Investigation of a Model-Based Approach for Dynamical Manipulation of Deformable Objects

Deformable object manipulation is a rapidly evolving field in robotics with applications in various domains such as manufacturing, healthcare, robotics-assisted surgery and rehabilitation. Traditional motion planning algorithms designed for rigid objects are inadequate for deformable objects, necessitating the development of tailored trajectory optimization techniques. This thesis contributes to the field by investigating a model-based technique for deformable object manipulation. The proposed task involves a dynamical movement to be executed by a robotic arm, fixed at the base. This led to assume that the operational space where the end-effector can move is approximated as a sphere, constraining the manipulated mass within this volume. To tackle this task, the chosen method is the iterative Linear Quadratic Regulator (iLQR) one to solve unconstrained trajectory optimization problems in non-rigid object manipulation. However, since the proposed problem is a constrained one, the Augmented Lagrangian and Method of Multipliers technique is employed to handle them. The Mass-Spring-System (MSS) was chosen for modeling the non-rigid object, specifically a rope. This approach involves representing the rope using five nodes connected by three different types of springs and a damping system, all governed by Hooke's law. The three types of springs employed are elastic, shear and flexion. The elastic and shear springs connect adjacent nodes, while the flexion spring connects two diagonal masses. One notable advantage of the implemented model is its differentiability, which is facilitated by the JAX environment. Extensive tuning of the rope model is performed to approximate real-world behavior, and the entire AL-iLQR algorithm is tested and fine-tuned for optimal performance. Parameter variations, including the cost function, horizon length and frequency rate, are analyzed to understand their impact on the controller's behavior. The importance of selecting an appropriate cost function is emphasized through an extensive analysis on the parameters and its shape. The limitations of the Augmented Lagrangian and Method of Multipliers (ALMM) algorithm, particularly the influence of the penalty parameter μ, are deeply discussed. Furthermore, an in-depth analysis is conducted on the horizon length, highlighting its task-dependence and significance in achieving desirable performance. In conclusion, the research highlights the importance of accurate models, suitable cost functions, and the trade-offs involved in balancing simulation and control aspects. It provides valuable insights and establishes foundations for further advancements in constrained trajectory optimization for non-rigid object manipulation.