A direct adaptive control scheme for under-actuated dynamic systems

This paper presents a class of under-actuated dynamic systems and the adaptive control methodology. A system is said to be under-actuated if it has at least one passive joint (i.e. not driven by actuators). The under-actuated dynamic systems have found many meaningful applications in either space explorations or advanced manufacturing operations. Due to the passive joints, input channels become deficient, and dynamic characteristics fundamentally differ from a full-actuated system. The dynamic parameter-linearity is destroyed by the under-actuated nature. To overcome the difficulty, an extended dynamic model and a normal-form augmentation approach are proposed. Using the normal-form augmentation approach, the parameter-linearity can be recovered, and a direct adaptive control scheme can be developed to stabilize the system against parameter uncertainty