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In order for robots to interact safely and intelligently with their environment they must be able to reliably estimate and localize external contacts. This paper introduces CPF, the Contact Particle Filter, which is a general algorithm for detecting and localizing external contacts on rigid body robots without the need for external sensing. CPF finds external contact points that best explain the observed external joint torque, and returns sensible estimates even when the external torque measurement is corrupted with noise. We demonstrate the capability of the CPF to track multiple external contacts on a simulated Atlas robot, and compare our work to existing approaches. Keywords: Robot sensing systems; Collision avoidance; Legged locomotion; Torque; Observers

We present a new approach to the design of smooth trajectories for quadrotor unmanned aerial vehicles (UAVs), which are free of collisions with obstacles along their entire length. To avoid the non-convex constraints normally required for obstacle-avoidance, we perform a mixed-integer optimization in which polynomial trajectories are assigned to convex regions which are known to be obstacle-free. Prior approaches have used the faces of the obstacles themselves to define these convex regions. We instead use IRIS, a recently developed technique for greedy convex segmentation [1], to pre-compute convex regions of safe space. This results in a substantially reduced number of integer variables, which improves the speed with which the optimization can be solved to its global optimum, even for tens or hundreds of obstacle faces. In addition, prior approaches have typically enforced obstacle avoidance at a finite set of sample or knot points. We introduce a technique based on sums-of-squares (SOS) programming that allows us to ensure that the entire piecewise polynomial trajectory is free of collisions using convex constraints. We demonstrate this technique in 2D and in 3D using a dynamical model in the Drake toolbox for Matlab [2]., Hertz Foundation, MIT Energy Initiative, Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory

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)

We present a novel stereo vision algorithm that is capable of obstacle detection on a mobile ARM processor at 120 frames per second. Our system performs a subset of standard block-matching stereo processing, searching only for obstacles at a single depth. By using an onboard IMU and state-estimator, we can recover the position of obstacles at all other depths, building and updating a local depth-map at framerate. Here, we describe both the algorithm and our implementation on a high-speed, small UAV, flying at over 20 MPH (9 m/s) close to obstacles. The system requires no external sensing or computation and is, to the best of our knowledge, the first high-framerate stereo detection system running onboard a small UAV., United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051), National Science Foundation (U.S.). Graduate Research Fellowship

The goal of this work is to develop a soft robotic manipulation system that is capable of autonomous, dynamic, and safe interactions with humans and its environment. First, we develop a dynamic model for a multi-body fluidic elastomer manipulator that is composed entirely from soft rubber and subject to the self-loading effects of gravity. Then, we present a strategy for independently identifying all unknown components of the system: the soft manipulator, its distributed fluidic elastomer actuators, as well as drive cylinders that supply fluid energy. Next, using this model and trajectory optimization techniques we find locally optimal open-loop policies that allow the system to perform dynamic maneuvers we call grabs. In 37 experimental trials with a physical prototype, we successfully perform a grab 92% of the time. By studying such an extreme example of a soft robot, we can begin to solve hard problems inhibiting the mainstream use of soft machines., National Science Foundation (U.S.) (Grant 1117178), National Science Foundation (U.S.) (Grant EAGER 1133224), National Science Foundation (U.S.) (Grant IIS1226883), National Science Foundation (U.S.) (Grant CCF1138967), National Science Foundation (U.S.). Graduate Research Fellowship (Award 1122374)

We present a new method for planning footstep placements for a robot walking on uneven terrain with obstacles, using a mixed-integer quadratically-constrained quadratic program (MIQCQP). Our approach is unique in that it handles obstacle avoidance, kinematic reachability, and rotation of footstep placements, which typically have required non-convex constraints, in a single mixed-integer optimization that can be efficiently solved to its global optimum. Reachability is enforced through a convex inner approximation of the reachable space for the robot's feet. Rotation of the footsteps is handled by a piecewise linear approximation of sine and cosine, designed to ensure that the approximation never overestimates the robot's reachability. Obstacle avoidance is ensured by decomposing the environment into convex regions of obstacle-free configuration space and assigning each footstep to one such safe region. We demonstrate this technique in simple 2D and 3D environments and with real environments sensed by a humanoid robot. We also discuss computational performance of the algorithm, which is currently capable of planning short sequences of a few steps in under one second or longer sequences of 10-30 footsteps in tens of seconds to minutes on common laptop computer hardware. Our implementation is available within the Drake MATLAB toolbox [1]., Hertz Foundation, MIT Energy Initiative, Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory, United States. Defense Advanced Research Projects Agency (Robotics Challenge)

In this paper, we present an approach for designing feedback controllers for polynomial systems that maximize the size of the time-limited backwards reachable set (BRS). We rely on the notion of occupation measures to pose the synthesis problem as an infinite dimensional linear program (LP) and provide finite dimensional approximations of this LP in terms of semidefinite programs (SDPs). The solution to each SDP yields a polynomial control policy and an outer approximation of the largest achievable BRS. In contrast to traditional Lyapunov based approaches, which are non-convex and require feasible initialization, our approach is convex and does not require any form of initialization. The resulting time-varying controllers and approximated backwards reachable sets are well-suited for use in a trajectory library or feedback motion planning algorithm. We demonstrate the efficacy and scalability of our approach on four nonlinear systems., United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051), National Science Foundation (U.S.) (Contract IIS-1161679), Thomas and Stacey Siebel Foundation

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)

Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities. These certificates, together with our proposed polynomial controllers, can be efficiently obtained via semidefinite optimization. Our approach can handle time-varying dynamics resulting from tracking a given trajectory, input saturations (e.g. torque limits), and can be extended to deal with uncertainty in the dynamics and state. The resulting controllers can be used by space-filling feedback motion planning algorithms to fill up the space with significantly fewer trajectories. We demonstrate our approach on a severely torque limited underactuated double pendulum (Acrobot) and provide extensive simulation and hardware validation., United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051), Siebel Scholars Foundation

We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the simulated Atlas robot in the DARPA Virtual Robotics Challenge., United States. Air Force Research Laboratory (Contract FA8750-12-1-0321), National Science Foundation (U.S.) (Contract ERC-1028725), National Science Foundation (U.S.) (Contract IIS-1161909), National Science Foundation (U.S.) (Contract IIS-0746194)

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., United States. Defense Advanced Research Projects Agency. Maximum Mobility and Manipulation Program (Grant W91CRB-11-1-0001), National Science Foundation (U.S.) (Grant IIS-0746194), National Science Foundation (U.S.) (Grant IIS-1161909), National Science Foundation (U.S.) (Grant IIS-0915148)

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)

We explore region of attraction (ROA) estimation for polynomial systems via the numerical solution of polynomial equations. Computing an optimal, stable sub-level set of a Lyapunov function is first posed as a polynomial optimization problem. Solutions to this optimization problem are found by solving a polynomial system of equations using techniques from numerical algebraic geometry. This system describes KKT points and singular points not satisfying a regularity condition. Though this system has exponentially many solutions, the proposed method trivially parallelizes and is practical for problems of moderate dimension and degree. In suitably generic settings, the method can solve the underlying optimization problem to arbitrary precision, which could make it a useful tool for studying popular semidefinite programming based relaxations used in ROA analysis.

We show that for continuous time dynamical systems described by polynomial differential equations of modest degree (typically equal to three), the following decision problems which arise in numerous areas of systems and control theory cannot have a polynomial time (or even pseudo-polynomial time) algorithm unless P=NP: local attractivity of an equilibrium point, stability of an equilibrium point in the sense of Lyapunov, boundedness of trajectories, convergence of all trajectories in a ball to a given equilibrium point, existence of a quadratic Lyapunov function, invariance of a ball, invariance of a quartic semialgebraic set under linear dynamics, local collision avoidance, and existence of a stabilizing control law. We also extend our earlier NP-hardness proof of testing local asymptotic stability for polynomial vector fields to the case of trigonometric differential equations of degree four.

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron., National Science Foundation (U.S.). (Grant number 0835947)

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain., National Science Foundation (U.S.) (grant 0746194), Swiss National Science Foundation (grant PBZH2-114461), Swiss National Science Foundation (grant PP00P2_123387/1)

We present an algorithm that probabilistically covers a bounded region of the state space of a nonlinear system with a sparse tree of feedback stabilized trajectories leading to a goal state. The generated tree serves as a lookup table control policy to get any reachable initial condition within that region to the goal. The approach combines motion planning with reasoning about the set of states around a trajectory for which the feedback policy of the trajectory is able to stabilize the system. The key idea is to use a random sample from the bounded region for both motion planning and approximation of the stabilizable sets by falsification; this keeps the number of samples and simulations needed to generate covering policies reasonably low. We simulate the nonlinear system to falsify the stabilizable sets, which allows enforcing input and state constraints. Compared to the algebraic verification using sums of squares optimization in our previous work, the simulation-based approximation of the stabilizable set is less exact, but considerably easier to implement and can be applied to a broader range of nonlinear systems. We show simulation results obtained with model systems and study the performance and robustness of the generated policies.

A new framework for nonlinear system identification is presented in terms of optimal fitting of stable nonlinear state space equations to input/output/state data, with a performance objective defined as a measure of robustness of the simulation error with respect to equation errors. Basic definitions and analytical results are presented. The utility of the method is illustrated on a simple simulation example as well as experimental recordings from a live neuron., National Science Foundation (U.S.). (Grant number 0835947)

Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the “stochastic stability” of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability—the mean first-passage time—and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.

In this video, we demonstrate the effectiveness of a kinodynamic planning strategy that allows a high-impedance quadruped to operate across a variety of rough terrain. At one extreme, the robot can achieve precise foothold selection on intermittent terrain. More surprisingly, the same inherently-stiff robot can also execute highly dynamic and underactuated motions with high repeatability. This range of dynamic motion is possible through careful reasoning about the coupled dynamics during underactuated phases of motion. Our results demonstrate visceral progress toward realization of one of the central theoretically claims giving legged locomotion a “leg-up” over wheeled robotics: that appropriate design of control can produce a set of capabilities which span a dynamic range from deliberate foothold selection through acrobatic-style motion on a single, particular robot., United States. Defense Advanced Research Projects Agency (Learning Locomotion program (AFRL contract # FA8650-05-C-7262))

Reinforcement Learning offers a very general framework for learning controllers, but its effectiveness is closely tied to the controller parameterization used. Especially when learning feedback controllers for weakly stable systems, ineffective parameterizations can result in unstable controllers and poor performance both in terms of learning convergence and in the cost of the resulting policy. In this paper we explore four linear controller parameterizations in the context of REINFORCE, applying them to the control of a reaching task with a linearized flexible manipulator. We find that some natural but naive parameterizations perform very poorly, while the Youla Parameterization (a popular parameterization from the controls literature) offers a number of robustness and performance advantages., National Science Foundation (U.S.) (Award IIS-0746194)

URL to paper listed on conference page, Choosing features for the critic in actor-critic algorithms with function approximation is known to be a challenge. Too few critic features can lead to degeneracy of the actor gradient, and too many features may lead to slower convergence of the learner. In this paper, we show that a wellstudied class of actor policies satisfy the known requirements for convergence when the actor features are selected carefully. We demonstrate that two popular representations for value methods - the barycentric interpolators and the graph Laplacian proto-value functions - can be used to represent the actor in order to satisfy these conditions. A consequence of this work is a generalization of the proto-value function methods to the continuous action actor-critic domain. Finally, we analyze the performance of this approach using a simulation of a torque-limited inverted pendulum.

Reinforcement Learning offers a very general framework for learning controllers, but its effectiveness is closely tied to the controller parameterization used. Especially when learning feedback controllers for weakly stable systems, ineffective parameterizations can result in unstable controllers and poor performance both in terms of learning convergence and in the cost of the resulting policy. In this paper we explore four linear controller parameterizations in the context of REINFORCE, applying them to the control of a reaching task with a linearized flexible manipulator. We find that some natural but naive parameterizations perform very poorly, while the Youla Parameterization (a popular parameterization from the controls literature) offers a number of robustness and performance advantages., National Science Foundation (U.S.) (Award IIS-0746194)

We propose a constructive control design for stabilization of non-periodic trajectories of underactuated robots. An important example of such a system is an underactuated “dynamic walking” biped robot traversing rough or uneven terrain. The stabilization problem is inherently challenging due to the nonlinearity, open-loop instability, hybrid (impact) dynamics, and target motions which are not known in advance. The proposed technique is to compute a transverse linearization about the desired motion: a linear impulsive system which locally represents “transversal” dynamics about a target trajectory. This system is then exponentially stabilized using a modified receding-horizon control design, providing exponential orbital stability of the target trajectory of the original nonlinear system. The proposed method is experimentally verified using a compass-gait walker: a two-degree-of-freedom biped with hip actuation but pointed stilt-like feet. The technique is, however, very general and can be applied to a wide variety of hybrid nonlinear systems., National Science Foundation (U.S.) (Grant 0746194)

Recent advances in the direct computation of Lyapunov functions using convex optimization make it possible to efficiently evaluate regions of stability for smooth nonlinear systems. Here we present a feedback motion planning algorithm which uses these results to efficiently combine locally valid linear quadratic regulator (LQR) controllers into a nonlinear feedback policy which probabilistically covers the reachable area of a (bounded) state space with a region of stability, certifying that all initial conditions that are capable of reaching the goal will stabilize to the goal. We investigate the properties of this systematic nonlinear feedback control design algorithm on simple underactuated systems and discuss the potential for control of more complicated control problems like bipedal walking.

Rapidly-exploring random trees (RRTs) are widely used to solve large planning problems where the scope prohibits the feasibility of deterministic solvers, but the efficiency of these algorithms can be severely compromised in the presence of certain kinodynamics constraints. Obstacle fields with tunnels, or tubes are notoriously difficult, as are systems with differential constraints, because the tree grows inefficiently at the boundaries. Here we present a new sampling strategy for the RRT algorithm, based on an estimated feasibility set, which affords a dramatic improvement in performance in these severely constrained systems. We demonstrate the algorithm with a detailed look at the expansion of an RRT in a swing up task, and on path planning for a nonholonomic car., United States. Defense Advanced Research Projects Agency (Learning Locomotion program (AFRL contract # FA8650-05-C-7262))

In this video, we demonstrate the effectiveness of a kinodynamic planning strategy that allows a high-impedance quadruped to operate across a variety of rough terrain. At one extreme, the robot can achieve precise foothold selection on intermittent terrain. More surprisingly, the same inherently-stiff robot can also execute highly dynamic and underactuated motions with high repeatability. This range of dynamic motion is possible through careful reasoning about the coupled dynamics during underactuated phases of motion. Our results demonstrate visceral progress toward realization of one of the central theoretically claims giving legged locomotion a “leg-up” over wheeled robotics: that appropriate design of control can produce a set of capabilities which span a dynamic range from deliberate foothold selection through acrobatic-style motion on a single, particular robot., United States. Defense Advanced Research Projects Agency (Learning Locomotion program (AFRL contract # FA8650-05-C-7262))

We cast the partially observable control problem as a fully observable underactuated stochastic control problem in belief space and apply standard planning and control techniques. One of the difficulties of belief space planning is modeling the stochastic dynamics resulting from unknown future observations. The core of our proposal is to define deterministic beliefsystem dynamics based on an assumption that the maximum likelihood observation (calculated just prior to the observation) is always obtained. The stochastic effects of future observations are modelled as Gaussian noise. Given this model of the dynamics, two planning and control methods are applied. In the first, linear quadratic regulation (LQR) is applied to generate policies in the belief space. This approach is shown to be optimal for linear- Gaussian systems. In the second, a planner is used to find locally optimal plans in the belief space. We propose a replanning approach that is shown to converge to the belief space goal in a finite number of replanning steps. These approaches are characterized in the context of a simple nonlinear manipulation problem where a planar robot simultaneously locates and grasps an object., United States. Dept. of Defense (Air Force contract FA8721-05-C-0002)

A motion planning algorithm is described for bounding over rough terrain with the LittleDog robot. Unlike walking gaits, bounding is highly dynamic and cannot be planned with quasi-steady approximations. LittleDog is modeled as a planar five-link system, with a 16-dimensional state space; computing a plan over rough terrain in this high-dimensional state space that respects the kinodynamic constraints due to underactuation and motor limits is extremely challenging. Rapidly Exploring Random Trees (RRTs) are known for fast kinematic path planning in high-dimensional configuration spaces in the presence of obstacles, but search efficiency degrades rapidly with the addition of challenging dynamics. A computationally tractable planner for bounding was developed by modifying the RRT algorithm by using: (1) motion primitives to reduce the dimensionality of the problem; (2) Reachability Guidance, which dynamically changes the sampling distribution and distance metric to address differential constraints and discontinuous motion primitive dynamics; and (3) sampling with a Voronoi bias in a lower-dimensional “task space” for bounding. Short trajectories were demonstrated to work on the robot, however open-loop bounding is inherently unstable. A feedback controller based on transverse linearization was implemented, and shown in simulation to stabilize perturbations in the presence of noise and time delays., United States. Defense Advanced Research Projects Agency. Learning Locomotion Program (AFRL contract # FA8650-05-C-7262)

The reduction of the kinematics and/or dynamics of a high-DOF robotic manipulator to a low-dimension ldquotask spacerdquo has proven to be an invaluable tool for designing feedback controllers. When obstacles or other kinodynamic constraints complicate the feedback design process, motion planning techniques can often still find feasible paths, but these techniques are typically implemented in the high-dimensional configuration (or state) space. Here we argue that providing a Voronoi bias in the task space can dramatically improve the performance of randomized motion planners, while still avoiding non-trivial constraints in the configuration (or state) space. We demonstrate the potential of task-space search by planning collision-free trajectories for a 1500 link arm through obstacles to reach a desired end-effector position., United States. Defense Advanced Research Projects Agency (Learning Locomotion program (AFRL contract # FA8650-05-C-7262))

Legged robots that operate in the real world are inherently subject to stochasticity in their dynamics and uncertainty about the terrain. Owing to limited energy budgets and limited control authority, these “disturbances” cannot always be canceled out with high-gain feedback. Minimally actuated walking machines subject to stochastic disturbances no longer satisfy strict conditions for limit-cycle stability; however, they can still demonstrate impressively long-living periods of continuous walking. Here, we employ tools from stochastic processes to examine the “stochastic stability” of idealized rimless-wheel and compass-gait walking on randomly generated uneven terrain. Furthermore, we employ tools from numerical stochastic optimal control to design a controller for an actuated compass gait model which maximizes a measure of stochastic stability—the mean first-passage time—and compare its performance with a deterministic counterpart. Our results demonstrate that walking is well characterized as a metastable process, and that the stochastic dynamics of walking should be accounted for during control design in order to improve the stability of our machines.

Creating autonomous robots that can learn to act in unpredictable environments has been a long-standing goal of robotics, artificial intelligence, and the cognitive sciences. In contrast, current commercially available industrial and service robots mostly execute fixed tasks and exhibit little adaptability. To bridge this gap, machine learning offers a myriad set of methods, some of which have already been applied with great success to robotics problems. As a result, there is an increasing interest in machine learning and statistics within the robotics community. At the same time, there has been a growth in the learning community in using robots as motivating applications for new algorithms and formalisms.

The ability of birds to perch robustly and effectively is a powerful demonstration of the capabilities of nature's control systems. Their apparent robustness to gust disturbances is particularly remarkable because when the airspeed approaches zero just before acquiring a perch, the influence of aerodynamic forces, and therefore potentially the control authority, is severely compromised. In this paper we present a simplified closed-form model for a fixed-wing aircraft which closely agrees with experimental indoor perching data. We then carefully examine the LTV controllability along an optimized perching trajectory for three different actuation scenarios - a glider (no powerplant), a fixed propeller, and a propeller with thrust vectoring. The results reveal that while all three vehicles are LTV controllable along the trajectory, the additional actuators allow the perch to be more easily acquired with less control surface deflections. However, in all three cases, disturbances experienced just before reaching the perch cannot be effectively rejected., National Science Foundation (U.S.). Graduate Fellowship Program, Microsoft Research. New Faculty Fellowship program

We present a kinodynamic planning methodology for a high-impedance quadruped robot to negotiate a wide variety of terrain types with high reliability. We achieve motion types ranging from dynamic, double-support lunges for efficient locomotion over extreme obstacles to careful, deliberate foothold and body pose selections which allow for precise foothold placement on rough or intermittent terrain.

The ability of birds to perch robustly and effectively is a powerful demonstration of the capabilities of nature's control systems. Their apparent robustness to gust disturbances is particularly remarkable because when the airspeed approaches zero just before acquiring a perch, the influence of aerodynamic forces, and therefore potentially the control authority, is severely compromised. In this paper we present a simplified closed-form model for a fixed-wing aircraft which closely agrees with experimental indoor perching data. We then carefully examine the LTV controllability along an optimized perching trajectory for three different actuation scenarios - a glider (no powerplant), a fixed propeller, and a propeller with thrust vectoring. The results reveal that while all three vehicles are LTV controllable along the trajectory, the additional actuators allow the perch to be more easily acquired with less control surface deflections. However, in all three cases, disturbances experienced just before reaching the perch cannot be effectively rejected., National Science Foundation (U.S.). Graduate Fellowship Program, Microsoft Research. New Faculty Fellowship program

We present a kinodynamic planning methodology for a high-impedance quadruped robot to negotiate a wide variety of terrain types with high reliability. We achieve motion types ranging from dynamic, double-support lunges for efficient locomotion over extreme obstacles to careful, deliberate foothold and body pose selections which allow for precise foothold placement on rough or intermittent terrain.

Creating autonomous robots that can learn to act in unpredictable environments has been a long-standing goal of robotics, artificial intelligence, and the cognitive sciences. In contrast, current commercially available industrial and service robots mostly execute fixed tasks and exhibit little adaptability. To bridge this gap, machine learning offers a myriad set of methods, some of which have already been applied with great success to robotics problems. As a result, there is an increasing interest in machine learning and statistics within the robotics community. At the same time, there has been a growth in the learning community in using robots as motivating applications for new algorithms and formalisms.

Although there has been an increasing interest in dynamic bipedal locomotion for significant improvement of energy efficiency and dexterity of mobile robots in the real world, their locomotion capabilities are still mostly restricted on flat surfaces. The difficulty of dynamic locomotion in rough terrain is mainly originated in the stability and controllability of gait patterns while exploiting the natural mechanical dynamics of the robots. For a systematic investigation of the challenging problem, this paper presents the simplest control architecture for the compass gait model which can be used for locomotion in rough terrain. Locomotion of the model is mainly achieved by an open-loop oscillator which induces self-stabilizing gait patterns, and we test the proposed control architecture in a real-world robotic platform. In addition, we also found that this controller is capable of varying stride length with a minimum change of control parameters, which enables locomotion in rough terrains. By using these basic principles of self-stability and gait variability, we extended the proposed controller with a simple sensory feedback about the location in the environment, which makes the robot possible to control gait patterns autonomously for traversing a rough terrain. We describe a set of experimental results and discuss how the proposed minimalistic control architecture can be enhanced for dynamic locomotion control in more complex environment., National Science Foundation (U.S.) (Grant No. 0746194), Swiss National Science Foundation (Grant No. PBZH2-114461)