88 research outputs found
LQR-Trees: Feedback motion planning on sparse randomized trees
No full textRecent 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
Reachability-guided sampling for planning under differential constraints
No full textRapidly-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)
Stable dynamic walking over uneven terrain
No full textWe 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
Path planning in 1000+ dimensions using a task-space Voronoi bias
No full textThe 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)
Feedback controller parameterizations for reinforcement learning
No full textReinforcement 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
Robot learning [TC Spotlight]
No full textCreating 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
Tracking objects with point clouds from vision and touch
No full textWe present an object-tracking framework that fuses point cloud information from an RGB-D camera with tactile information from a GelSight contact sensor. GelSight can be treated as a source of dense local geometric information, which we incorporate directly into a conventional point-cloud-based articulated object tracker based on signed-distance functions. Our implementation runs at 12 Hz using an online depth reconstruction algorithm for GelSight and a modified second-order update for the tracking algorithm. We present data from hardware experiments demonstrating that the addition of contact-based geometric information significantly improves the pose accuracy during contact, and provides robustness to occlusions of small objects by the robot's end effector
Belief space planning assuming maximum likelihood observations
No full textWe 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
Bounding on Rough Terrain with the LittleDog Robot
No full textA 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
Toward Fast Policy Search for Learning Legged Locomotion
No full text18.10.13 KB. Ok to add author version to spiral. IEE
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