Shape control involves deforming objects to achieve a desired shape. One of the main challenges of this task is to define a suitable control reference, especially when 3D objects that lack distinctive visual texture and geometric features are involved. This paper addresses the problem of generating a suitable shape control reference using surface maps for 3D texture-less objects. The proposed surface mapping method is based on functional maps and ensures time consistency with robustness to non-isometries. Our time consistent method is validated within a shape control strategy, where local exponential stability analysis is provided. The effectiveness of the framework is illustrated through simulations and experiments. Note to Practitioners—We present a method for shape comparison to analyse the geometric similarities between the shape of an object and a desired target shape. The goal is to generate a point map between both surfaces so that, with the use of robots that grasp the object, a control strategy can deform the object towards the desired shape. The point map we compute, while adapting to the changing shape of the deforming object, remains stable enough to enable the shape control task. This can be of use for the automation of processes that involve shape control (e.g., object packaging, moulding, etc.). Our proposed shape control framework combines computer graphics, computer vision, and automation techniques to create a system that is well-suited for industrial setups equipped with commonly used range sensors like RGB-D cameras. Regarding the experiments presented in this paper, controlled lighting conditions are recommendable in order to perform the colour-based object segmentation (e.g. avoidance of abrupt light variations, uniform illumination). Automating the grasping process is not within the scope of this paper, therefore, in each experiment we manually defined the object grasping points according to the shape control task involved. The proposed framework has the potential to increase productivity, reduce costs and, improve safety in hazardous tasks by automating the manipulation of 3D objects that lack distinctive visual texture and geometric features.

Shape control involves bringing a deformable object to a desired shape. In the shape control literature, the positioning of the grippers on the object is usually predefined (user-defined) and therefore considered as input information. In this paper we address the gripper positioning problem for shape control. We propose a deformation process within a simulated fully-actuated scenario and introduce multi-scale centroid paths as geometry describing points for which we prove individual control feasibility. Analysis on the evolution of multi-scale centroid paths through the fully-actuated deformation process allows us to define an importance metric for gripper candidates. Final gripper positions, based on the importance metric, are obtained through optimisation. We present simulation results for global and local shape control problems.

Shape control has become a prominent research field as it enables the automation of tasks in many applications. Overall, deforming an object to a desired target shape by using few grippers is a major challenge. The limited information about the object dynamics, the need to combine small and large deformations in order to achieve certain target shapes and the non-linear nature of most deformable objects are factors that significantly hamper shape control performance. In this paper, we propose a shape control method for multi-robot manipulation of large-strain deformable objects. Our approach is based on multi-scale Laplacian descriptors that feed an FMM (Fast Marching Method) for elastic shape contour matching. The FMM's resulting path and the Laplacian operator are used to define a control strategy for the robot grippers. Simulation experiments carried out with an ARAP (As Rigid As Possible) deformation model provide satisfactory results.