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An underactuated wheeled inverted pendulum (UWIP) is a nonlinear mechanical system that has two degrees of freedom and has only one control input. The motion planning problem for this nonlinear system is difficult to solve because of the existence of an uncontrollable manifold in the configuration space. In this paper, we present a method of designing motion trajectory for this underactuated system. The design of trajectory is based on the dynamic properties of the UWIP system. Furthermore, the tracking control of the UWIP for the constructed trajectory is also studied. A tracking control law is designed by using quadratic optimal control theory. Numerical simulation results verify the effectiveness of the presented theoretical results.

Aiming at tracking maneuvering target of SMR (Surface Movement Radar), this paper establishes a constant acceleration motion model, constant turn motion model and constant velocity motion model according to the actual movement of aircraft. On the base of these models, the IMM-UKF filter tracking algorithm is designed by introducing Unscented Kalman filter (UKF) into the interacting multiple model (IMM) algorithm. And IMM-UKF is compared with IMM-EKF (extended Kalman filter) algorithms. Simulation results show that IMM-UKF algorithm has good stability, and it overcomes the divergence problem of the EKF filter. The tracking accuracy and the model of transition speed are better than IMM-EKF algorithm.