Volume 22 Issue 7/8 - Publication Date: 1 July - August 2003
Special Issue on the 3rd International Conference on Field and Service Robotics
Reactive Nonholonomic Trajectory Generation via Parametric Optimal Control
A. Kelly and B. Nagy Robotics Institute, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA

There are many situations for which a feasible nonholonomic motion plan must be generated immediately based on real-time perceptual information. Parametric trajectory representations limit computation because they reduce the search space for solutions (at the cost of potentially introducing suboptimality). The use of any parametric trajectory model converts the optimal control formulation into an equivalent nonlinear programming problem. In this paper, curvature polynomials of arbitrary order are used as the assumed form of solution. Polynomials sacrifice little in terms of spanning the set of feasible controls while permitting an expression of the general solution to the system dynamics in terms of decoupled quadratures. These quadratures are then readily linearized to express the necessary conditions for optimality. Resulting trajectories are convenient to manipulate and execute in vehicle controllers and they can be computed with a straightforward numerical procedure in real time.

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