Discovering Optimal Natural Gaits of Dissipative Systems via Virtual Energy Injection

Legged robots offer several advantages when navigating unstructured environments, but they often fall short of the efficiency achieved by wheeled robots. One promising strategy to improve their energy economy is to leverage their natural (unactuated) dynamics using elastic elements. This work explores that concept by designing energy-optimal control inputs through a unified, multi-stage framework. It starts with a novel energy injection technique to identify passive motion patterns by harnessing the system's natural dynamics. This enables the discovery of passive solutions even in systems with energy dissipation caused by factors such as friction or plastic collisions. Building on these passive solutions, we then employ a continuation approach to derive energy-optimal control inputs for the fully actuated, dissipative robotic system. The method is tested on simulated models to demonstrate its applicability in both single- and multi-legged robotic systems. This analysis provides valuable insights into the design and operation of elastic legged robots, offering pathways to improve their efficiency and adaptability by exploiting the natural system dynamics.

Energy-Aware Hierarchical Control of Joint Velocities

Nowadays, robots are applied in dynamic environments. For a robust operation, the motion planning module must consider other tasks besides reaching a specified pose: (self) collision avoidance, joint limit avoidance, keeping an advantageous configuration, etc. Each task demands different joint control commands, which may counteract each other. We present a hierarchical control that, depending on the robot and environment state, determines online a suitable priority among those tasks. Thereby, the control command of a lower-prioritized task never hinders the control command of a higher-prioritized task. We ensure smooth control signals also during priority rearrangement. Our hierarchical control computes reference joint velocities. However, the underlying concepts of hierarchical control differ when using joint accelerations or joint torques as control signals instead. So, as a further contribution, we provide a comprehensive discussion on how joint velocity control, joint acceleration control, and joint torque control differ in hierarchical task control. We validate our formulation in an experiment on hardware.