Shape Control of Deformable Structures Using Iterative Multi-Modal Density Steering

Abstract We present an iterative algorithm for shape control of deformable structures based on multi-modal density steering methods. In our approach, the dynamics of a deformable structure are described by a mass-spring-damper (MSD) network, and its shape is represented by a multi-modal density model, and in particular, a Gaussian Mixture Model (GMM). This modeling setup allows us to pose the shape control problem as a GMM (density) steering problem, eliminating the point-to-point correspondence required by conventional configuration control methods. The proposed density steering algorithm for shape control must be applied iteratively because the dynamics of the MSD network are nonlinear. The convergence of the proposed algorithm is demonstrated through extensive numerical simulations (Monte Carlo analysis). Benchmarking against a basic Model Predictive Control (MPC) scheme shows that our proposed shape control approach achieves significantly faster solve times while introducing only a small point-wise position error, offering a scalable alternative for high-dimensional deformable systems.