Using the Chebyshev Basis for Energy Optimal Motion Profiles in Path-Constrained Applications
Nick Van Oosterwyck, Robbe De Laet, Lorenzo Scalera, Annie Cuyt, Alessandro Gasparetto, Stijn Derammelaere
AI summary
Problem
Existing path-constrained motion optimization methods are often computationally complex, require numerous design parameters, and frequently neglect energy minimization for fixed-duration tasks.
Approach
The temporal profile along a fixed geometric path is represented as a linear combination of Chebyshev polynomials, transforming nonlinear constraints into linear inequalities to simplify optimization and improve global convergence.
Key results
- Up to 15% reduction in measured root-mean-square torque across multiple test paths
- Significant energy savings achieved with only two design parameters
- Successful experimental validation on a 7-DOF Franka Panda robot across four distinct trajectories
- Improved global convergence and avoidance of local minima compared to classical polynomial bases
Why it matters
Provides a computationally efficient, model-independent framework for industrial robots to meet strict energy and path-adherence requirements.
Abstract
Motion profile optimization is a powerful opti- mization technique that allows to reduce the energy consump- tion 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 parame- ters. 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.