Abstract
This paper discusses a sufficient condition for manipulation of Envelope Family, where multiple contacts are allowed between chains and object (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.
