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

Design of rehabilitation and physical assistance robots that work safely and efficiently despite uncertain operational conditions remains an important challenge. Current methods for the design of energy efficient series elastic actuators use an optimization formulation that typically assumes known operational requirements. This approach could lead to actuators that cannot satisfy elongation, speed, or torque requirements when the operation deviates from nominal conditions. Addressing this gap, we propose a convex optimization formulation to design the stiffness of series elastic actuators to minimize energy consumption and satisfy actuator constraints despite uncertainty due to manufacturing of the spring, unmodeled dynamics, efficiency of the transmission, and the kinematics and kinetics of the load. To achieve convexity, we write energy consumption as a scalar convex-quadratic function of compliance. As actuator constraints, we consider peak motor torque, peak motor velocity, limitations due to the speed-torque relationship of DC motors, and peak elongation of the spring. We apply our formulation to the robust design of a series elastic actuator for a powered prosthetic ankle. Our simulation results indicate that a small trade-off between energy efficiency and robustness is justified to design actuators that can operate with uncertainty.

A GENERAL FRAMEWORK FOR MINIMIZING ENERGY CONSUMPTION OF SERIES ELASTIC ACTUATORS WITH REGENERATION.

The use of actuators with inherent compliance, such as series elastic actuators (SEAs), has become traditional for robotic systems working in close contact with humans. SEAs can reduce the energy consumption for a given task compared to rigid actuators, but this reduction is highly dependent on the design of the SEA's elastic element. This design is often based on natural dynamics or a parameterized optimization, but both approaches have limitations. The natural dynamics approach cannot consider actuator constraints or arbitrary reference trajectories, and a parameterized elastic element can only be optimized within the given parameter space. In this work, we propose a solution to these limitations by formulating the design of the SEA's elastic element as a non-parametric convex optimization problem, which yields a globally optimal conservative elastic element while respecting actuator constraints. Convexity is proven for the case of an arbitrary periodic reference trajectory with a SEA capable of energy regeneration. We discuss the optimization results for the tasks defined by the human ankle motion during level-ground walking and the natural motion of a single mass-spring system with a nonlinear spring. For all these tasks, the designed SEA reduces energy consumption and satisfies the actuator's constraints.