Optimal planning and control of a segway model taking into account spatial obstacles

This contribution focuses on the optimal trajectory planning for a Segway model (inverted pendulum on two independently actuated wheels). Basis for this planning is the dynamical model for this under-actuated, non-holonomic multibody system. For the stabilization as well as the trajectory control, a partial input/output linearization is performed, where the orientation of the robot w.r.t. the horizontal plane and the inclination angle of the pendulum are used as output. The remaining non-linear part is linearized about the upright equilibrium position and stabilized with an LQR controller. The trajectory optimization is based on the partially linearized system, where the output (orientation and inclination) is parameterized by B-Splines. The system is required to move through predefined points in the horizontal plane. For the optimization the control points of the B-Splines serve as optimization variables and the overall energy of the robot serves as cost functional. Maximum motor velocities, motor torques and the ground reaction forces are the constraints. The latter are crucial when planning trajectories where the robot must pass (swing) under vertical obstacles while not losing ground contact. These maneuvers are characterized by high horizontal accelerations in order to lower the head of the robot and bring it back to upright equilibrium.