Shape Servoing of Deformable Objects using Adaptive Deformation Model Estimation

In this paper, we propose an adaptive shape servoing method to deform a soft object into a desired 3-D shape. The high dimensional representation and the unknown deformation properties of the soft object pose a challenge to actively manipulate its shape. To address this issue, we develop a method to compute the deformation Jacobian matrix in real-time. The Jacobian is estimated using a set of basis functions and its corresponding parameters to capture the dynamics of the system and relate the applied input motion to changes in the soft object's shape. An integral concurrent learning (ICL) based adaptive update law is derived using Lyapunov analysis to estimate the deformation parameters and prove its convergence. A physics-based simulation is used to validate the proposed method and controller by performing manipulation tasks with different desired configurations. The performance is compared with a standard gradient update law to demonstrate the accuracy and robustness of our approach.