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Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. However, formal (Lyapunov) stability guarantees over the region-of-attraction (ROA) for NN controllers with nonlinear dynamical systems are challenging to obtain, and most existing approaches rely on expensive solvers such as sums-of-squares (SOS), mixed-integer programming (MIP), or satisfiability modulo theories (SMT). In this paper, we demonstrate a new framework for learning NN controllers together with Lyapunov certificates using fast empirical falsification and strategic regularizations. We propose a novel formulation that defines a larger verifiable region-of-attraction (ROA) than shown in the literature, and refines the conventional restrictive constraints on Lyapunov derivatives to focus only on certifiable ROAs. The Lyapunov condition is rigorously verified post-hoc using branch-and-bound with scalable linear bound propagation-based NN verification techniques. The approach is efficient and flexible, and the full training and verification procedure is accelerated on GPUs without relying on expensive solvers for SOS, MIP, nor SMT. The flexibility and efficiency of our framework allow us to demonstrate Lyapunov-stable output feedback control with synthesized NN-based controllers and NN-based observers with formal stability guarantees, for the first time in literature. Source code at https://github.com/Verified-Intelligence/Lyapunov_Stable_NN_Controllers, Comment: Paper accepted by ICML 2024

Understanding the geometry of collision-free configuration space (C-free) in the presence of task-space obstacles is an essential ingredient for collision-free motion planning. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing C-free regions with rigorous certificates due to the complexity of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge rigorous method for approximately decomposing a rational parametrization of C-free into certified polyhedral regions. Our method, called C-IRIS (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parameterization of the configuration space which are rigorously certified to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Based on convex optimization, our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and is fast enough to scale to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in several 2-DOF examples where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa, a 6-DOF UR3e and 12-DOF bimanual manipulators. An implementation of our algorithm is open-sourced in Drake. We furthermore provide examples of our algorithm in interactive Python notebooks.

Simulation parameter settings such as contact models and object geometry approximations are critical to training robust robotic policies capable of transferring from simulation to real-world deployment. Previous approaches typically handcraft distributions over such parameters (domain randomization), or identify parameters that best match the dynamics of the real environment (system identification). However, there is often an irreducible gap between simulation and reality: attempting to match the dynamics between simulation and reality across all states and tasks may be infeasible and may not lead to policies that perform well in reality for a specific task. Addressing this issue, we propose AdaptSim, a new task-driven adaptation framework for sim-to-real transfer that aims to optimize task performance in target (real) environments -- instead of matching dynamics between simulation and reality. First, we meta-learn an adaptation policy in simulation using reinforcement learning for adjusting the simulation parameter distribution based on the current policy's performance in a target environment. We then perform iterative real-world adaptation by inferring new simulation parameter distributions for policy training, using a small amount of real data. We perform experiments in three robotic tasks: (1) swing-up of linearized double pendulum, (2) dynamic table-top pushing of a bottle, and (3) dynamic scooping of food pieces with a spatula. Our extensive simulation and hardware experiments demonstrate AdaptSim achieving 1-3x asymptotic performance and $\sim$2x real data efficiency when adapting to different environments, compared to methods based on Sys-ID and directly training the task policy in target environments. Website: https://irom-lab.github.io/AdaptSim, Comment: Conference on Robot Learning (CoRL), 2023

Sums-of-squares (SOS) optimization is a promising tool to synthesize certifiable controllers for nonlinear dynamical systems. Building upon prior works, we demonstrate that SOS can synthesize dynamic controllers with bounded suboptimal performance for various underactuated robotic systems by finding good approximations of the value function. We summarize a unified SOS framework to synthesize both under- and over- approximations of the value function for continuous-time, control-affine systems, use these approximations to generate approximate optimal controllers, and perform regional analysis on the closed-loop system driven by these controllers. We then extend the formulation to handle hybrid systems with contacts. We demonstrate that our method can generate tight under- and over- approximations of the value function with low-degree polynomials, which are used to provide stabilizing controllers for continuous-time systems including the inverted pendulum, the cart-pole, and the quadrotor as well as a hybrid system, the planar pusher. To the best of our knowledge, this is the first time that a SOS-based time-invariant controller can swing up and stabilize a cart-pole, and push the planar slider to the desired pose.

Gradient-based methods enable efficient search capabilities in high dimensions. However, in order to apply them effectively in offline optimization paradigms such as offline Reinforcement Learning (RL) or Imitation Learning (IL), we require a more careful consideration of how uncertainty estimation interplays with first-order methods that attempt to minimize them. We study smoothed distance to data as an uncertainty metric, and claim that it has two beneficial properties: (i) it allows gradient-based methods that attempt to minimize uncertainty to drive iterates to data as smoothing is annealed, and (ii) it facilitates analysis of model bias with Lipschitz constants. As distance to data can be expensive to compute online, we consider settings where we need amortize this computation. Instead of learning the distance however, we propose to learn its gradients directly as an oracle for first-order optimizers. We show these gradients can be efficiently learned with score-matching techniques by leveraging the equivalence between distance to data and data likelihood. Using this insight, we propose Score-Guided Planning (SGP), a planning algorithm for offline RL that utilizes score-matching to enable first-order planning in high-dimensional problems, where zeroth-order methods were unable to scale, and ensembles were unable to overcome local minima. Website: https://sites.google.com/view/score-guided-planning/home, Comment: Glen Chou, Hongkai Dai, and Lujie Yang contributed equally to this work. Accepted to CoRL 2023

Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions that satisfy input constraints and avoid unsafe regions of state-space. Designing CLFs and CBFs with rigorous performance guarantees is computationally challenging. To certify existence of control actions, current techniques not only design a CLF/CBF, but also a nominal controller. This can make the synthesis task more expensive, and performance estimation more conservative. In this work, we characterize polynomial CLFs/CBFs using sum-of-squares conditions, which can be directly certified using convex optimization. This yields a CLF and CBF synthesis technique that does not rely on a nominal controller. We then present algorithms for iteratively enlarging estimates of the stabilizable and safe regions. We demonstrate our algorithms on a 2D toy system, a pendulum and a quadrotor.

Configuration space (C-space) has played a central role in collision-free motion planning, particularly for robot manipulators. While it is possible to check for collisions at a point using standard algorithms, to date no practical method exists for computing collision-free C-space regions with rigorous certificates due to the complexities of mapping task-space obstacles through the kinematics. In this work, we present the first to our knowledge method for generating such regions and certificates through convex optimization. Our method, called C-Iris (C-space Iterative Regional Inflation by Semidefinite programming), generates large, convex polytopes in a rational parametrization of the configuration space which are guaranteed to be collision-free. Such regions have been shown to be useful for both optimization-based and randomized motion planning. Our regions are generated by alternating between two convex optimization problems: (1) a simultaneous search for a maximal-volume ellipse inscribed in a given polytope and a certificate that the polytope is collision-free and (2) a maximal expansion of the polytope away from the ellipse which does not violate the certificate. The volume of the ellipse and size of the polytope are allowed to grow over several iterations while being collision-free by construction. Our method works in arbitrary dimensions, only makes assumptions about the convexity of the obstacles in the task space, and scales to realistic problems in manipulation. We demonstrate our algorithm's ability to fill a non-trivial amount of collision-free C-space in a 3-DOF example where the C-space can be visualized, as well as the scalability of our algorithm on a 7-DOF KUKA iiwa and a 12-DOF bimanual manipulator., Comment: To be published in The Workshop on the Algorithmic Foundations of Robotics 2022. 14 pages, 7 figures

Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. However, caging is traditionally difficult to integrate as part of larger manipulation frameworks, where caging is not the goal but an intermediate condition. In this paper, we develop a convex-combinatorial model to characterize caging from an optimization perspective. More specifically, we derive a set of sufficient constraints to enclose the configuration of the object in a compact-connected component of its free-space. The convex-combinatorial nature of this approach provides guarantees on optimality and convergence, and its optimization nature makes it versatile for further applications on robot manipulation tasks. To the best of our knowledge, this is the first optimization-based approach to formulate the caging condition.

Deep learning has had a far reaching impact in robotics. Specifically, deep reinforcement learning algorithms have been highly effective in synthesizing neural-network controllers for a wide range of tasks. However, despite this empirical success, these controllers still lack theoretical guarantees on their performance, such as Lyapunov stability (i.e., all trajectories of the closed-loop system are guaranteed to converge to a goal state under the control policy). This is in stark contrast to traditional model-based controller design, where principled approaches (like LQR) can synthesize stable controllers with provable guarantees. To address this gap, we propose a generic method to synthesize a Lyapunov-stable neural-network controller, together with a neural-network Lyapunov function to simultaneously certify its stability. Our approach formulates the Lyapunov condition verification as a mixed-integer linear program (MIP). Our MIP verifier either certifies the Lyapunov condition, or generates counter examples that can help improve the candidate controller and the Lyapunov function. We also present an optimization program to compute an inner approximation of the region of attraction for the closed-loop system. We apply our approach to robots including an inverted pendulum, a 2D and a 3D quadrotor, and showcase that our neural-network controller outperforms a baseline LQR controller. The code is open sourced at \url{https://github.com/StanfordASL/neural-network-lyapunov}., Comment: Published at Robotics: Science and Systems (RSS) in July, 2021

We present an algorithm which learns an online trajectory generator that can generalize over varying and uncertain dynamics. When the dynamics is certain,the algorithm generalizes across model parameters. When the dynamics is partially observable, the algorithm generalizes across different observations. To do this, we employ recent advances in supervised imitation learning to learn a trajectory generator from a set of example trajectories computed by a trajectory optimizer. In experiments in two simulated domains, it finds solutions that are nearly as good as, and sometimes better than, those obtained by calling the trajectory optimizer online. The online execution time is dramatically decreased, and the off-line training time is reasonable.

In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints: a major improvement over existing approaches, which either solve the problem in only a local neighborhood of the user initial guess through nonlinear non-convex optimization, or address only a limited set of kinematics constraints. Specifically, we propose a mixed-integer convex relaxation of non-convex [Formula: see text] rotation constraints, and apply this relaxation on the IK problem. Our formulation can detect if an instance of the IK problem is globally infeasible, or produce an approximate solution when it is feasible. We show results on a seven-joint arm grasping objects in a cluttered environment, an 18-degree-of-freedom quadruped standing on stepping stones, and a parallel Stewart platform. Moreover, we show that our approach can find a collision free path for a gripper in a cluttered environment, or certify such a path does not exist. We also compare our approach against the analytical approach for a six-joint manipulator. The open-source code is available at http://drake.mit.edu .

This report describes our approach for Phase 3 of the Real Robot Challenge. To solve cuboid manipulation tasks of varying difficulty, we decompose each task into the following primitives: moving the fingers to the cuboid to grasp it, turning it on the table to minimize orientation error, and re-positioning it to the goal position. We use model-based trajectory optimization and control to plan and execute these primitives. These grasping, turning, and re-positioning primitives are sequenced with a state-machine that determines which primitive to execute given the current object state and goal. Our method shows robust performance over multiple runs with randomized initial and goal positions. With this approach, our team placed second in the challenge, under the anonymous name "sombertortoise" on the leaderboard. Example runs of our method solving each of the four levels can be seen in this video (https://www.youtube.com/watch?v=I65Kwu9PGmg&list=PLt9QxrtaftrHGXcp4Oh8-s_OnQnBnLtei&index=1)., Comment: For a video of our method, see https://www.youtube.com/watch?v=I65Kwu9PGmg&list=PLt9QxrtaftrHGXcp4Oh8-s_OnQnBnLtei&index=1 . For our code, visit https://github.com/stanford-iprl-lab/rrc_package

In this paper, we present a convex optimization problem to generate Center of Mass (CoM) and momentum trajectories of a walking robot, such that the motion robustly satisfies the friction cone constraints on uneven terrain. We adopt the Contact Wrench Cone (CWC) criterion to measure a robot's dynamical stability, which generalizes the venerable Zero Moment Point (ZMP) criterion. Unlike the ZMP criterion, which is ideal for walking on flat ground with unbounded tangential friction forces, the CWC criterion incorporates non-coplanar contacts with friction cone constraints. We measure the robustness of the motion using the margin in the Contact Wrench Cone at each time instance, which quantifies the capability of the robot to instantaneously resist external force/torque disturbance, without causing the foot to tip over or slide. For pre-specified footstep location and time, we formulate a convex optimization problem to search for robot linear and angular momenta that satisfy the CWC criterion. We aim to maximize the CWC margin to improve the robustness of the motion, and minimize the centroidal angular momentum (angular momentum about CoM) to make the motion natural. Instead of directly minimizing the non-convex centroidal angular momentum, we resort to minimizing a convex upper bound. We show that our CWC planner can generate motion similar to the result of the ZMP planner on flat ground with sufficient friction. Moreover, on an uneven terrain course with friction cone constraints, our CWC planner can still find feasible motion, while the outcome of the ZMP planner violates the friction limit. Keywords: Friction; Robustness; Legged locomotion; Robot kinematics; Foot; Convex functions, Navy - ONR / Fy AppropriationsUncapped Funds (6923036)

Operating a high degree of freedom mobile manipulator, such as a humanoid, in a field scenario requires constant situational awareness, capable perception modules, and effective mechanisms for interactive motion planning and control. A well-designed operator interface presents the operator with enough context to quickly carry out a mission and the flexibility to handle unforeseen operating scenarios robustly. By contrast, an unintuitive user interface can increase the risk of catastrophic operator error by overwhelming the user with unnecessary information. With these principles in mind, we present the philosophy and design decisions behind Director—the open-source user interface developed by Team MIT to pilot the Atlas robot in the DARPA Robotics Challenge (DRC). At the heart of Director is an integrated task execution system that specifies sequences of actions needed to achieve a substantive task, such as drilling a wall or climbing a staircase. These task sequences, developed a priori, make online queries to automated perception and planning algorithms with outputs that can be reviewed by the operator and executed by our whole-body controller. Our use of Director at the DRC resulted in efficient high-level task operation while being fully competitive with approaches focusing on teleoperation by highly trained operators. We discuss the primary interface elements that comprise Director, and we provide an analysis of its successful use at the DRC., United States. Defense Advanced Research Projects Agency. (Air Force Research Laboratory (award FA8750-12-1-0321)), United States. Office of Naval Research (Award N00014-12-1-0071)

Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time., Comment: 8 pages, IEEE Robotics and Automation Letters

Caging is a promising tool which allows a robot to manipulate an object without directly reasoning about the contact dynamics involved. Furthermore, caging also provides useful guarantees in terms of robustness to uncertainty, and often serves as a way-point to a grasp. Unfortunately, previous work on caging is often based on computational geometry or discrete topology tools, causing restriction on gripper geometry, and difficulty on integration into larger manipulation frameworks. In this paper, we develop a convex-combinatorial model to characterize caging from an optimization perspective. More specifically, we study the configuration space of the object, where the fingers act as obstacles that enclose the configuration of the object. The convex-combinatorial nature of this approach provides guarantees on optimality, convergence and scalability, and its optimization nature makes it adaptable for further applications on robot manipulation tasks., Comment: To Appear in the IEEE/RSJ International Conference On Intelligent Robots and Systems (IROS) 2019

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 127-142)., In this thesis, we seek to plan a robust motion for robot with multiple non-coplanar contact on the environment. When the robot interacts with the environment through contact, it relies on the contact forces to generate the desired acceleration. The contact forces have to satisfy some physical constraints, such as lying within the friction cones. These constraints limit the robot acceleration. The robustness of the motion can be measured as the margin to the boundary of these constraints. By planning motion with a large preserved margin, we enable the robot to withstand large disturbance in the online motion execution. In this thesis, we adopt the notion of contact wrench set to approximate the constraints on the robot dynamics. The margin of such set measures the capability of the motion to perfectly resist external wrench disturbance. We plan robust motion to increase this contact wrench set margin. We present two planners to improve this robustness metric. For the first simple-model planner, we pre-specify the contact locations, and it generates a Center of Mass trajectory and an angular momentum trajectory, by solving a convex optimization problem. We show that this planner has similar output as the widely-used walking pattern generator that relies on Zero Moment Point (ZMP) on flat ground. Moreover, it can plan feasible motion on uneven ground with friction cone limits, while the ZMP planner fails. For the second planner with robot whole-body model, we will search for the contact location and the robot whole-body motion simultaneously. We show that we can improve the robustness metric through certain non-convex optimization techniques. We apply our planner to three problems: 1) force closure grasp optimization, 2) static posture optimization, 3) trajectory optimization, achieving improved performance for all of them., by Hongkai Dai., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 127-142)., In this thesis, we seek to plan a robust motion for robot with multiple non-coplanar contact on the environment. When the robot interacts with the environment through contact, it relies on the contact forces to generate the desired acceleration. The contact forces have to satisfy some physical constraints, such as lying within the friction cones. These constraints limit the robot acceleration. The robustness of the motion can be measured as the margin to the boundary of these constraints. By planning motion with a large preserved margin, we enable the robot to withstand large disturbance in the online motion execution. In this thesis, we adopt the notion of contact wrench set to approximate the constraints on the robot dynamics. The margin of such set measures the capability of the motion to perfectly resist external wrench disturbance. We plan robust motion to increase this contact wrench set margin. We present two planners to improve this robustness metric. For the first simple-model planner, we pre-specify the contact locations, and it generates a Center of Mass trajectory and an angular momentum trajectory, by solving a convex optimization problem. We show that this planner has similar output as the widely-used walking pattern generator that relies on Zero Moment Point (ZMP) on flat ground. Moreover, it can plan feasible motion on uneven ground with friction cone limits, while the ZMP planner fails. For the second planner with robot whole-body model, we will search for the contact location and the robot whole-body motion simultaneously. We show that we can improve the robustness metric through certain non-convex optimization techniques. We apply our planner to three problems: 1) force closure grasp optimization, 2) static posture optimization, 3) trajectory optimization, achieving improved performance for all of them., by Hongkai Dai., Ph. D.

This paper describes a collection of optimization algorithms for achieving dynamic planning, control, and state estimation for a bipedal robot designed to operate reliably in complex environments. To make challenging locomotion tasks tractable, we describe several novel applications of convex, mixed-integer, and sparse nonlinear optimization to problems ranging from footstep placement to whole-body planning and control. We also present a state estimator formulation that, when combined with our walking controller, permits highly precise execution of extended walking plans over non-flat terrain. We describe our complete system integration and experiments carried out on Atlas, a full-size hydraulic humanoid robot built by Boston Dynamics, Inc., United States. Air Force Office of Scientific Research (FA8750-12-1-0321), United States. Office of Naval Research (N00014-12-1-0071), United States. Office of Naval Research (N00014-10-1-0951), National Science Foundation (U.S.) (IIS-0746194), National Science Foundation (U.S.) (IIS-1161909)

The motivation of our current research is to devise motion planners for legged locomotion that are able to exploit the robot's actuation capabilities. This means, when possible, to minimize joint torques or to propel as much as admissible when required. For this reason we define two new 6 dimensional bounded polytopes that we name Actuation-consistent Wrench Polytope (AWP) and Feasible Wrench Polytope (FWP). These objects turn out to be very useful in motion planning for the definition of constraints on the accelerations of the Center of Mass of the robot that respect the friction cones and the actuation limits. The AWP and the FWP could be used also in the robot design phase to size the actuators of the system based on some predefined reference motion.

Motion planning in multi-contact scenarios has recently gathered interest within the legged robotics community, however actuator force/torque limits are rarely considered. We believe that these limits gain paramount importance when the complexity of the terrains to be traversed increases. We build on previous research from the field of robotic grasping to propose two new six-dimensional bounded polytopes named the Actuation Wrench Polytope (AWP) and the Feasible Wrench Polytope (FWP). We define the AWP as the set of all the wrenches that a robot can generate while considering its actuation limits. This considers the admissible contact forces that the robot can generate given its current configuration and actuation capabilities. The Contact Wrench Cone (CWC), instead, includes features of the environment such as the contact normal or the friction coefficient. The intersection of the AWP and of the CWC results in a convex polytope, the FWP, which turns out to be more descriptive of the real robot capabilities than existing simplified models, while maintaining the same compact representation. We explain how to efficiently compute the vertex-description of the FWP that is then used to evaluate a feasibility factor that we adapted from the field of robotic grasping. This allows us to optimize for robustness to external disturbance wrenches. Based on this, we present an implementation of a motion planner for our quadruped robot HyQ that provides online Center of Mass (CoM) trajectories that are guaranteed to be statically stable and actuation consistent.

A linear correlation is found between the magnitude of nucleon-nucleon short-range correlations and the nuclear binding energy per nucleon with pairing energy removed. By using this relation, the strengths of nucleon-nucleon short-range correlations of some unmeasured nuclei are predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon short-range correlations are made. The found nuclear dependence of nucleon-nucleon short-range correlations may shed some lights on the short-range structure of nucleus., Comment: 7 pages, 3 figures, some modifications, and added some discussions on the EMC effect

To plan dynamic, whole-body motions for robots, one conventionally faces the choice between a complex, full-body dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We exploit the fact that while the full dynamics of humanoid robots are complicated, their centroidal dynamics (the evolution of the angular momentum and the center of mass (COM) position) are much simpler. By treating the dynamics of the robot in centroidal form and directly optimizing the joint trajectories for the actuated degrees of freedom, we arrive at a method that enjoys simpler dynamics, while still having the expressiveness required to handle kinematic constraints such as collision avoidance or reaching to a target. We further require that the robot's COM and angular momentum as computed from the joint trajectories match those given by the centroidal dynamics. This ensures that the dynamics considered by our optimization are equivalent to the full dynamics of the robot, provided that the robot's actuators can supply sufficient torque. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot. Additionally, we show that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance., United States. Defense Advanced Research Projects Agency (Air Force Research Laboratory (Wright-Patterson Air Force Base, Ohio) Award FA8750-12-1-0321)

The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robot's sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation, and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule., United States. Defense Advanced Research Projects Agency (United States. Air Force Research Laboratory Award FA8750-12-1-0321), United States. Office of Naval Research (Award N00014-12-1-0071)

To plan dynamic, whole-body motions for robots one conventionally faces the choice between a complex, fullbody dynamic model containing every link and actuator of the robot, or a highly simplified model of the robot as a point mass. In this paper we explore a powerful middle ground between these extremes. We present an approach to generate whole-body motions using a simple dynamics model, which enforces that the linear and angular momentum of the robot be consistent with the external wrenches on the robot, and a full-body kinematics model that enforces rich geometric constraints, such as end-effector positioning or collision avoidance. We obtain a trajectory for the robot and profiles of contact wrenches by solving a nonlinear optimization problem (NLP). We further demonstrate that we can plan without pre-specifying the contact sequence by exploiting the complementarity conditions between contact forces and contact distance. We demonstrate that this algorithm is capable of generating highly-dynamic motion plans with examples of a humanoid robot negotiating obstacle course elements and gait optimization for a quadrupedal robot., Under review, 2014.

The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robot's sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule., Sponsored in part by ONR and DARPA.

The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robot's sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule.

The DARPA Robotics Challenge Trials held in December 2013 provided a landmark demonstration of dexterous mobile robots executing a variety of tasks aided by a remote human operator using only data from the robot's sensor suite transmitted over a constrained, field-realistic communications link. We describe the design considerations, architecture, implementation and performance of the software that Team MIT developed to command and control an Atlas humanoid robot. Our design emphasized human interaction with an efficient motion planner, where operators expressed desired robot actions in terms of affordances fit using perception and manipulated in a custom user interface. We highlight several important lessons we learned while developing our system on a highly compressed schedule.

In this paper we seek to quantify and explicitly optimize the robustness of a control system for a robot walking on terrain with uncertain geometry. Geometric perturbations to the terrain enter the equations of motion through a relocation of the hybrid event “guards” which trigger an impact event; these perturbations can have a large effect on the stability of the robot and do not fit into the traditional robust control analysis and design methodologies without additional machinery. We attempt to provide that machinery here. In particular, we quantify the robustness of the system to terrain perturbations by defining an L[subscript 2] gain from terrain perturbations to deviations from the nominal limit cycle. We show that the solution to a periodic dissipation inequality provides a sufficient upper bound on this gain for a linear approximation of the dynamics around the limit cycle, and we formulate a semidefinite programming problem to compute the L[subscript 2] gain for the system with a fixed linear controller. We then use either binary search or an iterative optimization method to construct a linear robust controller and to minimize the L[subscript 2] gain. The simulation results on canonical robots suggest that the L[subscript 2] gain is closely correlated to the actual number of steps traversed on the rough terrain, and our controller can improve the robot's robustness to terrain disturbances., National Science Foundation (U.S.) (Contract CNS-0960061), United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation Program (BAA-10-65-M3-FP-024)

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012., Cataloged from PDF version of thesis., Includes bibliographical references (p. 57-60)., A wide variety of bipedal robots have been constructed with the goal of achieving natural and efficient walking in outdoor environments. Unfortunately, there is still a lack of general schemes enabling the robots to reject terrain disturbances. In this thesis, two approaches are presented to enhance the performance of bipedal robots walking on modest terrain. The first approach searches for a walking gait that is intrinsically easily stabilized. The second approach constructs a robust controller to steer the robot towards the designated walking gait. Mathematically, the problem is modeled as rejecting the uncertainty in the guard function of a hybrid nonlinear system. Two metrics are proposed to quantify the robustness of such systems. The first metric concerns the 'average performance' of a robot walking over a stochastic terrain. The expected LQR cost-to-go for the post-impact states is chosen to measure the difficulty of steering those perturbed states back to the desired trajectory. A nonlinear programming problem is formulated to search for a trajectory which takes the least effort to stabilize. The second metric deals with the 'worst case performance', and defines the L₂ gain for the linearization of the hybrid nonlinear system around a nominal periodic trajectory. In order to reduce the L₂ gain, an iterative optimization scheme is presented. In each iteration, the algorithm solves a semidefinite programming problem to find the quadratic storage function and integrates a periodic differential Riccati equation to compute the linear controller. The simulation results demonstrate that both metrics are correlated to the actual number of steps the robot can traverse on the rough terrain without falling down. By optimizing these two metrics, the robot can walk a much longer distance over the unknown landscape., by Hongkai Dai., S.M.