Three Benefits of Using Nonlinear Compliance in Robotic Systems Performing Cyclic Tasks: Energy Efficiency, Control Robustness, and Gait Optimality

Nonlinearity in parallel compliance can be exploited to improve the performance of locomotion systems in terms of (1) energy efficiency, (2) control robustness, and (3) gait optimality; that is, attaining energy efficiency across a set of motions. Thus far, the literature has investigated and validated only the first two benefits. In this study, we present a new mathematical framework for designing nonlinear compliances in cyclic tasks encompassing all three benefits. We present an optimization-based formulation for each benefit to obtain the desired compliance profile. Furthermore, we analytically prove that, compared to linear compliance, using nonlinear compliance leads to (1) lower energy consumption, (2) better closed-loop performance, specifically in terms of tracking error, and (3) a higher diversity of natural frequencies. To compare the performance of linear and nonlinear compliance, we apply the proposed methods to a diverse set of robotic systems performing cyclic tasks, including a 2-DOF manipulator, a 3-DOF bipedal walker, and a hopper model. Compared to linear compliance, the nonlinear compliance leads to better performance in all aspects; for example, a 70% reduction in energy consumption and tracking error for the manipulator simulation. Regarding gait optimality, for all robotic simulation models, compared to linear compliance, the nonlinear compliance has lower energy consumption and tracking error over the considered set of motions. The proposed analytical studies and simulation results strongly support the idea that using nonlinear compliance significantly improves robotic system performance in terms of energy efficiency, control robustness, and gait optimality.