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

2025-08-31

AI Summary

Soft robotic systems exhibit high compliance, leading to significant motion uncertainty and strong nonlinear dynamics that challenge conventional open-loop control strategies and deterministic modeling approaches. To address this, we propose a novel probabilistic control framework grounded in the Fokker–Planck equation (FPE), marking the first application of FPE to soft robot control. Our approach formulates a model predictive control (MPC) scheme wherein the control objective is the evolution of the state probability density function—explicitly modeling and regulating stochastic state dynamics even under open-loop (i.e., feedback-free) conditions. This overcomes inherent limitations of deterministic models in characterizing uncertainty. We validate the method via two simulation studies: FPE-MPC significantly improves trajectory accuracy and robustness for a soft robotic finger operating under stochastic dynamics. The results establish a verifiable, distributional control paradigm for highly uncertain soft robotic systems.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization

Abstract

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.

Problem

• Control soft robotic finger with stochastic behavior uncertainty
• Manage probabilistic distribution using Fokker-Planck Equation
• Implement model predictive control for nonlinear flexible systems

Innovation

• FPE-based Model Predictive Control
• Probabilistic distribution control strategy
• Stochastic process master equation