Energy-efficient motion planning for robotic systems using polynomials in the Chebyshev basis

Motion profile optimization is a powerful technique for enhancing the efficiency of robotic systems without necessitating hardware modifications. Nonetheless, the prevailing usage of piecewise or polynomial position functions can often require a high number of design parameters or result in unbounded optimization problems. This paper presents a novel approach employing polynomials expressed in the Chebyshev basis for the position function of multi-degree-of-freedom (DOF) systems, enabling substantial performance improvements with a minimal number of design parameters while enabling the use of a bounded design space. More specifically, this work focuses on reducing energy consumption while maintaining a fixed motion time. Moreover, by symbolically formulating the motion profile, it is demonstrated that kinematic constraints can be linearized, leading to accelerated convergence in the optimization process. To illustrate the robustness of the proposed method under different operational conditions, optimizations were executed on three distinct motion tasks and a range of payload values, and compared to a state-of-the-art method. Experimental results strongly validate the effectiveness of the proposed approach, demonstrating a reduction in root mean square (rms) torque by up to-47.6% with a limited number of design parameters for each joint.