A convex optimization framework for robust-feasible series elastic actuators

Abstract Kinematic and kinetic requirements for robotic actuators are subject to uncertainty in the motion of the load. Safety factors account for uncertainty in the design stage, but defining factors that translate to reliable systems without over-designing is a challenge. Bulky or heavy actuators resulting from overdesign are undesirable in wearable or mobile robots, which are prone to uncertainty in the load due to human–robot or robot–environment interaction. In this paper, we use robust optimization to account for uncertainty in the design of series elastic actuators. We formulate a robust-feasible convex optimization program to select the optimal compliance–elongation profile of the series spring that minimizes one or multiple of the following objectives: spring elongation, motor energy consumption, motor torque, or motor velocity. To preserve convexity when minimizing energy consumption, we lump the energy losses in the transmission as viscous friction losses, which is a viable approximation for series elastic actuators powered by direct or quasi-direct drives. Our formulation guarantees that the motor torque, winding temperature, and speed are feasible despite uncertainty in the load kinematics, kinetics, or manufacturing of the spring. The globally optimal spring could be linear or nonlinear. As simulation case studies, we design the optimal compliance–elongation profiles for multiple series springs for a robotic prosthetic ankle. The simulation case studies illustrate examples of our methodology, evaluate the performance of robust feasible designs against optimal solutions that neglect uncertainty, and provide insight into the selection of different objective functions. With this framework the designer specifies uncertainty directly in the optimization and over the specific kinematics, kinetics, or manufacturing parameters, aiming for reliable robots that reduce overdesign.