Minimum Gain Requirements for Trajectory Tracking of Compliant Robots in Divergent Force Fields

The future of robotics involves a growing need for robots to perform everyday tasks in dynamic and unstructured environments. This often requires them to handle complex and unstable interactions with various objects, including mechanical tools, flexible objects such as food items and fruits, and more. Robots must be able to interact with their environment like humans, who rely on the compliance of their musculoskeletal system to achieve safe and effective interaction. Previous research has analyzed the benefits of incorporating mechanical compliance in parallel and series configurations to address this requirement. In this work, we introduce a novel approach to parallel compliance, where the mean position is adjusted based on desired trajectories and study its advantages. The unstable interactions are modeled as a position-based divergent force field. A generalized theory is presented that determines the minimum gains required for trajectory tracking in all types of compliance configurations in the presence of divergent force fields. The results are demonstrated through simulations of 1-DOF and 2-DOF robots and provides insight into the associated control effort.