Marc Gouttefarde

Effects of non-negligible cable mass on the static behavior of large workspace cable-driven parallel mechanisms

Cable-driven robots are currently extensively studied. Generally, for this type of manipulators, cables are considered to be massless and inextensible. But for large working volume applications, their mass cannot be neglected. Based on a well-known model which describes the profile of a cable under the action of its own weight, the inverse and forward kinematics of minimally constrained cable-driven manipulators can be numerically computed. This paper studies the effects of taking cable mass into account by comparison to classical massless cable model. It highlights the real effects of such a model on cable lengths to reach a given position. The effects on cable tensions are also studied.

Simplified static analysis of large-dimension parallel cable-driven robots

This paper introduces a new simplified static analysis of parallel robots driven by inextensible cables of non-negligible mass. It is based on a known hefty cable static modeling which seems to have been overlooked in previous works on parallel cable-driven robots. This cable modeling is obtained from a well-known sagging cable modeling, known as the catenary, by assuming that cable sag is relatively small. The use of the catenary has been shown to lead to a non-linear set of equations describing the kinetostatic behavior of parallel robots driven by cables of non-negligible mass. On the contrary, the proposed simplified static analysis yields a linear relationship between (components of) the forces in the cables and the external wrench applied to the robot mobile platform. As a consequence, by means of the simplified static analysis, useful wrench-based analysis and design techniques devised for parallel robots driven by massless cables can now be extended to cases in which cable mass is to be accounted for.

Control of a large redundantly actuated cable-suspended parallel robot

This paper deals with the control of a 6-DOF cable-suspended parallel robot (CSPR) able to perform tasks such as pick-and-place trajectories over a large workspace. In order to maximize the ratio between the robot workspace and its overall dimensions, actuation redundancy can be used. The control of such a redundantly actuated CSPR turns to be challenging as a realtime embeddable algorithm for distributing the cable tensions should be used, together with a suitable control scheme. This paper proposes a computationally efficient tension distribution algorithm implemented within a dual-space feedforward scheme in order to properly control the moving platform. Experimentations are performed on a large 6-DOF CSPR prototype equipped with 8 actuators.

Towards 100G with PKM. Is actuation redundancy a good solution for pick-and-place?

This paper analyzes the possible contribution of actuation redundancy in obtaining very high acceleration with Parallel Kinematic Machines (PKM). This study is based on redundant and non-redundant Delta/Par4-like robots (frequently used for pick-and-place applications). The dynamic model, valid for both redundant and non-redundant robots, is used to analyze the traveling plate acceleration capabilities: (i) at zero speed and in any directions, (ii) at zero speed in the “best” direction. The results show that actuation redundancy allows to homogenize the dynamic capabilities throughout the workspace and to increase the traveling plate acceleration capability. Finally, the design of a redundant Delta/Par4-like robot optimized for typical pick-and-place trajectories is presented.

A Tension Distribution Method with Improved Computational Efficiency

This paper introduces a real-time capable tension distribution algorithm for n degree-of-freedom cable-driven parallel robots (CDPR) actuated by \(n+2\) cables. It is based on geometric considerations applied to the two-dimensional convex polytope of feasible cable tension distribution. This polytope is defined as the intersection between the set of inequality constraints on the cable tension values and the affine space of tension solutions to the mobile platform static or dynamic equilibrium. The algorithm proposed in this paper is dedicated to \(n\) degree-of-freedom CDPR actuated by \(n+2\) cables. Indeed, it takes advantage of the two-dimensional nature of the corresponding feasible tension distribution convex polytope to improve the computational efficiency of a tension distribution strategy proposed elsewhere. The fast computation of the polytope vertices and of its barycenter made us successfully validate the real-time compatibility of the presented algorithm.

Towards vision-based control of cable-driven parallel robots

This paper deals with the vision-based control of cable-driven parallel robots. First, a 3D pose visual servoing is proposed, where the end-effector pose is indirectly measured and used for regulation. This method is illustrated and validated on a cable-driven parallel robot prototype. Second, to take into account the dynamics of the platform and using a Cartesian pose and velocity estimator, a vision-based computed torque control is developed and validated in simulation.

On the determination of cable characteristics for large dimension cable-driven parallel mechanisms

Generally, the cables of a parallel cable-driven robot are considered to be massless and inextensible. These two characteristics cannot be neglected anymore for large dimension mechanisms in order to obtain good positioning accuracy. A well-known model which describes the profile of a cable under the action of its own weight allows us to take mass and elasticity into account. When designing a robot, and choosing actuator and cable characteristics, a calculation of maximal tension has to be done. However, because cable mass has a significant effect on cable tensions, a model including cable mass has to be included in the design step. This paper proposes two methods to determine the appropriate cable and hence the maximal tensions in the cables. Applied to a large dimension robot, taking cable mass into account is proved to be necessary in comparison with an equivalent method based on the massless cable modeling. In this paper, only moving platform static equilibria are considered (slow enough motions).

A Versatile Tension Distribution Algorithm for

Redundancy resolution of redundantly actuated cable-driven parallel robots (CDPRs) requires the computation of feasible and continuous cable tension distributions along a trajectory. This paper focuses on n-DOF CDPRs driven by n + 2 cables, since, for n = 6, these redundantly actuated CDPRs are relevant in many applications. The set of feasible cable tensions of n-DOF (n + 2)-cable CDPRs is a 2-D convex polygon. An algorithm that determines the vertices of this polygon in a clockwise or counterclockwise order is first introduced. This algorithm is efficient and can deal with infeasibility. It is then pointed out that straightforward modifications of this algorithm allow the determination of various (optimal) cable tension distributions. A self-contained and versatile tension distribution algorithm is thereby obtained. Moreover, the worst-case maximum number of iterations of this algorithm is established. Based on this result, its computational cost is analyzed in detail, showing that the algorithm is efficient and real-time compatible even in the worst case. Finally, experiments on two six-degree-of-freedom eight-cable CDPR prototypes are reported.

n

This paper addresses the simplification of cable model in static analysis of large-dimension cable-driven parallel robots (CDPR). An approach to derive a simplified hefty cable model is presented. The approach provides an insight into the limitation of such a simplification. The resulting cable tension computation is then used to solve the inverse kinematic problem of CDPR. A new expression of cable length taking into account both the non-negligible cable mass and elasticity is also introduced. Finally, simulations and experiments on a large CDPR prototype are provided. The results show that taking into account both cable mass and elasticity improves the robot accuracy.

-DOF Parallel Robots Driven by

Cable-driven parallel robots (CDPR) are efficient manipulators able to carry heavy payloads across large workspaces. Therefore, the dynamic parameters such as the mobile platform mass and center of mass location may considerably vary. Without any adaption, the erroneous parametric estimate results in mismatch terms added to the closed-loop system, which may decrease the robot performances. In this paper, we introduce an adaptive dual-space motion control scheme for CDPR. The proposed method aims at increasing the robot tracking performances, while keeping all the cable tensed despite uncertainties and changes in the robot dynamic parameters. Reel-time experimental tests, performed on a large redundantly actuated CDPR prototype, validate the efficiency of the proposed control scheme. These results are compared to those obtained with a non-adaptive dual-space feedforward control scheme.