Computational design of energy-efficient legged robots: Optimizing for size and actuators

Abstract

This paper presents a computational framework for the design of high-performance legged robotic systems. The framework relies on the concurrent optimization of hardware parameters and control trajectories to find the best robot design for a given task. In particular, we focus on energy efficiency, presenting novel electro-mechanical models to account for the losses of the actuators due to friction and Joule effects. Thanks to a bi-level optimization scheme, featuring a genetic algorithm in the outer loop, our framework can also optimize for the duration of the motion, the actuators, and the size of the robot. We present a novel approach to scale both the actuators and the robot structure in a way that ensures structural integrity by maintaining constant the normalized deflection of the links. We validated our approach by designing a two-joint monoped robot to execute a jumping task. Our simulation results show that our framework can lead to remarkable energy savings (up to 60%) thanks to the concurrent optimization of robot size, motion duration, and actuators.

Co-Designing Robots by Differentiating Motion Solvers

“…For instance, Wampler et al [3] used a variant of CMA-ES to co-design various creatures in simulation, and Digumarti et al [4] co-designed the legs of the quadruped StarlETH to optimize its running speed. Most recently, Chadwick et al [5] optimized the legs of quadrupeds and bipeds over uneven terrain for different user-defined co-design metrics, and Fadini et al [6] computed the actuator properties of a monoped using CMA-ES.…”

Simulation Aided Co-Design for Robust Robot Optimization

“…This comes at the price of the blindness of the inner loop (DDP) to perturbations, which theoretically limits the quality of the design outcome. However, our tests show extremely promising results for the design of an energyefficient robot manipulator and a jumping monoped, which proved to perform much better under perturbations than their counterparts designed with our previous framework [4].…”

“…Our approach is to introduce robustness information in the bi-level optimization structure introduced in [4], by adding a simulation step with perturbations and a controller as shown in Fig. 1 and in Algorithm 1 line 7.…”

“…a) Joint dynamics: In a realistic application, to implement a control law such as (1) on the robot, an actuator model has to be considered. In order to deal with joint dynamics, the same methodology as in [4] is used: the OCP solution provides the joint trajectories that minimize the electrical energy consumption, without modeling friction in the robot dynamics, but considering it only in the cost function. Then the reference control 𝝉 is computed so to compensate for friction:…”

“…This becomes even more challenging for inherently unstable systems, such as legged robots. Following a common assumption in co-design, our previous work [4] was mainly targeting the adequacy of the hardware for optimizing the motion. However, optimal trajectories may be unfeasible on a real system, e.g., because the system cannot reject external perturbations due to unmodeled dynamics, noise, delays, saturation or actuator dynamics.…”