Using the Chebyshev Basis for Energy Optimal Motion Profiles in Path-Constrained Applications

Abstract

Motion profile optimization is a powerful optimization technique that allows to reduce the energy consumption of robotic systems by changing the temporal profile of the joint position setpoints. However, despite the extensive exploration of these techniques for robotic systems following constrained paths, many existing methodologies rely on complex optimization processes or a larger number of design parameters. This paper introduces a novel approach that leverages the Chebyshev basis to optimize the motion along a fixed geometric path, thereby achieving a measured torque difference of -15% while requiring only a limited number of design parameters. By employing the Chebyshev basis, the formulation leads to a smooth objective function and enables the definition of linear inequality constraints that accurately enclose the feasible design space. This unique combination of features not only simplifies the optimization problem but also enhances the probability of locating the global optimum, particularly illustrated in the two-dimensional case. The methodology is established in a generic and model-independent manner, setting a promising direction for future research in motion profile optimization for constrained-path robotic systems.