrete level (e.g., first-order logic) with continuous motion planning such as nonlinear trajectory optimization. The action sequences represent the discrete decisions on a symbolic level, which, in turn, parameterize a nonlinear trajectory optimization problem. Owing to the great combinatorial complexity of possible discrete action sequences, a large number of optimization/motion planning problems have to be solved to find a solution, which limits the scalability of these approaches. To circumvent this combinatorial complexity, we introduce deep visual reasoning: based on a segmented initial image of the scene, a neural network directly predicts promising discrete action sequences such that ideally only one motion planning problem has to be solved to find a solution to the overall TAMP problem. Our method generalizes to scenes with many and varying numbers of objects, although being trained on only two objects at a time. This is possible by encoding the objects of the scene and the goal in (segmented) images as input to the neural network, instead of a fixed feature vector. We show that the framework can not only handle kinematic problems such as pick-and-place (as typical in TAMP), but also tool-use scenarios for planar pushing under quasi-static dynamic models. Here, the image-based representation enables generalization to other shapes than during training. Results show runtime improvements of several orders of magnitudes by, in many cases, removing the need to search over the discrete action sequences. [ABSTRACT FROM AUTHOR]

This article presents a novel optimization method that handles collision constraints with complex, non-convex 3D geometries. The optimization problem is cast as a semi-infinite program in which each collision constraint is implicitly treated as an infinite number of numeric constraints. The approach progressively generates some of these constraints for inclusion in a finite nonlinear program. Constraint generation uses an oracle to detect points of deepest penetration, and this oracle is implemented efficiently via signed distance field (SDF) versus point cloud collision detection. This approach is applied to pose optimization and trajectory optimization for both free-flying rigid bodies and articulated robots. Experiments demonstrate performance improvements compared with optimizers that handle only convex polyhedra, and demonstrate efficient collision avoidance between non-convex CAD models and point clouds in a variety of pose and trajectory optimization settings. [ABSTRACT FROM AUTHOR]

We focus on decentralized navigation among multiple non-communicating agents in continuous domains without explicit traffic rules, such as sidewalks, hallways, or squares. Following collision-free motion in such domains requires effective mechanisms of multiagent behavior prediction. Although this prediction problem can be shown to be NP-hard, humans are often capable of solving it efficiently by leveraging sophisticated mechanisms of implicit coordination. Inspired by the human paradigm, we propose a novel topological formalism that explicitly models multiagent coordination. Our formalism features both geometric and algebraic descriptions enabling the use of standard gradient-based optimization techniques for trajectory generation but also symbolic inference over coordination strategies. In this article, we contribute (a) HCP (Hamiltonian Coordination Primitives), a novel multiagent trajectory-generation pipeline that accommodates spatiotemporal constraints formulated as symbolic topological specifications corresponding to a desired coordination strategy; (b) HCPnav, an online planning framework for decentralized collision avoidance that generates motion by following multiagent trajectory primitives corresponding to high-likelihood, low-cost coordination strategies. Through a series of challenging trajectory-generation experiments, we show that HCP outperforms a trajectory-optimization baseline in generating trajectories of desired topological specifications in terms of success rate and computational efficiency. Finally, through a variety of navigation experiments, we illustrate the efficacy of HCPnav in handling challenging multiagent navigation scenarios under homogeneous or heterogeneous agents across a series of environments of different geometry. [ABSTRACT FROM AUTHOR]

We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and extends sequential action control to stochastic dynamics. The resulting algorithm, which we name SACBP, does not require discretization of spaces or time and synthesizes control signals in near real-time. SACBP is an anytime algorithm that can handle general parametric Bayesian filters under certain assumptions. We demonstrate the effectiveness of our approach in an active sensing scenario and a model-based Bayesian reinforcement learning problem. In these challenging problems, we show that the algorithm significantly outperforms other existing solution techniques including approximate dynamic programming and local trajectory optimization. [ABSTRACT FROM AUTHOR]

We propose a novel belief space planning technique for continuous dynamics by viewing the belief system as a hybrid dynamical system with time-driven switching. Our approach is based on the perturbation theory of differential equations and extends sequential action control to stochastic dynamics. The resulting algorithm, which we name SACBP, does not require discretization of spaces or time and synthesizes control signals in near real-time. SACBP is an anytime algorithm that can handle general parametric Bayesian filters under certain assumptions. We demonstrate the effectiveness of our approach in an active sensing scenario and a model-based Bayesian reinforcement learning problem. In these challenging problems, we show that the algorithm significantly outperforms other existing solution techniques including approximate dynamic programming and local trajectory optimization. [ABSTRACT FROM AUTHOR]

We focus on decentralized navigation among multiple non-communicating agents in continuous domains without explicit traffic rules, such as sidewalks, hallways, or squares. Following collision-free motion in such domains requires effective mechanisms of multiagent behavior prediction. Although this prediction problem can be shown to be NP-hard, humans are often capable of solving it efficiently by leveraging sophisticated mechanisms of implicit coordination. Inspired by the human paradigm, we propose a novel topological formalism that explicitly models multiagent coordination. Our formalism features both geometric and algebraic descriptions enabling the use of standard gradient-based optimization techniques for trajectory generation but also symbolic inference over coordination strategies. In this article, we contribute (a) HCP (Hamiltonian Coordination Primitives), a novel multiagent trajectory-generation pipeline that accommodates spatiotemporal constraints formulated as symbolic topological specifications corresponding to a desired coordination strategy; (b) HCPnav, an online planning framework for decentralized collision avoidance that generates motion by following multiagent trajectory primitives corresponding to high-likelihood, low-cost coordination strategies. Through a series of challenging trajectory-generation experiments, we show that HCP outperforms a trajectory-optimization baseline in generating trajectories of desired topological specifications in terms of success rate and computational efficiency. Finally, through a variety of navigation experiments, we illustrate the efficacy of HCPnav in handling challenging multiagent navigation scenarios under homogeneous or heterogeneous agents across a series of environments of different geometry. [ABSTRACT FROM AUTHOR]

This article presents a novel optimization method that handles collision constraints with complex, non-convex 3D geometries. The optimization problem is cast as a semi-infinite program in which each collision constraint is implicitly treated as an infinite number of numeric constraints. The approach progressively generates some of these constraints for inclusion in a finite nonlinear program. Constraint generation uses an oracle to detect points of deepest penetration, and this oracle is implemented efficiently via signed distance field (SDF) versus point cloud collision detection. This approach is applied to pose optimization and trajectory optimization for both free-flying rigid bodies and articulated robots. Experiments demonstrate performance improvements compared with optimizers that handle only convex polyhedra, and demonstrate efficient collision avoidance between non-convex CAD models and point clouds in a variety of pose and trajectory optimization settings. [ABSTRACT FROM AUTHOR]

Existing motion planning methods often have two drawbacks: (1) goal configurations need to be specified by a user, and (2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist to achieve a task. Although the choice of the goal configuration significantly affects the quality of the resulting trajectory, it is not trivial for a user to specify the optimal goal configuration. In addition, the objective function used in the trajectory optimization is often non-convex, and it can have multiple solutions that achieve comparable costs. In this study, we propose a framework that determines multiple trajectories that correspond to the different modes of the cost function. We reduce the problem of identifying the modes of the cost function to that of estimating the density induced by a distribution based on the cost function. The proposed framework enables users to select a preferable solution from multiple candidate trajectories, thereby making it easier to tune the cost function and obtain a satisfactory solution. We evaluated our proposed method with motion planning tasks in 2D and 3D space. Our experiments show that the proposed algorithm is capable of determining multiple solutions for those tasks. [ABSTRACT FROM AUTHOR]

Manifolds are used in almost all robotics applications even if they are not modeled explicitly. We propose a differential geometric approach for optimizing trajectories on a Riemannian manifold with obstacles. The optimization problem depends on a metric and collision function specific to a manifold. We then propose our safe corridor on manifolds (SCM) method of computationally optimizing trajectories for robotics applications via a constrained optimization problem. Our method does not need equality constraints, which eliminates the need to project back to a feasible manifold during optimization. We then demonstrate how this algorithm works on an example problem on SO (3) and a perception-aware planning example for visual–inertially guided robots navigating in three dimensions. Formulating field of view constraints naturally results in modeling with the manifold R 3 × S 2 , which cannot be modeled as a Lie group. We also demonstrate the example of planning trajectories on SE (3) for a formation of quadrotors within an obstacle filled environment. [ABSTRACT FROM AUTHOR]

Contact constraints arise naturally in many robot planning problems. In recent years, a variety of contact-implicit trajectory optimization algorithms have been developed that avoid the pitfalls of mode pre-specification by simultaneously optimizing state, input, and contact force trajectories. However, their reliance on first-order integrators leads to a linear tradeoff between optimization problem size and plan accuracy. To address this limitation, we propose a new family of trajectory optimization algorithms that leverage ideas from discrete variational mechanics to derive higher-order generalizations of the classic time-stepping method of Stewart and Trinkle. By using these dynamics formulations as constraints in direct trajectory optimization algorithms, it is possible to perform contact-implicit trajectory optimization with significantly higher accuracy. For concreteness, we derive a second-order method and evaluate it using several simulated rigid-body systems, including an underactuated biped and a quadruped. In addition, we use this second-order method to plan locomotion trajectories for a complex quadrupedal microrobot. The planned trajectories are evaluated on the physical platform and result in a number of performance improvements. [ABSTRACT FROM AUTHOR]

The ability to generate accurate terrain models is of key importance in a wide variety of robotics tasks, ranging from path planning and trajectory optimization to environment exploration and mining applications. This paper introduces a novel regression methodology for terrain modeling that can approximate arbitrarily complex functions based on a series of simple kernel calculations, using variational Bayesian inference. A sparse feature vector is used to efficiently project input points into a high-dimensional reproducing kernel Hilbert space, according to a set of inducing points automatically generated from clustering available data. Each inducing point maintains its own regression model in addition to individual kernel parameters, and the entire set is iteratively optimized as more data are collected in order to maximize a global variational lower bound. We also show how kernel and regression model parameters can be jointly learned, to achieve a better approximation of the underlying function. Experimental results show that the proposed methodology consistently outperforms current state-of-the-art techniques, while producing a continuous model with a fully probabilistic treatment of uncertainties, well-defined gradients, and highly scalable to large-scale datasets. As a practical application of the proposed terrain modeling technique, we explore the problem of trajectory optimization, deriving gradients that allow the efficient generation of continuous paths using standard optimization algorithms, minimizing a series of useful properties (i.e. distance traveled, changes in elevation, and terrain variance). [ABSTRACT FROM AUTHOR]

To overcome the obstructions imposed by high-dimensional bipedal models, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The process begins with trajectory optimization to design an open-loop periodic walking motion of the high-dimensional model and then adding to this solution a carefully selected set of additional open-loop trajectories of the model that steer toward the nominal motion. A drawback of trajectories is that they provide little information on how to respond to a disturbance. To address this shortcoming, supervised machine learning is used to extract a low-dimensional state-variable realization of the open-loop trajectories. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The design procedure is first developed for ordinary differential equations and illustrated on a simple model. The methods are subsequently extended to a class of hybrid models and then realized experimentally on an Atrias-series 3D bipedal robot. [ABSTRACT FROM AUTHOR]

We present an approach to synthesize robot arm trajectories that effectively communicate the robot’s intent to a human collaborator while achieving task goals. Our approach uses nonlinear constrained optimization to encode task requirements and desired motion properties. Our implementation allows for a wide range of constraints and objectives. We introduce a novel objective function to optimize robot arm motions for intent-expressiveness that works in a range of scenarios and robot arm types. Our formulation supports experimentation with different theories of how viewers interpret robot motion. Through a series of human-subject experiments on real and simulated robots, we demonstrate that our method leads to improved collaborative performance against other methods, including the current state of the art. These experiments also show how our perception heuristic can affect collaborative outcomes. [ABSTRACT FROM AUTHOR]

We introduce a novel formulation of motion planning, for continuous-time trajectories, as probabilistic inference. We first show how smooth continuous-time trajectories can be represented by a small number of states using sparse Gaussian process (GP) models. We next develop an efficient gradient-based optimization algorithm that exploits this sparsity and GP interpolation. We call this algorithm the Gaussian Process Motion Planner (GPMP). We then detail how motion planning problems can be formulated as probabilistic inference on a factor graph. This forms the basis for GPMP2, a very efficient algorithm that combines GP representations of trajectories with fast, structure-exploiting inference via numerical optimization. Finally, we extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan when conditions change. We benchmark our algorithms against several sampling-based and trajectory optimization-based motion planning algorithms on planning problems in multiple environments. Our evaluation reveals that GPMP2 is several times faster than previous algorithms while retaining robustness. We also benchmark iGPMP2 on replanning problems, and show that it can find successful solutions in a fraction of the time required by GPMP2 to replan from scratch. [ABSTRACT FROM AUTHOR]

The goal of this paper is to propose a coupling between the execution of an image-based visual servoing task and an active structure from motion strategy. The core idea is to modify online the camera trajectory in the null-space of the (main) servoing task for rendering the camera motion ‘more informative’ with respect to the estimation of the 3-D structure. Consequently, the structure from motion convergence rate and accuracy is maximized during the servoing transient. The improved structure from motion performance also benefits the servoing execution, since a higher accuracy in the 3-D parameters involved in the interaction matrix improves the image-based visual servoing convergence by significantly mitigating the negative effects (instability, loss of feature visibility) of a poor knowledge of the scene structure. Active maximization of the structure from motion performance results, in general, in a deformed camera trajectory with respect to what would be obtained with a classical image-based visual servoing: therefore, we also propose an adaptive strategy able to automatically activate/deactivate the structure from motion optimization as a function of the current level of accuracy in the estimated 3-D structure. We finally report a thorough experimental validation of the overall approach under different conditions and case studies. The reported experiments support well the theoretical analysis and clearly show the benefits of the proposed coupling between visual control and active perception. [ABSTRACT FROM AUTHOR]

Rotating shafts are prone to vibration and it is necessary to mitigate these vibrations to ensure proper operation of the machine. Such mitigation can be performed by active control. Among the available control strategies, one can apply the methodology proposed by Udwadia and Kalaba for trajectory control of nonlinear systems. In this work, such methodology is analyzed for controlling the lateral vibrations of a rotating shaft. First, this control technique is evaluated by placing the sensor-actuator pair in the point of interest for control (disc position of the shaft). Results show that the kinematic constraints applied by the control strategy are exactly tracked and lateral vibration of the shaft is significantly reduced. Second, the control technique is evaluated by placing the sensor-actuator pair at the bearing position of the shaft, thus far from the point of interest for control (disc position). In this case, vibration is reduced at the point of actuation, but not at the point of interest for control. However, the application of the methodology in an on/off strategy resulted in a successful reduction of the lateral vibrations of the shaft at the point of interest for control when crossing the first critical speeds. [ABSTRACT FROM AUTHOR]

This paper introduces a method to minimize norms on nonlinear trajectory sensitivities during open-loop trajectory optimization. Specifically, we derive new parametric sensitivity terms that measure the variation in nonlinear (continuous-time) trajectories due to variations in model parameters, and hybrid sensitivities, which account for variations in trajectory caused by sudden transitions from nominal dynamics to alternative dynamic modes. We adapt continuous trajectory optimization to minimize these sensitivities while only minimally changing a nominal trajectory. We provide appended states, cost, and linearizations, required so that existing open-loop optimization methods can generate minimally sensitive feedforward trajectories. Although there are several applications for sensitivity optimization, this paper focuses on robot motion planning, where popular sample-based planners rely on local trajectory generation to expand tree/graph structures. While such planners often use stochastic uncertainty propagation to model and reduce uncertainty, this paper shows that trajectory uncertainty can be reduced by minimizing first-order sensitivities. Simulated vehicle examples show parametric sensitivity optimization generates trajectories optimally insensitive to parametric model uncertainty. Similarly, minimizing hybrid sensitivities reduces uncertainty in crossing mobility hazards (e.g. rough terrain, sand, ice). Examples demonstrate the process yields a planner that uses approximate hazard models to automatically and optimally choose when to avoid hazardous terrain and when controls can be adjusted to traverse hazards with reduced uncertainty. Sensitivity optimization offers a simple alternative to stochastic simulation and complicated uncertainty modeling for nonlinear systems. [ABSTRACT FROM AUTHOR]

Nowadays, autonomously operated nonholonomic vehicles are employed in a wide range of applications, ranging from relatively simple household chores (e.g. carpet vacuuming and lawn mowing) to highly sophisticated assignments (e.g. outer space exploration and combat missions). Each application may require different levels of accuracy and capabilities from the vehicles, yet, all expect the same critical outcome: to safely complete the task while avoiding collisions with obstacles and the environment. Herein, we report on a bounded control law for nonholonomic systems of unicycle-type that satisfactorily drive a vehicle along a desired trajectory while guaranteeing a minimum safe distance from another vehicle or obstacle at all times. The control law is comprised of two parts. The first is a trajectory tracking and set-point stabilization control law that accounts for the vehicle’s kinematic and dynamic constraints (i.e. restrictions on velocity and acceleration). We show that the bounded tracking control law enforces global asymptotic convergence to the desired trajectory and local exponential stability of the full state vector in the case of set-point stabilization. The second part is a real-time avoidance control law that guarantees collision-free transit for the vehicle in noncooperative and cooperative scenarios independently of bounded uncertainties and errors in the obstacles’ detection process. The avoidance control acts locally, meaning that it is only active when an obstacle is close and null when the obstacle is safely away. Moreover, the avoidance control is designed according to the vehicle’s acceleration limits to compensate for lags in the vehicle’s reaction time. The performance of the synthesized control law is then evaluated and validated via simulation and experimental tests. [ABSTRACT FROM AUTHOR]

The construction of feedback control laws for underactuated nonlinear robotic systems with input saturation limits is crucial for dynamic robotic tasks such as walking, running, or flying. Existing techniques for feedback control design are either restricted to linear systems, rely on discretizations of the state space, or require solving a nonconvex optimization problem that requires feasible initialization. This paper presents a method for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). In contrast to traditional approaches based on Lyapunov’s criteria for stability, we rely on the notion of occupation measures to pose this problem as an infinite-dimensional linear program which can then be approximated in finite dimension via semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS which is well suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on six nonlinear systems. Comparisons to an infinite-horizon linear quadratic regulator approach and an approach relying on Lyapunov’s criteria for stability are also included in order to illustrate the improved performance of the presented technique. [ABSTRACT FROM AUTHOR]

This paper presents a method for generating dynamically feasible, keyframe-interpolating motions for robots undergoing contact, such as in legged locomotion and manipulation. The first stage generates a twice-differentiable interpolating path that obeys kinematic contact constraints up to a user-specified tolerance. The second stage optimizes speeds along the path to minimize time while satisfying dynamic constraints. The method supports velocity, acceleration, and torque constraints, and polyhedral contact friction constraints at an arbitrary number of contact points. The method is numerically stable, and empirical running time is weakly linear in the number of degrees of freedom and polynomial in the time-domain grid resolution. Experiments demonstrate that full-body motions for robots with 100 degrees of freedom and dozens of contact points are calculated in seconds. [ABSTRACT FROM AUTHOR]

We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naïve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt.We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http://rll.berkeley.edu/trajopt/ijrr. [ABSTRACT FROM AUTHOR]

Direct methods for trajectory optimization are widely used for planning locally optimal trajectories of robotic systems. Many critical tasks, such as locomotion and manipulation, often involve impacting the ground or objects in the environment. Most state-of-the-art techniques treat the discontinuous dynamics that result from impacts as discrete modes and restrict the search for a complete path to a specified sequence through these modes. Here we present a novel method for trajectory planning of rigid-body systems that contact their environment through inelastic impacts and Coulomb friction. This method eliminates the requirement for a priori mode ordering. Motivated by the formulation of multi-contact dynamics as a Linear Complementarity Problem for forward simulation, the proposed algorithm poses the optimization problem as a Mathematical Program with Complementarity Constraints. We leverage Sequential Quadratic Programming to naturally resolve contact constraint forces while simultaneously optimizing a trajectory that satisfies the complementarity constraints. The method scales well to high-dimensional systems with large numbers of possible modes. We demonstrate the approach on four increasingly complex systems: rotating a pinned object with a finger, simple grasping and manipulation, planar walking with the Spring Flamingo robot, and high-speed bipedal running on the FastRunner platform. [ABSTRACT FROM PUBLISHER]

Action prediction and fluidity are key elements of human–robot teamwork. If a robot’s actions are hard to understand, it can impede fluid human–robot interaction. Our goal is to improve the clarity of robot motion by making it more human-like. We present an algorithm that autonomously synthesizes human-like variants of an input motion. Our approach is a three-stage pipeline. First we optimize motion with respect to spatiotemporal correspondence (STC), which emulates the coordinated effects of human joints that are connected by muscles. We present three experiments that validate that our STC optimization approach increases human-likeness and recognition accuracy for human social partners. Next in the pipeline, we avoid repetitive motion by adding variance, through exploiting redundant and underutilized spaces of the input motion, which creates multiple motions from a single input. In two experiments we validate that our variance approach maintains the human-likeness from the previous step, and that a social partner can still accurately recognize the motion’s intent. As a final step, we maintain the robot’s ability to interact with its world by providing it the ability to satisfy constraints. We provide experimental analysis of the effects of constraints on the synthesized human-like robot motion variants. [ABSTRACT FROM AUTHOR]

This paper characterizes time-optimal trajectories in anisotropic (direction-dependent) environments where path curvatures are bounded by the inverse of the minimum-turning radius of a mobile agent. Such problems are often faced in the navigation of aerial, ground and naval vehicles when a mobile agent cannot instantaneously change its heading angle. The work presented is a generalization of the Dubins car problem, which considers the fastest paths with bounded curvature while assuming constant speed and minimum-turning radius. We relax this assumption and discuss fastest-path finding problems for the generalized direction-dependent speed and minimum-turning radius functions, to account for the effects of waves, winds and slope of the terrain on the agent’s motions. We establish that there exists an optimal path such that it is a portion of a path of the type CSCSC where C denotes a sharpest-turn curve and S a straight-line segment. We further analyze a special case wherein the speed polar plot is convex, and show that in that case there exists an optimal path with the same structure as for the Dubins problem: CCC or CSC. An algorithm that implements our results for the convex speed polar plot is also presented. [ABSTRACT FROM PUBLISHER]

We present a class of methods for optimal holonomic planning in high-dimensional spaces that automatically learns and leverages low-dimensional structure to efficiently find high-quality solutions. These methods are founded on the principle that problems possessing such structure are inherently simple to solve. This is demonstrated by presenting algorithms to solve these problems in time that scales with the dimension of a salient subspace, as opposed to the scaling with configuration-space dimension that would result from a naive approach. For generic problems possessing only approximate low-dimensional structure, we give iterative algorithms that are guaranteed convergence to local optima while making non-local path adjustments to escape poor local minima. We detail the theoretical underpinnings of these methods as well as give simulation and experimental results demonstrating the ability of our approach to efficiently find solutions of a quality exceeding that of known methods, and in problems of high dimensionality. [ABSTRACT FROM PUBLISHER]

We have designed, developed, and evaluated the performance of a multi-degree-of-freedom discretely actuated steerable cannula with shape-memory alloy (SMA) actuators. This will enable us to deliver diagnostic as well as therapeutic devices to the target location through the hollow inner core of the cannula. We propose to use SMAs to generate bending forces due to its small size and high power density. We annealed the SMA wires through a customized training process in an arc shape and mounted them at discrete locations on the outer surface of the cannula to enable joint motion. A pulse-width modulation (PWM)-based control scheme was implemented to control all SMA actuators simultaneously to enable multiple joint motion using a single power supply. The proposed controller was validated through an experiment inside gelatin to mimic the motion of the cannula inside a medium which requires a significant amount of force to move the joints of the cannula. Trajectory planning using a suitable metric and trajectory execution were successfully implemented. To demonstrate the delivery of a diagnostic tool through our cannula, we demonstrate that we can pass an optical coherence tomography probe through the cannula and perform in situ microscale imaging. [ABSTRACT FROM PUBLISHER]

We study the problem of designing dynamically feasible trajectories and controllers that drive a quadrotor to a desired state in state space. We focus on the development of a family of trajectories defined as a sequence of segments, each with a controller parameterized by a goal state or region in state space. Each controller is developed from the dynamic model of the robot and then iteratively refined through successive experimental trials in an automated fashion to account for errors in the dynamic model and noise in the actuators and sensors. We show that this approach permits the development of trajectories and controllers enabling such aggressive maneuvers as flying through narrow, vertical gaps and perching on inverted surfaces with high precision and repeatability. [ABSTRACT FROM PUBLISHER]

This paper deals with the trajectory generation problem faced by an autonomous vehicle in moving traffic. Being given the predicted motion of the traffic flow, the proposed semi-reactive planning strategy realizes all required long-term maneuver tasks (lane-changing, merging, distance-keeping, velocity-keeping, precise stopping, etc.) while providing short-term collision avoidance. The key to comfortable, human-like as well as physically feasible trajectories is the combined optimization of the lateral and longitudinal movements in street-relative coordinates with carefully chosen cost functionals and terminal state sets (manifolds). The performance of the approach is demonstrated in simulated traffic scenarios. [ABSTRACT FROM AUTHOR]

One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high degree-of-freedom (DOF) robotic tasks. In this contribution, we accomplish such variable impedance control with the reinforcement learning (RL) algorithm PI2 (PolicyImprovement withPath Integrals). PI2is a model-free, sampling-based learning method derived from first principles of stochastic optimal control. The PI2algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on the cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PI2is that it can scale to problems of many DOFs, so that reinforcement learning on real robotic systems becomes feasible. We sketch the PI2algorithm and its theoretical properties, and how it is applied to gain scheduling for variable impedance control. We evaluate our approach by presenting results on several simulated and real robots. We consider tasks involving accurate tracking through via points, and manipulation tasks requiring physical contact with the environment. In these tasks, the optimal strategy requires both tuning of a reference trajectory and the impedance of the end-effector. The results show that we can use path integral based reinforcement learning not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications. [ABSTRACT FROM AUTHOR]

A new controller for the end-effector trajectory tracking (EETT) of a class of flexible link manipulators which consists of a chain of rigid links with a flexible end-link (CRFE) is introduced. To design this new controller, a dynamic model of the CRFE is expressed in the singularly perturbed form; that is, decomposed into slow and fast subsystems. The states of the slow subsystem are the joints’ rotations and their time derivative, while the states of the fast subsystem are the flexible variables, which model the lateral deflection of the end-link, and their time derivative. For the slow subsystem, the new controller requires only ‘‘one’’ corrective torque in addition to the computed torque command of the rigid link counterpart of the CRFE for the reduction of the EETT error. This corrective torque is derived based on the concept of the integral manifold of the singularly perturbed differential equations. The need for only one corrective torque and its derivation are among the contributions of the new controller. To stabilize the fast subsystem, an observer-based controller is designed according to the gain-scheduling technique. Due to the application of the observer-based controller there is no need for the measurement of the time derivative of the flexible link’s lateral deflection, in which its measurement is difficult if not impossible in practice. This feature of the new controller is an advantage for it. To facilitate the derivation and implementation of this controller, several properties of the matrices in the dynamic model of the CRFE are introduced and used which are other contributions of this research. The effectiveness and feasibility of the new controller are shown by simulation and experimental studies. [ABSTRACT FROM PUBLISHER]

This paper presents a novel approach to computing feedback laws in the presence of obstacles. Instead of computing a trajectory between a pair of initial and goal states, our algorithms compute a vector field over the entire state space; all trajectories obtained from following this vector field are guaranteed to asymptotically reach the goal state. As a result, the vector field globally solves the navigation problem and provides robustness to disturbances in sensing and control. The vector field's integral curves (system trajectories) are guaranteed to avoid obstacles and are C∞ smooth. We construct a vector field with these properties by partitioning the space into simple cells, defining local vector fields for each cell, and smoothly interpolating between them to obtain a global vector field. We present an algorithm that computes these feedback controls for a kinematic point robot in an arbitrary dimensional space with piecewise linear boundary; the algorithm requires minimal preprocessing of the environment and is extremely fast during execution. For many practical applications in two-dimensional environments, full computation can be done in milliseconds. We also present an algorithm for computing feedback laws over cylindrical algebraic decompositions, thereby solving a smooth feedback version of the generalized piano movers' problem. [ABSTRACT FROM AUTHOR]

It is known that a parallel manipulator at a singular configuration can gain one or more degrees of freedom and become uncontrollable, that is, it might not reproduce a stable motion along a prescribed trajectory. However, it is proved experimentally that there is possible passing through the singular zones. This was simulated and shown through numerical examples and illustrated on several parallel structures. In this paper, we determine the optimal dynamic conditions generating a stable motion inside the singular zones. The obtained results show that the general condition for passing through a singularity can be defined as follows: the end-effector of the parallel manipulator can pass through the singular positions without perturbation of motion if the wrench applied on the end-effector by the legs and external efforts of the manipulator are orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained from the inverse dynamics and analytically demonstrated by the study of the Lagrangian of a general parallel manipulator. Numerical simulations are carried out using the software ADAMS and validated through experimental tests. [ABSTRACT FROM AUTHOR]

This article deals with feedforward control of very lightweight, flexible robotic arms. In particular, we develop a new, objective method of designing a trajectory that can be used as a modified input, to cancel tip vibrations during robot manoeuvres. This method takes into account the constraints found in real actuators (DC-motors), such as the maximum torque the motor can supply, and also those due to the mechanical limits of the link, like the maximum deflection before reaching the elastic limit of the link. The parameters of the internal control of the actuators are also derived from the design process, achieving the fastest performance possible without saturating the motor. Lastly, we show some experimental results which clearly demonstrate the benefits of the new trajectories by comparing them to a ramp one. [ABSTRACT FROM AUTHOR]

This paper deals with minimum time trajectory optimization along a specified path subject to thermal constraints. We point out here that robots are often integrated into complex robotic cells, and the interactions between the robot and its environment are often difficult or even impossible to model. The structure of the optimization problem allows us to decompose the optimization into two levels, the first being based on models and results of the theory of the calculus of variations, the second being based on measurements and derivative free algorithms. This decomposition allows us to optimize the velocity profiles efficiently wit/lout any advance knowledge of the interactions between the robot and its environment. We propose here two numerical algorithms for these two levels of the decomposition which show good convergence properties. The resulting optimal velocity profiles are 5-10% faster than classical profiles, and have been executed successfully on a real Stäubli Rx90 manipulator robot. [ABSTRACT FROM AUTHOR]

Supercavitating vehicles are characterized by substantially reduced hydrodynamic drag, in comparison with fully wetted underwater vehicles. Drag is localized at the nose of the vehicle, where a cavitator generates a cavity that completely envelopes the body, at the fins, and on the vehicle after-body. This unique loading configuration, the complex and non-linear nature of the interaction forces between vehicle and cavity, the unsteady behavior of the cavity itself and memory effects associated with its formation process make the control and maneuvering of supercavitating vehicles particularly challenging. This study presents an initial effort towards the evaluation of optimal trajectories for this class of underwater vehicles. Flight trajectories and maneuvering strategies for supercavitating vehicles are obtained through the solution of an optimal control problem. Given a cost function, and general constraints and bounds on states and controls, the solution of the optimal control problem yields control time histories that maneuver the vehicle according to the desired strategy, together with the associated flight path. The optimal control problem is solved using the direct transcription method, which does not require the derivation of the equations of optimal control and leads to the solution of a discrete parameter optimization problem. Examples of maneuvers and resulting trajectories are given to demonstrate the effectiveness of the proposed methodology and the generality of the formulation. [ABSTRACT FROM AUTHOR]

Automatically building maps from sensor data is a necessary and fundamental skill for mobile robots; as a result, considerable research attention has focused on the technical challenges inherent in the mapping problem. While statistical inference techniques have led to computationally efficient mapping algorithms, the next major challenge in robotic mapping is to automate the data collection process. in this paper we address the problem of how a robot should plan to explore an unknown environment and collect data in order to maximize the accuracy of the resulting map. We formulate exploration as a constrained optimization problem and use reinforcement learning to find trajectories that lead to accurate maps. We demonstrate this process in simulation and show that the learned policy not only results in improved map building, but that the learned policy also transfers successfully to a real robot exploring on MIT campus. [ABSTRACT FROM AUTHOR]

This paper presents a time invariant kinematic motion controller for wheeled mobile robots. Actuator capability, mechanical design, and traction forces governed by terrain features provide velocity and curvature limitations that are used in the design of the controller. A novel path manifold that considers curvature limitations is introduced to provide a desired path shape and convergence to the reference posture or trajectory. Lyapunov techniques are then used to derive a control law that asymptotically converges the robot to an arbitrarily small neighborhood of the path manifold. Posture regulation, path following, and trajectory tracking capability to a similarly scaled neighborhood of the target are provided. Controller parameters are optimized and initial conditions are identified that satisfy physical constraints of the robot and provide smooth commands. Curvature boundaries and asymptotic convergence naturally limit allowable initial conditions and are resolved by driving the robot to intermediate goal points within regions of allowable initial conditions. Posture regulation is evaluated in simulation and experiment on a Compliant Framed wheeled Modular Mobile Robot (CFMMR) for two different terrain surfaces. Trajectory tracking and path following of constant curvature references are evaluated in simulation and experiment, respectively. [ABSTRACT FROM AUTHOR]

Efficient algorithms for collision-free energy sub-optimal path planning for formations of spacecraft flying in deep space are presented. The idea is to introduce a set of way-points through which the space- craft are required to pass, combined with parameterizations of the trajectories which are energy-optimal for each spacecraft. The resulting constrained optimization problem is formulated as a quasi- quadratic parameter optimization problem in terms of the way-points parameters. The mathematical structure of the problem is further exploited to develop gradient-based algorithms in which the gradients are computed analytically. The collision avoidance constraints are approximated such that closed form solutions are generated. This combination results in fast and robust numerical algorithms which work very well for scenarios involving a large number of spacecraft (e.g. 20). [ABSTRACT FROM AUTHOR]

We describe the design features that underlie the operation of iSprawl, a small (0.3 kg) autonomous, bio-inspired hexapod that runs at 15 body-lengths/second (2.3 m/s). These features include a tuned set of leg compliances for efficient running and a light and flexible power transmission system. This transmission system permits high speed rotary power to be converted to periodic thrusting and distributed to the tips of the rapidly swinging legs. The specific resistance of iSprawl is approximately constant at 1.75for speeds between 1.25 m/s and 2.5 m/s. Examination of the trajectory of the center of mass and the ground reaction forces for iSprawl show that it achieves a stable, bouncing locomotion similar to that seen in insects and in previous (slower) bio-inspired robots, but with an unusually high stride frequency for its size. [ABSTRACT FROM AUTHOR]

A real-time joint trajectory generator for planar walking bipeds is proposed. In the near future this trajectory planner will be implemented on the robot ‘Lucy ’, which is actuated by pleated pneumatic artificial muscles. The trajectory planner generates dynamically stable motion patterns by using a set of objective locomotion parameters as its input, and by tuning and exploiting the natural upper body dynamics. The latter can be determined and manipulated by using the angular momentum equation. Basically, trajectories for hip and swing foot motion are generated, which guarantee that the objective locomotion parameters attain certain prescribed values. Additionally, the hip trajectories are slightly modified such that the upper body motion is steered naturally, meaning that it requires practically no actuation. This has the advantage that the upper body actuation hardly influences the position of the Zero Moment Point. The effectiveness of the strategy developed is demonstrated by simulation results. A first simulation is performed under the assumption of perfect tracking by the controllers of the different actuators. This allows one to verify the effectiveness of the trajectory planner and to evaluate the postural stability. A second simulation is performed while taking the control architecture of the real robot into account. In order to have a more realistic simulation the proposed control architecture is evaluated with a full hybrid dynamic simulation model of the biped ‘Lucy ’. This simulator combines the dynamical behaviour of the robot with the thermodynamical effects that take place in the muscle-valves actuation system. The observed hardware limitations of the real robot and expected model errors are taken into account in order to give a realistic qualitative evaluation of the control performance and to test the robustness. [ABSTRACT FROM AUTHOR]

The basic difficulty in the control of flexible link manipulators stems from the fact that the link deflections cannot be controlled directly. Since the number of control inputs, applied by the actuators, is less than the total number of variables to be controlled, control approaches aiming at the suppression of deflections and vibrations are generally insufficient. Another possible approach is to determine new joint trajectories to minimize the error of the end-effector in the operational space. In this paper, a neural network is designed to compute incremental changes for the reference values of the joint angles to achieve successful tip tracking in the operational space. Tip position errors in the x- and y-directions are utilized as inputs to the neural network. The cost function, which is minimized in training the neural network, is also chosen as the sum of squares of the tip position error in both directions. Joint angle control is provided by a PD controller. Simulations are carried out to evaluate the performance of the neural-network-based trajectory tracking method, and the results are depicted in both joint and operational spaces. [ABSTRACT FROM AUTHOR]

"Variational Hilbert regression for terrain modeling and trajectory optimization", by V Guizilini and F Ramos, describes a novel regression methodology for modeling terrains. "Learning to calibrate: Reinforcement learning for guided calibration of visual-inertial rigs", by F Nobre and C Heckman, presents a calibration system that guides the operator by suggesting easy motions where calibration parameters can be observed. "Communicating and controlling robot arm motion intent through mixed reality head-mounted displays", by E Rosen, D Whitney, E Phillips, G Chien, J Tompkin, G Konidaris, and S Tellex, expresses the robot arm's intended motion to a collaborating human operator. [Extracted from the article]

In this paper we present the system design of a machine that we have constructed to study a quadrupedal gallop gait The gallop gait is the preferred high-speed gait of most cursorial quadrupeds. To gallop, an animal must generate ballistic trajectories with characteristic strong impacts, coordinate leg movements with asymmetric footfall phasing, and effectively use compliant members, all the while maintaining dynamic stability. In this paper we seek to further understand the primary biological features necessary for galloping by building and testing a robotic quadruped similar in size to a large goat or antelope. These features include high-speed actuation, energy storage, on-line learning control, and high-performance attitude sensing. Because body dynamics are primarily influenced by the impulses delivered by the legs, the successful design and control of single leg energetics is a major focus of this work. The leg stores energy during flight by adding tension to a spring acting across an articulated knee. During stance, the spring energy is quickly released using a novel capstan design. As a precursor to quadruped control, two intelligent strategies have been developed for verification on a one-legged system. The Levenberg--Marquardt on-line learning method is applied to a simple heuristic controller and provides good control over height and forward velocity. Direct adaptive fuzzy control, which requires no system modeling but is more computationally expensive, exhibits better response. Using these techniques we have been successful in operating one leg at speeds necessary for a dynamic gallop of a machine of this scale. Another necessary component of quadruped locomotion is high-resolution and high-bandwidth attitude sensing. The large ground impact accelerations, which cause problems for any single traditional sensor, are overcome through the use of an inertial sensing approach using updates from optical sensors and vehicle kinematics. [ABSTRACT FROM AUTHOR]

Neither of the classical visual servoing approaches, position-based and image-based, are completely satisfactory. In position-based visual servoing the trajectory of the robot is well stated, but the approach suffers mainly from the image features going out of the visual field of the cameras. On the other hand, image-based visual servoing has been found generally satisfactory and robust in the presence of camera and hand-eye calibration errors. However, in some cases, singularities and local minima may arise, and the robot can go further from its joint limits. This paper is a step towards the synthesis of both approaches with their particular advantages, i.e., the trajectory of the camera motion is predictable and the image features remain in the field of view of the camera. The basis is the introduction of three-dimensional information in the feature vector. Point depth and object pose produce useful behavior in the control of the camera. Using the task-function approach, we demonstrate the relationship between the velocity screw of the camera and the current and desired poses of the object in the camera frame. Camera calibration is assumed, at least coarsely. Experimental results on real robotic platforms illustrate the presented approach. [ABSTRACT FROM AUTHOR]

In this paper we present a complete system for segmenting, matching, tracking, and visual servoing with respect to unknown planar contours. Our system can be used with arbitrary contours of any shape and without any prior knowledge of their models. The system is first shown the target view. A selected contour is automatically extracted and its image shape is stored. The robot and object are then moved and the system automatically identifies the target. The matching step is performed together with the estimation of the homography matrix between the two views of the contour. Then, a 2&frac;12D visual servoing technique is used to reposition the end-effector of a robot at the reference position relative to the planar contour. The system has been successfully tested on several contours with very complex shapes such as leaves, keys, and coastal outlines of islands. Experiments using a ship mock-up without any artificial marker proves that the system can be applied to the ship-building industry. [ABSTRACT FROM AUTHOR]

In this paper we present new uncalibrated control schemes for vision-guided robotic tracking of a moving target using a moving camera. These control methods are applied to an uncalibrated robotic system with eye-in-hand visual feedback. Without a priori knowledge of the robot's kinematic model or camera calibration, the system is able to track a moving object through a variety of motions and maintain the object's image features in a desired position in the image plane. These control schemes estimate the system Jacobian as well as changes in target features due to target motion. Four novel strategies are simulated and a variety of parameters are investigated with respect to performance. Simulation results suggest that a Gauss-Newton method utilizing a partitioned Broyden's method for model estimation provides the best steady-state tracking behavior. [ABSTRACT FROM AUTHOR]

Image-based servo is a local control solution. Thanks to the feedback loop closed in the image space, local convergence and stability in the presence of modeling errors and noise perturbations are ensured when the error is small. The principal deficiency of this approach is that the induced (3D) trajectories are not optimal and sometimes, especially when the displacement to realize is large, these trajectories are not physically valid leading to the failure of the servoing process. In this paper we address the problem of finding realistic image-space trajectories that correspond to optimal 3D trajectories. The camera calibration and the model of the observed scene are assumed unknown. First, a smooth closed-form collineation path between given start and end points is obtained. This path is generated in order to correspond to an optimal camera path. The trajectories of the image features are then derived and efficiently tracked using a purely image-based control. A second path planning scheme, based on the potential field method is briefly presented. It allows us to introduce constraints in the desired trajectory to be realized. Such constraints are, for instance, to ensure that the object of interest remains in the camera field of view and to avoid the robot joints limits. Experimental results obtained on a six-degrees-of-freedom eye-in-hand robotic system are presented and confirm the validity of the proposed approach. [ABSTRACT FROM AUTHOR]