In this paper, a method for 3D non-rigid motion estimation of a surface using an RGB-D camera in eye-in-hand configuration is presented. The eye-in-hand configuration eliminates errors typically associated with camera-end-effector calibration, and is thus desirable for task on moving surfaces such as bioprinting. However, its implementation is challenging since camera and surface of interest are moving, making mesh-based approaches unsuitable. Thus, the proposed method operates directly on point clouds, benefiting from accurate and simplified data processing. A point cloud contains both intensity and depth data, with the former used to estimate in-plane deformation and the latter to compute full 3D deformation. Surface deformation is modeled via a Thin Plate Spline model. The method accuracy is assessed at 0.1 mm accuracy in simulated datasets, rendering it suitable for precision tasks, and its feasibility is validated experimentally on a moving platform that deforms at a rate of 0.8 Hz with a 4 mm in-plane amplitude and a 20 mm elevation amplitude.

This article proposes a nonlinear model predictive control (NMPC) strategy for the position tracking of cable-driven parallel robots (CDPRs). The NMPC formulation handles explicitly the cable tensions and their limits. Accordingly, the cable tension distribution is performed as an integral part of the NMPC feedback control strategy, which notably allows the CDPR to operate on the wrench-feasible workspace boundaries without failure. In order to integrate the cable tension minimization within the NMPC formulation, the concept of wrench equivalent optimality (WEO) is introduced. The WEO is a nonnegative measure able to evaluate if the wrench generated by a given cable tension vector can be generated by an alternative tension vector with smaller 2-norm. The redundancy resolution performed by means of the minimization of the WEO enables the stability of the closed-loop system to be proved. More precisely, sufficient conditions for the uniform asymptotic stability are deduced using results from the analysis of NMPC schemes without terminal constraints and costs. Furthermore, the proposed NMPC strategy is validated experimentally on a fully constrained 6 degree-of-freedom CDPR.

The maximum cable tension is a crucial parameter in the design of a cable-driven parallel robot (CDPR) since the various mechanical components of the CDPR must be designed to safely withstand the loads induced by this maximum tension. For CDPRs having a number of cables at least equal to its number of degree of freedoms (DOFs), this article deals with the determination of the smallest maximum cable tension vectors allowing a required wrench set to be feasible. The problem is formulated as the minimization of the maximum cable tension infinity norm under linear inequality constraints, which include the wrench-feasibility constraints. The solution to this minimization problem is not unique, and the solution set is shown to be a convex polytope in the maximum tension space. Hence, various smallest maximum tension vectors generally exist and the computations of two different solution vectors are introduced. The first vector has all its components equal to the minimum infinity norm, which can be directly obtained from the minimization problem inequality constraints. An algorithm is proposed to determine the second vector as the solution vector having the least possible value for each of its components. The computation of the smallest maximum tension vectors for general required wrench sets are then presented. The cases of particular wrench set definitions relevant to heavy payload manipulation applications are also introduced. Finally, these contributions are applied to the configuration (geometry) optimization of a large-dimension 6-DOF CDPR installed on a building facade to manipulate heavy payloads.

This paper introduces a Model Predictive Control (MPC) strategy for fully-constrained Cable-Driven Parallel Robots. The main advantage of the proposed scheme lies in its ability to explicitly handle cable tension limits. Indeed, the cable tension distribution is performed as an integral part of the main control architecture. This characteristic significantly improves the safety of the system. Experimental results demonstrate this advantage addressing a typical pick-and-place task with two different scenarios: nominal cable tension limits and reduced maximum tension. Satisfactory tracking errors were obtained in the first scenario. In the second scenario, the desired trajectory escapes from the workspace defined by the new set of tension limits. The proposed MPC scheme is able to minimize the tracking errors without violating the tension limits. Satisfying results were also obtained regarding robustness against uncertainties on the payload mass.

This paper deals with the optimization of the geometry of a Cable-Driven Parallel Robot (CDPR) dedicated to large-scale construction applications. Since the maximum cable tension is a critical parameter in the design of the CDPR components, the geometry of the CDPR is optimized by minimizing the lowest maximum cable tension that ensures the validity of wrench-feasibility constraints. The geometric design procedure used in this paper consists of two phases, the CDPR cable connections is selected in the first phase followed by a second phase where the geometric parameters are optimized. The result of this procedure is an original fully-constrained CDPR geometry.