A Novel Optimized Trajectory Planning Method via Spline Function Theorems

Trajectory planning of dynamical control systems (e.g., robots and aircrafts) undergoes some constraints on input signals and output transients. It can be viewed as a special class of optimal control problems. But, solving these problems is not an easy task. We consider the optimal output trajectory planning problem of a singal input and single output system with controllable canonical form under some constraints on input and output signals. A novel method is proposed that applies polynomical spline functions to delineate the output trajectory profile. Particular properties on spline functions are proved theoretically to ensure that the constrained dynamical optimization problem is converted to a constrained static optimization problem. The latter can be solved easily through the nonlinear programming approaches (e.g. SQP), where a set of optimal spline functions for output trajectory tracking are derived.