Model Predictive Control for a Soft Robotic Finger with Stochastic Behavior based on Fokker-Planck Equation

The inherent flexibility of soft robots offers numerous advantages, such as enhanced adaptability and improved safety. However, this flexibility can also introduce challenges regarding highly uncertain and nonlinear motion. These challenges become particularly problematic when using open-loop control methods, which lack a feedback mechanism and are commonly employed in soft robot control. Though one potential solution is model-based control, typical deterministic models struggle with uncertainty as mentioned above. The idea is to use the Fokker-Planck Equation (FPE), a master equation of a stochastic process, to control not the state of soft robots but the probabilistic distribution. In this study, we propose and implement a stochastic-based control strategy, termed FPE-based Model Predictive Control (FPE-MPC), for a soft robotic finger. Two numerical simulation case studies examine the performance and characteristics of this control method, revealing its efficacy in managing the uncertainty inherent in soft robotic systems.