Elastic actuation can improve human-robot interaction and energy efficiency for wearable robots. Previous work showed that the energy consumption of series elastic actuators can be a convex function of the series spring compliance. This function is useful to optimally select the series spring compliance that reduces the motor energy consumption. However, series springs have limited influence on the motor torque, which is a major source of the energy losses due to the associated Joule heating. Springs in parallel to the motor can significantly modify the motor torque and therefore reduce Joule heating, but it is unknown how to design springs that globally minimize energy consumption for a given motion of the load. In this work, we introduce the stiffness design of linear and nonlinear parallel elastic actuators via convex optimization. We show that the energy consumption of parallel elastic actuators is a convex function of the spring stiffness and compare the energy savings with that of optimal series elastic actuators. We analyze robustness of the solution in simulation by adding uncertainty of 20% of the RMS load kinematics and kinetics for the ankle, knee, and hip movements for level-ground human walking. When the winding Joule heating losses are dominant withmore »
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.
- Award ID(s):
- Publication Date:
- NSF-PAR ID:
- Journal Name:
- IEEE International Conference on Rehabilitation Robotics
- Page Range or eLocation-ID:
- 740 to 747
- Sponsoring Org:
- National Science Foundation
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Natural dynamics, nonlinear optimization, and, more recently, convex optimization are available methods for stiffness design of energy-efficient series elastic actuators. Natural dynamics and general nonlinear optimization only work for a limited set of load kinetics and kinematics, cannot guarantee convergence to a global optimum, or depend on initial conditions to the numerical solver. Convex programs alleviate these limitations and allow a global solution in polynomial time, which is useful when the space of optimization variables grows (e.g., when designing optimal nonlinear springs or co-designing spring, controller, and reference trajectories). Our previous work introduced the stiffness design of series elastic actuators via convex optimization when the transmission dynamics are negligible, which is an assumption that applies mostly in theory or when the actuator uses a direct or quasi-direct drive. In this work, we extend our analysis to include friction at the transmission. Coulomb friction at the transmission results in a non-convex expression for the energy dissipated as heat, but we illustrate a convex approximation for stiffness design. We experimentally validated our framework using a series elastic actuator with specifications similar to the knee joint of the Open Source Leg, an open-source robotic knee-ankle prosthesis.
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