Optimal Cosserat-based deformation control for robotic manipulation of linear objects

Deformable object manipulation is a challenging research subject that draws a growing interest in the robotic field as new methods to tackle this problem have emerged. So far, most of the proposed approaches in the literature focused solely on shape control. The strain applied to the object is disregarded, thus excluding a large part of industrial applications where fragile products are manipulated, like the demolding of rubber and plastic objects, or the handling of food. These applications require a tradeoff between accuracy and careful manipulation in order to preserve the manipulated object. In this article, we propose an approach to optimally control the deformation of linear and planar deformable objects while also minimizing the deformation energy of the object. First, we modify the framework initially developed for linear soft robot control in order to adapt it to deformable object robotic manipulation. To do so, we reformulate the problem as an optimization problem where the whole shape of the object is taken into account instead of solely focusing on the tip of the object’s position and orientation. We then include an energy term in the cost function to find the solution that minimizes the potential elastic energy in the manipulated object while reaching the desired shape. Solutions to problems with high non-linearities are notoriously difficult to find and sensitive to local minima. We define intermediate optimal steps connecting the known initial and final configurations of the object and sequentially solve the problem, thus enhancing the robustness of the algorithm and ensuring the optimality of the solution. The intermediate optimal configurations are then used to define an end-effector trajectory for the robot to deform the object from an initial to the desired configuration.