  Parallel-elastic joints can improve the efficiency and strength of robots by
assisting the actuators with additional torques. For these benefits to be
realized, a spring needs to be carefully designed. However, designing robots is
an iterative and tedious process, often relying on intuition and heuristics. We
introduce a design optimization framework that allows us to co-optimize a
parallel elastic knee joint and locomotion controller for quadrupedal robots
with minimal human intuition. We design a parallel elastic joint and optimize
its parameters with respect to the efficiency in a model-free fashion. In the
first step, we train a design-conditioned policy using model-free Reinforcement
Learning, capable of controlling the quadruped in the predefined range of
design parameters. Afterwards, we use Bayesian Optimization to find the best
design using the policy. We use this framework to optimize the parallel-elastic
spring parameters for the knee of our quadrupedal robot ANYmal together with
the optimal controller. We evaluate the optimized design and controller in
real-world experiments over various terrains. Our results show that the new
system improves the torque-square efficiency of the robot by 33% compared to
the baseline and reduces maximum joint torque by 30% without compromising
tracking performance. The improved design resulted in 11% longer operation time
on flat terrain.
