Trajectory Synthesis and Optimization of an Underactuated Microrobotic System with Dynamic Constraints and Couplings

Motivated by the desire to optimally control the friction-induced stick-slip locomotion and sufficiently improve the energy efficacy, a novel trajectory synthesis and optimization scheme is proposed in this paper for a underactuated microrobotic system with dynamic constraints and couplings. The nonlinear microrobotic model utilizes combined tangential-wise and normal-wise vibrations for underactuated locomotion, which features a generic significance for the studies on microrobotic systems. Specifically, an analytical two-stage velocity trajectory is constructed under control indexes and physical constraints. Subsequently, the dynamic coupling behavior and the qualitative variation laws are characterized through rigorous bifurcation analysis. The synthesized trajectory is optimized and tuned via rigorous analysis based on the robot dynamics. The proposed trajectory planning mechanism provides a promising approach in determining the optimal viscoelastic parameters and trajectory parameters such that the optimal locomotion indexes can be met. Simulation results are presented to demonstrate the efficacy and feasibility of the proposed scheme.