Fixed-Time Consensus for Multiple Tractor-Trailer Vehicles With Dynamics Control: A Distributed Internal Model Approach.

Recently, the fixed-time consensus problem for multiple nonholonomic robot systems has gained much attention due to its practical value, high accuracy and strong robustness, and almost all of the existing studies have focused on kinematics control. However, the actual system is essentially dynamic, and the generalized force or torque driven by the design meets the actual requirements. Given this consideration, the fixed-time posture and velocity leader-following consensus problem is investigated for a class of nonholonomic robots, namely, the tractor-trailer vehicles with dynamics control. A nonlinear leader system capable of generating reference postures and velocities applicable to tractor-trailer vehicles is first formulated. Utilizing the newly proposed distributed observer capable of estimating the state and output matrix of the leader system in fixed time and the distributed internal model capable of reconstructing information in fixed time, all the tractor-trailer vehicles can acquire and construct the necessary reference information through the communication network in fixed time. Then, by combining the dynamic gain and state constraint methods, a fixed-time velocity ideal controller capable of overcoming nonholonomic constraints, exerting the desired control over postures, and with first-order derivability capable of being tracked by the actual velocity through the design of the control torque is devised at the kinematic level, which ensures that the fixed-time dynamics controller designed around it accomplishes the control objectives while sidestepping potential singularity issues that may arise from the use of existing non-smooth fixed-time control strategies.