A novel trajectory tracking control of AGV based on Udwadia-Kalaba approach

Several control approaches have been used in order to achieve the trajectory tracking control of automated guided vehicle (AGV). But they are all based on the D'Alembert principle which requires to determine the Lagrangian multipliers. Unlike those control methods, in this paper, a novel approach of trajectory tracking control is presented, which is based on Udwadia-Kalaba approach. This approach presents a novel, concise and explicit equation of motion for constrained mechanical systems with holonomic and/or nonholonomic constraints as well as constraints that may be ideal or non-ideal. The Udwadia-Kalaba equation is uncoupled and free from the Lagrangian multipliers. In this paper, we classify constraints into structural constraints and performance constraints. Structural constraints are set up regardless of trajectory control and we use structural constraints to establish the dynamic model. Then the desired trajectory is set as performance constraints and constraint torques are solved by analyzing Udwadia-Kalaba equation. For AGV, a nonholonomic mechanical system, second-order constraints are used to get constraint forces and the numerical simulation is conducted by using Matlab. The results show that the AGV's movement meets the requirement and the tracking trajectory is exact and perfect. Compared with other approaches, this approach requires very little computation. Through two cases of tracking a circle and a line, how to use Udwadia-Kalaba equation to realize trajectory tracking control is shown in detail.