Design of a generalized dynamic model and a trajectory control and position strategy for n-link underactuated revolute planar robots

Nowadays, underactuated systems are present in diverse fields of application. However, their mathematical modeling of underactuated revolute planar robots and the design of their control systems have not been thoroughly researched. Consequently, this paper presents both the generalized dynamic model and the design of a new control strategy for n-link underactuated revolute planar robots. The dynamic model includes both the friction torques present in the joint of this robot type and the mathematical formulations that represent the no-actuation of some robot joints. The requirements for the initial angular conditions of the links and for the design parameters of this type of robots are established and then optimized through a metaheuristic technique that uses GA.(1) Applying LaSalle's theorem and a Lyapunov function, the asymptotic stability of the behavior of these robots is calculated. The new control strategy allows the non-actuated joint to be indirectly controlled through the torques of the adjacent actuated joints (iota(n-1),iota(n+1)), thanks to the design and online tracking of a complementary composed trajectory. In this way, the non-actuated joint performs a tracking trajectory similar to that of joint q(1), despite the addition of an external pulse-type perturbation torque applied to this type of robot some seconds after the start of trajectory tracking. The validation of this control strategy is conducted using a 3-DoF(2) underactuated revolute planar robot with an APA(3) configuration. First, simulations are conducted and then a real robot is used. In addition, to analyze, compare, and evaluate the performance of the control strategy in the real robot, the performance indicators IA,(4) RMS(5 )and RSD6 are used.