A sufficient condition for manipulation of envelope family

This paper discusses a sufficient condition for manipulation of envelope family, where multiple contacts are allowed between object and chains (or environment). All chains are assigned by either position controlled chain (P-chain) or torque controlled chain (T-chain). While the object motion under multiple contacts can not be uniquely specified by T-chains only, we show a sufficient condition ensuring that a given set of torque commands for T-chains always move the object toward the goal along the surface of P-chain (or a fixed environment). Experiments as well as simulations are also shown to verify the basic idea