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

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


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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.


Keywords
nonholonomic control, time-scaling, mobile manipulation, task freedoms, shape freedoms

Notes
Sponsor: NSF
Grant ID: IIS-9820180, IIS-9900322, IIS-0082339 and IIS-0222875
Associated Center(s) / Consortia: Center for the Foundations of Robotics
Associated Lab(s) / Group(s): Manipulation Lab
Associated Project(s): Desktop Robotics
Number of pages: 6

Text Reference
Siddhartha Srinivasa, Michael Erdmann, and Matthew T. Mason, "Bilateral time-scaling for control of task freedoms of a constrained nonholonomic system," Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA '03), May, 2003, pp. 3391 - 3396.

BibTeX Reference
@inproceedings{Srinivasa_2003_4314,
   author = "Siddhartha Srinivasa and Michael Erdmann and Matthew T. Mason",
   title = "Bilateral time-scaling for control of task freedoms of a constrained nonholonomic system",
   booktitle = "Proceedings of the 2003 IEEE International Conference on Robotics and Automation (ICRA '03)",
   pages = "3391 - 3396",
   publisher = "IEEE",
   month = "May",
   year = "2003",
   volume = "3",
}