9813099 Wen This research project deals with the development of path planning methods using a feedback controller for a variety of fully and under-actuated mechanical systems, including robots and spacecrafts. The proposed scheme can guarantee the closed-loop asymptotic stability when information is imperfect. Furthermore, by using interior penalty functions, inequality constraints can also be handled by the algorithm. This type of feedback control law can be considered as a special class of model predictive control (MPC), since the control action at each time instance is determined based on the future trajectory. However, in contrast with the standard MPC schemes where an optimization problem needs to be solved at each control time interval, only one Newton step needs to be computed involving a fixed amount of computation. The efficacy of this algorithm has been demonstrated on a number of difficult examples, including the kinematic control of wheeled vehicles, stabilization of underactuated 6-DOF satellites, and stabilization of underactuated manipulators. The key research thrusts in the proposed research include: i)develop parameter selection rule in the algorithm that will grarantee closed loop stability; ii) quantify the stability robustness margin when the vector field is perturbed due to model imperfection and external disturbances; iii)enhance robustness through parameter adaptation; iv)utilize null space in the gradient operator for singularity avoidance and constraint handling; v)develop stategies for choosing the approximation basis in control computation and analyze the effect of approximation on convergences, and vi) apply to a number of experiments involving nonlinear mechanical systems. ***
