Comprehensive Gradient Computation Framework of PCS Model for Soft Robot Simulation.

Dynamic simulation of soft and flexible bodies is important for the motion planning and control of soft robot systems. This study presents a fast real-time simulation of the piecewise constant strain (PCS) model proposed in soft robotics research to calculate the dynamics of a beam or rod structure. We extend the theory of comprehensive motion transformation matrix (CMTM) to the PCS model, which allows us to systematically calculate the gradients in the equations of motion. Using the dynamic gradient, we perform a dynamic simulation of the PCS model via implicit integration. Compared to explicit integration, implicit integration allows us to use a larger time-step width for the integration without a flexible deformation divergence, which decreases the computational time. We present several examples of dynamic simulations, including a relatively rigid material such as carbon-fiber-reinforced plastics used in a leaf-spring-type sports prosthesis.