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Design of robotic systems that safely and efficiently operate in uncertainoperational conditions, such as rehabilitation and physical assistance robots,remains an important challenge in the field. Current methods for the design ofenergy efficient series elastic actuators use an optimization formulation thattypically assumes known operational conditions. This approach could lead toactuators that cannot perform in uncertain environments because elongation,speed, or torque requirements may be beyond actuator specifications when theoperation deviates from its nominal conditions. Addressing this gap, we proposea convex optimization formulation to design the stiffness of series elasticactuators to minimize energy consumption and satisfy actuator constraintsdespite uncertainty due to manufacturing of the spring, unmodeled dynamics,efficiency of the transmission, and the kinematics and kinetics of the load. Inour formulation, we express energy consumption as a scalar convex-quadraticfunction of compliance. In the unconstrained case, this quadratic equationprovides an analytical solution to the optimal value of stiffness thatminimizes energy consumption for arbitrary periodic reference trajectories. Asactuator constraints, we consider peak motor torque, peak motor velocity,limitations due to the speed-torque relationship of DC motors, and peakelongation of the spring. As a simulation case study, we apply our formulationto the robust design of a series elastic actuator for a powered prostheticankle. Our simulation results indicate that a small trade-off between energyefficiency and robustness is justified to design actuators that can operatewith uncertainty.

Robust Optimal Design of Energy Efficient Series Elastic Actuators: Application to a Powered Prosthetic Ankle