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This paper discusses the stabilization and position tracking control of the linear motion of an underactuated spherical robot. Including the actuator dynamics, the complete dynamic model of the robot is deduced, which is a third order, two-variable nonlinear differential system that holds underactuation, strong coupling characteristics brought by the mechanism structure of the robot. Different from traditional treatments no linearization is applied, whereas a singleinput multiple-output PID (SIMO_PID) controller is proposed with a neural network controller to compensate the actuator nonlinearity. A six-input single-output CMAC_GBF (Cerebellar Model Articulation Controller with General Basis Function) neural network is employed, while the Credit Assignment (CA) learning method is adopted to obtain faster convergence rate than the classical backpropagation (BP) learning method. The proposed controller can be generalizable to other single-input multiple-output system with good real-time capability. MATLAB simulations are used to validate the control effects.

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Due to the nonholonomic and underactutated properties of spherical robot, to realize its steady motion control is usually difficult. This paper presents a linear motion control method for an underactuated spherical robot. The linear motion dynamic model of the spherical robot is deduced with Euler-Lagrange method, which is a second order, nonlinear differential system with two coupled variables. Without any linearization a single-input multiple-output PID controller to realize the position control and pendulum angle control simultaneously is designed. Simulation results about the position stabilization and path tracking control are provided separately to show the control effects of the proposed controller.