Solving the direct geometrico-static problem of underconstrained cable-driven parallel robots by interval analysis

This paper presents an efficient interval-analysis-based algorithm to solve the direct geometrico-static problem (DGP) of underconstrained cable-driven parallel robots (CDPRs). Solving the DGP for a generic CDPR consists of finding all possible equilibrium poses of the end effector for the given cable lengths. Since cables impose unilateral constraints, configurations with one or more slack cables may occur. When the number of taut cables is smaller than six the robot is underconstrained and the DGP solutions must be found considering loop-closure and mechanical equilibrium equations simultaneously. The presented algorithm can find all DGP solutions of a generic CDPR in a numerically robust and safe way. By using interval analysis the proposed procedure can directly search for real solutions with non-negative cable tensions and it can take advantage of the physical constraints of the robot. The implemented procedure is discussed in detail, and the testing and experimental validation on working prototypes are presented.