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

Generating optimal excitation trajectories is crucial for ensuring that the observation matrix is well conditioned in robot dynamic identification. This task is a typical optimization problem involving explicit physical constraints defined by initial conditions (zero initial joint velocity and acceleration) and physical limits (joint position, velocity, and acceleration within specified bounds). Physical constraints complicate problem-solving, necessitating the use of heuristic or gradient-based iteration methods. Despite extensive study of this problem over many years, the success rate of finding feasible solutions that do not violate physical constraints within a limited number of iteration steps is lower than desired, and two major challenges remain: 1) a low success rate; and 2) high time consumption, which adversely affect practical applications. This article presents an analytical approach to address these physical constraints for excitation optimization. Feasible solutions are ensured through a deterministic calculation of the Fourier series-based parameterization rather than relying on iterative searches. Specifically, initial conditions are met by assigning offsets directly, while scaling and central-translation operations ensure adherence to physical limits. Our approach achieves a 100% success rate in generating physically executable excitation trajectories. Extensive experiments indicate that our approach has improved optimization efficiency by an order of magnitude compared to available methods, while delivering excellent excitation performance. For practitioners, our method renders excitation optimization a viable approach for time-critical payload identification tasks.