Optimal path planning for continuum systems

Soft robotics is a field of tremendous promise, opening opportunities for operations in new domains where rigid systems cannot reach. In particular, soft continuum robots offer safer interactions with their environments and significant improvements in dexterous movements over conventional counterparts. These advantages have allowed this class of robot to enter previously unreachable territories in medical and exploratory applications. Despite their clear advantages, the near infinite degrees of freedom offered by continuum systems come with significant challenges in modeling and control. In this thesis, we extend previous work done in the field of optimal control to encompass path planning for continuum robots characterized by the set of partial differential equations which make up the Cosserat rod model. This model captures the dynamics of the central cord of a continuum system with minimal assumptions, allowing it to describe all possible modes of deformation. The path planning problem is formulated as an optimal control problem which is solved as a nonlinear programming problem discretized by bivariate Bernstein polynomials. Experimental results with a cable driven soft continuum robot are presented to demonstrate the efficacy of the planning method. Finally, the developed optimal control framework is extended to higher dimensional continuum dynamics problems to demonstrate its potential impact in other fields outside of soft robotics.