Date of Original Version

9-2003

Type

Conference Proceeding

Abstract or Description

We explore the control of a nonholonomic robot subject to additional constraints on the state variables. In our problem, the user specifies the path of a subset of the state variables (the task freedoms xP ), i.e. a curve xP (s) where s ∈ [0, 1] is a parametrization that the user chooses. We control the trajectory of the task freedoms by specifying a bilateral time-scaling s(t) which assigns a point on the path for each time t. The time-scaling is termed bilateral because there is no restriction on ˙ s(t), the task freedoms are allowed to move backwards along the path. We design a controller that satisfies the user directive and controls the remaining state variables (the shape freedoms xR ) to satisfy the constraints. Furthermore, we attempt to reduce the number of control switchings, as these result in relatively large errors in our system state. If a constraint is close to being violated (at a switching point), we back up xP along the path for a small time interval and move xR to an open region. We show that there are a finite number of switching points for arbitrary task freedom paths. We implement our control scheme on the Mobipulator and discuss a generalization to arbitrary systems satisfying similar properties.

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"©2003 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."

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Published In

Proceedings of IEEE International Conference on Robotics and Automation, ICRA '03, 3, 3391-3396.