Robot path optimization based on adaptive weight pseudospectral method

Abstract In complex work environments, improving efficiency and stability is an important issue in robot path planning. This article proposes a new path optimization algorithm based on pseudospectral methods. The algorithm includes an adaptive weighting factor in the objective function, which automatically adjusts the quality of the path while satisfying the performance indicators of the shortest time. It also considers kinematic, dynamic, boundary, and obstacle constraints, and applies the Separating Axis Theorem collision detection method to improve computational efficiency. To discretize the continuous path optimization problem into a nonlinear programming problem, the algorithm utilizes Chebyshev polynomials for the interpolation of state and control variables, along with the adoption of the Lagrange interpolation polynomial to approximate the curve. Finally, it solves the nonlinear programming problem numerically using CasADi, which supports automatic differentiation. The results of the simulation demonstrate that the path optimized by the adaptive-weight pseudospectral method can satisfy various constraints and optimization objectives simultaneously. Experimental verification confirms the efficiency and feasibility of the proposed algorithm.