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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]

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]

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 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]

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]

"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]