Energetic Efficiency of a Compositional Controller on a Monoped With an Articulated Leg and SLIP Dynamics

Embedding the dynamics of the Spring Loaded Inverted Pendulum (SLIP) and applying a compositional controller around it can simplify dynamic legged robot locomotion control, but what is the energetic cost of this convenience? This paper measures the magnitude of this effect in such a way that the results are applicable to a wide class of jumping robots. A three-link monoped model with revolute joints is used to compare the energetic costs of locomotion using two different control approaches: 1) SLIP-embedding with a Raibert-style controller optimized for energetic efficiency, and 2) a trajectory optimized only for energetic efficiency. By performing this comparison in simulation for a large number of different monopeds randomly sampled from a space of realistic robot designs, it is found that the SLIP-Raibert approach requires, on average, almost twice the energy of the trajectory-optimized controller to traverse a given distance. Furthermore, the increase in energetic cost does not depend much on the particulars of the robot design, as the SLIP-Raibert approach requires at least 50% more energy for approximately 88% of realistic robot designs.