Unified Inverse Dynamics of Modular Serial Mechanical Systems with Application to Soft Robotics

The robotic field has been witnessing a progressive departure from classic robotic systems composed of serial/stiff links interconnected by simple rigid joints. Novel robotic concepts, e.g., soft robots, often maintain a series-like structure, but their mechanical modules exhibit complex and unconventional articulation patterns. Research in efficient recursive formulations of the dynamic models for subclasses of these systems has been extremely active in the past decade. Yet, as of today, no single recursive inverse dynamics algorithm can describe the behavior of all these systems. This paper addresses this challenge by proposing a new iterative formulation based on Kane equations. Its computational complexity is optimal, i.e., linear with the number of modules. While the proposed formulation is not claimed to be necessarily more efficient than state-of-the-art techniques for specific subclasses of robots, we illustrate its usefulness in the modeling of different complex systems. We propose two new models of soft robots: (i) a class of pneumatically actuated soft arms that deform along their cross-sectional area, and (ii) a piecewise strain model with Gaussian functions.