Design and development of closed-loop controllers for trajectory tracking of a planar vibration-driven robot

Vibration-driven robots constitute an innovative paradigm for achieving locomotion, leveraging periodic vibrations to meticulously control the movement of an internal mass, thus affording them a high degree of precision while navigating surfaces with varying friction characteristics. This paper is dedicated to the refinement of trajectory tracking in planar vibration-driven robots, achieved through the meticulous design and implementation of a Proportional-Integral-Derivative (PID) controller and Sliding Mode Controller (SMC). The considered vibration-driven robot is propelled using two parallel reciprocating unbalanced masses which allows the robot to have various maneuvers in two dimensions. The movement of the robot is improved by employing bristles to make non-isotropic Coloumb’s friction on the surfaces. At first, the governing dynamic equations of the robot are derived by considering the stick-slip effect and using the Euler–Lagrange method. Moreover, a PID controller for accurate trajectory tracking within the robot’s natural coordinate system is designed and employed. The fine-tuning of the PID controller’s coefficients is accomplished through the application of the NSGA-II optimization method. Subsequently, a SMC strategy is introduced to enable the robot’s control in an absolute coordinate system. The paper culminates with the presentation, in-depth analysis, and evaluation of the simulation results, shedding light on the significant enhancements in performance and capabilities achieved by vibration-driven robots. In conclusion, the pivotal role of the NSGA II algorithm in optimizing controller parameters is emphasized, and although the PID controller excels in trajectory tracking, challenges with sudden acceleration changes are identified.