Differentiable ANCF-Based Kinematic Modeling of Soft Pneumatic Robots for Design Optimization

Soft pneumatic robots are widely developed for grasping and locomotion tasks, where the routing of embedded muscles plays a pivotal role in programming the deformation behavior. However, existing routing patterns are often limited to predefined regular configurations due to the absence of accurate and efficient design-oriented models. In this article, we propose a differentiable kinematic model based on the absolute nodal coordinate formulation to predict the global configuration and local deformation of soft robots with customizable fiber-reinforced pneumatic muscles. By parameterizing the freeform muscle routing using B-splines and accurately modeling the work done by distributed pneumatic forces, we ensure that the routing pathways are fully differentiable. We then integrate the kinematic model into an optimization framework to automatically design muscle routing pathways for achieving desired deformation behaviors. The inclusion of analytical shape derivative enables efficient exploration of the high-dimensional design space. We verify the proposed model through comparisons with finite element analysis and experiments on a three-channel robot. The average position error of the end effector is less than 5% of the workspace's characteristic length, with an average computational time of 0.11 s per point. In addition, we demonstrate robots capable of achieving desired complex out-of-plane configurations and multiple target shapes.