NDLI: Control by Gradient Collocation: Applications to optimal obstacle avoidance and minimum torque control

Content Provider	IEEE Xplore Digital Library
Author	Ruvolo, P. Tingfan Wu Movellan, J.R.
Copyright Year	2012
Description	Author affiliation: Machine Perception Laboratory, University of California, San Diego, La Jolla, USA (Ruvolo, P.; Tingfan Wu; Movellan, J.R.)
Abstract	We present a new machine learning algorithm for learning optimal feedback control policies to guide a robot to a goal in the presence of obstacles. Our method works by first reducing the problem of obstacle avoidance to a continuous state, action, and time control problem, and then uses efficient collocation methods to solve for an optimal feedback control policy. This formulation of the obstacle avoidance problem improves over standard approaches, such as potential field methods, by being resistant to local minima, allowing for moving obstacles, handling stochastic systems, and computing feedback control strategies that take into account the robot's (possibly non-linear) dynamics. In addition to contributing a new method for obstacle avoidance, our work contributes to the state-of-the-art in collocation methods for non-linear stochastic optimal control problems in two important ways: (1) we show that taking into account local gradient and second-order derivative information of the optimal value function at the collocation points allows us to exploit knowledge of the derivative information about the system dynamics, and (2) we show that computational savings can be achieved by directly fitting the gradient of the optimal value function rather than the optimal value function itself. We validate our approach on three problems: non-convex obstacle avoidance of a point-mass robot, obstacle avoidance for a 2 degree of freedom robotic manipulator, and optimal control of a non-linear dynamical system.
Starting Page	1173
Ending Page	1179
File Size	982231
Page Count	7
File Format	PDF
ISBN	9781467317375
ISSN	21530858
e-ISBN	9781467317368
DOI	10.1109/IROS.2012.6385556
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-10-07
Publisher Place	Portugal
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Collision avoidance Equations Robot kinematics Mathematical model Least squares approximation Optimal control
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Computer Science Applications Computer Vision and Pattern Recognition Software

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