Mobile inverted pendulum robots consist of an elongated pendulum body with two motors mounted on it for driving the wheels. The velocity and position control of such a vehicle is challenging because of the coupling of the pendulum’s pitch angle from the vertical and the Cartesian motion of the vehicle. On using a nonlinear transform to effect partial feedback linearization, the system dynamics transforms to two subsystems: a linear system with the vehicle’s pitch and in-plane orientation, and a nonlinear system of internal dynamics. In this paper, the problem of utilizing such a partial feedback linearization for optimal trajectory planning of such vehicles is considered. Due to the resulting linear subsystem with vehicle pitch and in-plane orientation, these configuration variables can be controlled by a linear controller (C) using a nonlinear feedback. The planning approach presented in this paper considers the time-constant (τ) of the linear controller C explicitly. A band-limited Sinc-function interpolation is used to plan the variables in the method of collocation. This ensures that high frequency signal content which cannot be handled by the controller C, is absent in the planned trajectory, making the plan better implementable by the controller. The planned trajectory takes the vehicle from point to point, while keeping the vehicle pitch bounded and avoiding obstacles. The optimality condition considered in the algorithm is the length of the path. The optimization problem posed after collocation, is then solved using a standard Sequential Quadratic Programming (SQP) solver. Simulation results show that the tracking controller C is able to follow the planned trajectory when no initial planar Cartesian error is present.

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