Geometric analysis-based trajectory planning and control for underactuated capsule systems with viscoelastic property

This paper proposes a novel geometric analysis-based trajectory planning approach for underactuated capsule systems with viscoelastic property. The idea is to reduce complexity and to characterize coupling by imposing a harmonic drive and then to compute the dynamics projection onto a hyper-manifold, such that the issue of trajectory planning is converted into geometric analysis and trajectory optimization. The objective is to obtain optimal locomotion performance in terms of tracking error, average capsule speed and energy efficacy. Firstly, an analytical two-stage velocity trajectory is given based on control indexes and dynamic constraints. A locomotion-performance index is then proposed and evaluated to identify the optimal viscoelastic parameters. The trajectory is optimally parameterized through rigorous analysis. A nonlinear tracking controller is designed using collocated partial feedback linearization. For the sake of efficiency in progression and energy, the proposed method provides a novel approach in characterizing and planning motion trajectory for underactuated capsule systems such that the optimal locomotion can be achieved. Simulation results demonstrate the effectiveness and feasibility of the proposed method.