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 deals with continuous tension validation for Cable-Driven Parallel Robots (CDPRs). The proposed method aims at determining whether or not a quasi-static path is feasible regarding cable tension limits. The available wrench set (AWS) is the set of wrenches that can be generated with cable tensions within given minimum and maximum limits. A pose of the robot is considered valid regarding the tensions if and only if the wrench induced by the platform weight is inside the AWS. The hyperplane shifting method gives a geometric representation of the AWS as the intersection of half-spaces. For each facet-defining hyperplane of the AWS, we define a value which is positive when the pose is valid, i.e. when the corresponding wrench lies on the proper side of the hyperplane. Using this value and an upper bound on its time derivative along the path, the half-length of a valid time interval is obtained. Intervals are repeatedly validated for each hyperplane until either the whole path is validated or a non-valid pose is found. The presented method is integrated within the open-source software Humanoid Path Planner (HPP) and implementation results using the configuration of the CDPR CoGiRo are presented.

A continuous collision checking method for a cable-driven parallel robot with an embarked robotic arm is proposed in this paper. The method aims at validating paths by checking for collisions between any pair of robot bodies (mobile platform, cables, and arm links). For a pair of bodies, an upper bound on their relative velocity and a lower bound on the distance between the bodies are computed and used to validate a portion of the path. These computations are done repeatedly until a collision is found or the path is validated. The method is integrated within the Humanoid Path Planner (HPP) software, tested with the cable-driven parallel robot CoGiRo, and compared to a discretized validation method.