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The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discretetime constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

By applying disturbance feedforward control in active suspension systems, knowledge of the road profile can be used to increase ride comfort and safety. As the assumed road profile will never match the real one perfectly, we examine the performance of different disturbance compensators under various deteriorations of the assumed road profile using both synthetic and measured profiles and two quarter vehicle models of different complexity. While a generally valid statement on the maximum tolerable deterioration cannot be made, we identify particularly critical factors and derive recommendations for practical use.