Real-time computation of inexact minimum-energy trajectories using parametric sensitivities

Abstract

The exact solution of practical trajectory optimization problems are usually not feasible in real time. The use of approximate solutions deduced form a nominal optimal solution is a potential alternative. This requires evaluation of parametric sensitivities of the nominal solution in real time. This is addressed in this paper. Improvements to existing methods are introduced that not only increase their efficiency but also ensure the constraint satisfaction of the approximation. The proposed methods are applied to a practical trajectory planning problem for a planar manipulator where the initial state is given but the final state is unknown prior to task execution.