Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators

Planar underactuated manipulators are widely used in aerospace and deep-sea exploration. Due to their passive joints without actuation, it is difficult to perform trajectory planning and direct control. In this paper, an angular velocity trajectory planning method is proposed, aiming to calculate the velocity trajectory by using a superposition of basis functions and transforming the planning problem into an optimization problem by using a metaheuristic algorithm. According to the underactuated constraint relationship, the planning trajectory of the passive joint is obtained, which ensures that the passive joint can be indirectly controlled to reach the target angle while tracking the trajectory of the active joint. For the tracking control problem, a sliding mode controller with an exponential convergence rate is used to track the trajectory. Lastly, three sets of simulations are run to demonstrate the efficacy of the suggested approach.