A Pseudospectral Method for Real-Time Motion Planning and Obstacle Avoidance
NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF MECHANICAL AND ASTRONAUTICAL ENGINEERING
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In recent years, pseudospectral PS methods have been successfully applied to solve a rich number of trajectory optimization problems arising in aerospace application. Motivated by the success of this approach, we consider the problem of generating minimum-time trajectories for unmanned ground vehicles. Shapes of arbitrary number, size and configuration are modelled in the form of path constraints in the resulting optimal control problem formulation. PS methods are used to solve the constrained, nonlinear optimal control problem. Solutions are obtained within a few seconds even under a MATLAB environment running on legacy computer hardware. A complete problem formulation is developed including a derivation of the necessary conditions for optimality. The trajectories are mathematical extremals as they satisfy all the optimality conditions. What is noteworthy about our approach is that the difficulties associated in solving the Hamiltonian equations are completely circumvented by an application of the Covector Mapping Theorem. Solved examples are provided to illustrate the tools and techniques.
- Numerical Mathematics
- Computer Programming and Software