Constraint Generation for Trajectory Planning Systems

In this paper we formulate the problem of determining constraints in the parameter space used for planning reference trajectories for tracking systems. The objective is to obtain parameter constraints which allow a maximal amount of maneuverability while assuring that operatmg limits will not be violated and that the system can execute the prescribed reference trajectory within a given error tolerance. We present a numerical algorithm for generating the parameter constrants based on previously computed constraints in the space of the continuous-time trajectory and its derivatives. A simplicial approximation method is used to generate a polyhedral approximation to a maximal set of parameters corresponding to executable trajectories. Supervisory planning and control can then be carried out in the reference trajectory parameter space without detailed simulation of the underlying system dynamics. We illustrate the computational algorithm and its application to trajectory planning for a two-axis CNC cutting tool.