# MPC and PSO Based Control Methodology for Path Tracking of 4 WS4 WD Vehicles  
[PERSON] 1,*  
1 School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China 1  
[PERSON] 2  
2 School of Mechanical and Mechatronic Engineering, University of Technology Sydney, Sydney, NSW 2007, Australia; [EMAIL_ADDRESS]  
[PERSON] 3  
3 School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia; [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (J.K.) 34  
[PERSON] 3  
3 School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, NSW 2052, Australia; [EMAIL_ADDRESS] (Z.Z. ); [EMAIL_ADDRESS] (J.K.) 34  
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forces. The majority of existing control methodologies for 4 WS4 WD vehicles are proposed based on the linearized dynamic model, which lead to the loss of input degree of freedom [2; 3]. Meanwhile, some other methods use nonlinear dynamic models in the control of 4 WS4 WD vehicles [4; 5], where control inputs are subjected to some relationship constraints to simplify the controller design. However, in practice, the four independent wheels may interact with different terrain conditions, where different slip, wheel forces and terrain disturbances are generated on the corresponding contact patches. Hence, it is desirable to make four wheels individually controlled, thereby limiting and/or overcoming different slip and disturbance on different contact patch. There is an abundance of literature that presents kinematic modelling of ground vehicles [6; 7; 8], in which the vehicles are assumed to operate at low speeds to reduce the dynamic effects. Most vehicle kinematic models are developed based on the non-integrable kinematic constraints, known as non-holonomic constraints. As a result, the wheel slip has to be ignored with the assumption of zero relative velocity between wheels and terrain [9; 10]. To utilize the kinematic model's advantage of keeping the steering control relatively independent of velocity control [11], it is desirable to incorporate wheel slip in the vehicle kinematic model so as to facilitate the accurate vehicle control in complex terrain conditions where the no-slip assumption is not applicable. To realize force control, a novel type of 4 WS4 WD vehicle with force sensors at each wheel has been designed as shown in Figure 1. This vehicle possesses the characteristics of independent steering and drive control at each wheel and force measurements. In this work, the dynamic model is partitioned into a hierarchy of three levels to facilitate the incorporation of force sensors and overcome uncertainties in the model. The force sensors at the drive unit allow the measurement of actual force data, while models of the drive unit and tire are used for simulation. Model predictive control (MPC) is selected for its ability in handling linear constraints and time-varying systems as well as its good performance in tracking problems. Particle swarm optimization (PSO) is also selected for its fast searching speed in global optimization. MPC and PSO have been successfully applied in the controller design of real-time control systems [12; 13; 14; 15; 16; 17]. In this work, MPC and PSO based control methods are proposed to realize the controlling aim of achieving good path following performance as well as high motion quality via vehicle steering control and independent force control at four wheels. As novel contributions, the MPC methodology is applied to achieve precise path tracking of 4 WS4 WD vehicle. Based on the MPC theory, an offline control law is proposed to guarantee the stability of the upper controller.