Robots are nowadays faced with the challenge of handling deformable objects in industrial operations. In particular, the problem of shape control, which aims at giving a specific deformation state to an object, has gained interest recently in the research community. Among the proposed solutions, approaches based on finite elements proved accurate and reliable but also complex and computationally-intensive.In order to mitigate these drawbacks, we propose a scheme for shape control that does not require to run a real-time simulation or to solve an implicit optimization problem for computing the control outputs. It is based on a partition of the nodal coordinates that allows deriving a control law directly from tangent stiffness matrices. This formulation is also coupled with the introduction of reduced finite element models. Simulation and experimental results in the context of linear deformable object manipulation demonstrate the interest of the proposed approach.

Increasing the size of operationnal workspace is one of the main problems parallel robots are faced with. Among all the proposed solutions to that, crossing Type 2 singularities using dedicated trajectory generation and multimodel controller has a great potential. Yet, this approach is not sufficient for the robot to operate autonomously, as assembly mode detection during the motion currently requires additional redundant information. To tackle this problem, we propose an algorithm based on Interval Analysis (IA) that is able to track the end-effector of the robot even under assembly mode change. IA-based solvers for the forward kinematic problem of parallel robots are well known, but they cannot be used under assembly mode change. Compared to those classical approaches, the major modification introduced is the tracking of end-effector velocity in addition to its pose. Using this new information of velocity, the algorithm is capable to monitor the assembly mode change of the robot happening when the singularities are crossed. The behavior and the reliability of this algorithm are analyzed experimentally on a five-bar planar parallel mechanism.

This article introduces a new geometric vector modeling method of serial kinematic robot consistent with the identification process. This method is based on the definition of position and orientation of the robot joint invariants. For example, the invariant of the rotational joint is a straight-line (rotational joint axis). Thus, only independent geometrical parameters are introduced to model the joint axis position and orientation in space. Note that, the orientation is not constrained as in the Denavit-Hartenberg (DH) formalism. This article presents the methodology to define these geometrical parameters and the geometrical model. In this context, the identification method relies on "Circle Point Analysis". The points are measured with a laser tracker. Indeed, with a relevant processing of the measured points, we directly identify the invariants of joints. This method is applied to a SCARA robot geometric modeling. After an identification process, this methodology allows improving inverse kinematic error compared to the classical DH geometrical model with first and second-order defects. Moreover, the obtained residual error mean value is close to the accuracy of the measurement process.