Abstract: For the under-constrained system that multi-robots cooperatively tow a payload by cables, the dynamic workspace can’t be found out by the principle of vector closure. The dynamic equations of the system were established by using the Newton-Euler equation. Then the geometric meaning of Farkas and Stiemke lemma and relationship with the dynamic equations of the system were introduced, and the solving of dynamic workspace was converted to the problem that whether there exists a hyper plane. For the under-constrained system, the dynamic equations also need to be split to get the dynamic workspace. Finally, simulations were conducted to validate the feasibility of the proposed method by Monte Carlo method, it validates that the payload acceleration has little effect on the dynamic workspace by comparing the two groups of simulation.

Key words: system of multi-robots, under-constrained, cable-driven, workspace