In this paper, a novel model following method based on sum of squares technique is proposed. The explicit model following (EMF) method had been developed more than three decades. However, the linearized mechanism and choice of LQ weighting matrices lead the controller into local optimum. Based on the model following schematism, a Lyapunov direct method is employed to stabilize the physical system instead of LQ regulation in our proposed control strategy. Moreover, the sum of squares programming (SOSP) optimization method is capable of optimal Lyapunov function assessment. The benefit of our proposed nonlinear controller is not merely designed systematical, but also stable globally. Finally, a four-wheel and front steering mechanism is employed to demonstrate the performance of our proposed control strategy.Keywords-Model following, Sum of squares programming, Lyapunov method, Vehicle dynaimcs.
The paper presents a sum of squares (SOS) based backstepping control design method for a three wheels omni-directional mobile robot. The characteristic of the strict-feedback system associated with mobile robots is considered to construct the backstepping controller. To account for the saturation problem in the mobile robot, the SOS conditions are developed based on the backstepping controller framework to achieve stability and enlarge the guaranteed region of convergence. Computer simulations for mobile robots demonstrate the effectiveness of the proposed SOS-based backstepping controller design method.
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