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14
LQRRRT ∗ : Optimal SamplingBased Motion Planning with Automatically Derived Extension Heuristics
"... Abstract — The RRT ∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT ∗ is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domainspecific extension heuristics: a d ..."
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Cited by 15 (1 self)
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Abstract — The RRT ∗ algorithm has recently been proposed as an optimal extension to the standard RRT algorithm [1]. However, like RRT, RRT ∗ is difficult to apply in problems with complicated or underactuated dynamics because it requires the design of a two domainspecific extension heuristics: a distance metric and node extension method. We propose automatically deriving these two heuristics for RRT ∗ by locally linearizing the domain dynamics and applying linear quadratic regulation (LQR). The resulting algorithm, LQRRRT ∗ , finds optimal plans in domains with complex or underactuated dynamics without requiring domainspecific design choices. We demonstrate its application in domains that are successively torquelimited, underactuated, and in belief space. I.
Simulationbased LQRtrees with input and state constraints
 In To appear in the Proceedings of the International Conference on Robotics and Automation (ICRA
, 2010
"... Abstract — 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 ..."
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Cited by 12 (7 self)
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Abstract — 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 simulationbased 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. I.
Optimizing Robust Limit Cycles for Legged Locomotion on Unknown Terrain
"... Abstract — While legged animals are adept at traversing rough landscapes, it remains a very challenging task for a legged robot to negotiate unknown terrain. Control systems for legged robots are plagued by dynamic constraints from underactuation, actuator power limits, and frictional ground contact ..."
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Cited by 7 (1 self)
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Abstract — While legged animals are adept at traversing rough landscapes, it remains a very challenging task for a legged robot to negotiate unknown terrain. Control systems for legged robots are plagued by dynamic constraints from underactuation, actuator power limits, and frictional ground contact; rather than relying purely on disturbance rejection, considerable advantage can be obtained by planning nominal trajectories which are more easily stabilized. In this paper, we present an approach for designing nominal periodic trajectories for legged robots that maximize a measure of robustness against uncertainty in the geometry of the terrain. We propose a direct collocation method which solves simultaneously for a nominal periodic control input, for many possible onestep solution trajectories (using ground profiles drawn from a distribution over terrain), and for the periodic solution to a jump Riccati equation which provides an expected infinitehorizon costtogo for each of these samples. We demonstrate that this trajectory optimization scheme can recover the known deadbeat openloop control solution for the Spring Loaded Inverted Pendulum (SLIP) on unknown terrain. Moreover, we demonstrate that it generalizes to other models like the bipedal compass gait walker, resulting in a dramatic increase in the number of steps taken over moderate terrain when compared against a limit cycle optimized for efficiency only. I.
Kinodynamic RRT ∗ : Optimal motion planning for systems with linear differential constraints,” arXiv:1205.5088v1, submitted
"... samplingbased approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots [8], by using a fixedfinalstatefreefinaltime controller that exactly and optimally connects any pair of states ..."
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Cited by 5 (0 self)
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samplingbased approach for asymptotically optimal motion planning for robots with linear differential constraints. Our approach extends RRT*, which was introduced for holonomic robots [8], by using a fixedfinalstatefreefinaltime controller that exactly and optimally connects any pair of states, where the cost function is expressed as a tradeoff between the duration of a trajectory and the expended control effort. Our approach generalizes earlier work on extending RRT * to kinodynamic systems, as it guarantees asymptotic optimality for any system with controllable linear dynamics, in state spaces of any dimension. Our approach can be applied to nonlinear dynamics as well by using their firstorder Taylor approximations. In addition, we show that for the rich subclass of systems with a nilpotent dynamics matrix, closedform solutions for optimal trajectories can be derived, which keeps the computational overhead of our algorithm compared to traditional RRT * at a minimum. We demonstrate the potential of our approach by computing asymptotically optimal trajectories in three challenging motion planning scenarios: (i) a planar robot with a 4D state space and double integrator dynamics, (ii) an aerial vehicle with a 10D state space and linearized quadrotor dynamics, and (iii) a carlike robot with a 5D state space and nonlinear dynamics. I.
Optimal SamplingBased Planning for LinearQuadratic Kinodynamic Systems
"... Abstract—We propose a new method for applying RRT ∗ to kinodynamic motion planning problems by using finitehorizon linear quadratic regulation (LQR) to measure cost and to extend the tree. First, we introduce the method in the context of arbitrary affine dynamical systems with quadratic costs. For ..."
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Abstract—We propose a new method for applying RRT ∗ to kinodynamic motion planning problems by using finitehorizon linear quadratic regulation (LQR) to measure cost and to extend the tree. First, we introduce the method in the context of arbitrary affine dynamical systems with quadratic costs. For these systems, the algorithm is shown to converge to optimal solutions almost surely. Second, we extend the algorithm to nonlinear systems with nonquadratic costs, and demonstrate its performance experimentally. I.
Egrrt: Environmentguided random trees for kinodynamic motion planning with uncertainty and obstacles
 In Proc. IEEE/RSJ Int Intelligent Robots and Systems (IROS) Conf
, 2011
"... Abstract — Existing samplingbased robot motion planning methods are often inefficient at finding trajectories for kinodynamic systems, especially in the presence of narrow passages between obstacles and uncertainty in control and sensing. To address this, we propose EGRRT, an EnvironmentGuided va ..."
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Abstract — Existing samplingbased robot motion planning methods are often inefficient at finding trajectories for kinodynamic systems, especially in the presence of narrow passages between obstacles and uncertainty in control and sensing. To address this, we propose EGRRT, an EnvironmentGuided variant of RRT designed for kinodynamic robot systems that combines elements from several prior approaches and may incorporate a cost model based on the LQGMP framework to estimate the probability of collision under uncertainty in control and sensing. We compare the performance of EGRRT with several prior approaches on challenging sample problems. Results suggest that EGRRT offers significant improvements in performance. I.
M.: Probabilistically complete kinodynamic planning for robot manipulators with acceleration limits
 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems (2014
"... Abstract — We introduce accelerationlimited planning for manipulators as a middle ground between pure geometric planning and planning with full robot dynamics. It is more powerful than geometric planning and can be solved more efficiently than planning with full robot dynamics. We present a probabi ..."
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Cited by 2 (1 self)
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Abstract — We introduce accelerationlimited planning for manipulators as a middle ground between pure geometric planning and planning with full robot dynamics. It is more powerful than geometric planning and can be solved more efficiently than planning with full robot dynamics. We present a probabilistically complete RRT motion planner that considers joint acceleration limits and potentially nonzero start and goal velocities. It uses a fast, noniterative steering method. We demonstrate both the power and efficiency of our planner using the problem of hitting a nail with a hammer, which requires the robot to reach a given goal velocity while avoiding obstacles. Our planner is able to solve this problem in less than 100 ms. In contrast, a purely geometric planner is unable to hit the nail at the desired velocity, whereas a standard kinodynamic RRT is multiple orders of magnitude slower. I.
PROGRAMME DOCTORAL EN SYSTÈMES DE PRODUCTION ET ROBOTIQUE ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES PAR
"... acceptée sur proposition du jury: Prof. H. Bleuler, président du jury Prof. A. Billard, directrice de thèse ..."
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acceptée sur proposition du jury: Prof. H. Bleuler, président du jury Prof. A. Billard, directrice de thèse
Robust Bipedal Locomotion on Unknown Terrain
, 2012
"... 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 ..."
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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 costtogo for the postimpact 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