An Analytical Approach for Dealing with Explicit Physical Constraints in Excitation Optimization Problems of Dynamic Identification

Generating optimal excitation trajectories for dynamic identification of robots is a typical constrained optimization problem, where the initial velocity/acceleration of all joints should be zero (initial conditions) and their allowable range of motion should not be violated (physical limits). Despite this problem being long defined, the following challenges remain unresolved: 1) low success rate and 2) time-consuming, which seriously plague applications. Specifically, these constraints make solving the problem difficult and time-consuming, requiring recourse to heuristic or gradient-based numerical iteration. In practice, the success rate of finding feasible solutions that do not violate physical constraints within a limited number of iteration steps is not as high as desired. This article presents, for the first time, an analytical approach to handle these physical constraints. Feasible solutions are ensured by a deterministic calculation of the Fourier series-based parameterization rather than relying on an iterative search approach. We achieve a 100% success rate in generating physically executable excitation trajectories. Extensive experiments indicate that our approach has achieved an order of magnitude improvement in optimization efficiency compared to available methods. For practitioners, our method opens up the possibility of implementing excitation optimization for time-critical payload identification tasks.