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Bilateral time-scaling for control of task freedoms of a constrained nonholonomic system

Siddhartha Srinivasa, Michael Erdmann and Matthew T. Mason
Carnegie Mellon University, Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA '03), Vol. 3, pp. 3391 - 3396, May, 2003

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Abstract

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 x_P), i.e. a curve x_P(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 t[0,T], where T is the time to completion of the path. The time-scaling is termed bilateral because there is no restriction on dot{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 x_R) such that the constraints are satisfied. 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 x_P along the path for a small time interval and move x_R 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.

BibTeX Reference
@conference{Srinivasa-2003-8638,
title = {Bilateral time-scaling for control of task freedoms of a constrained nonholonomic system},
author = {Siddhartha Srinivasa and Michael Erdmann and Matthew T. Mason},
booktitle = {Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA '03)},
keyword = {nonholonomic control, time-scaling, mobile manipulation, task freedoms, shape freedoms},
sponsor = {NSF},
publisher = {IEEE},
grantID = {IIS-9820180, IIS-9900322, IIS-0082339 and IIS-0222875},
school = {Robotics Institute , Carnegie Mellon University},
month = {May},
year = {2003},
volume = {3},
pages = {3391 - 3396},
address = {Pittsburgh, PA},
}
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