In this paper, a dynamic mathematical model of an autonomous ground vehicle was used to analyse its transient response and to design a heading-angle controller for the vehicle. A suitable 'control-oriented model' that could accurately characterize the phenomenon of interest was used to design the controller. The efficacy of this model was evaluated by corroborating its results with experimental data. This model included the cornering stiffness of the tyres as an unknown parameter, and two approaches were attempted to estimate its value. The dynamics of the actuator were included in the analysis since the response time to steer the front wheel is of the same order as that of the heading-angle dynamics of the vehicle. The performance of two controllers (namely a classical transfer-function-based controller and an optimal linear quadratic regulator) were evaluated using the IPG: CarMaker Ò simulation platform over a range of speeds. The transfer-function-based controller was also implemented on the experimental test vehicle at low speeds (high-speed experimental implementation was not possible because of safety concerns). It was found that control gain scheduling helped to track the desired heading angles of the vehicle at various speeds. Subsequently, a lane-change manoeuvre using the test vehicle was performed to evaluate the controller further. It was found that the transfer-function-based headingangle controller could provide a comparable performance with that of the linear quadratic regulator, while keeping the sensing requirements to a minimum; thus, it was suitable for real-time implementation in an autonomous ground vehicle.
This paper deals with tracking of desired yaw rate generated by the path planner of an Autonomous Ground Vehicle (AGV) in the presence of unmodeled dynamics, changes in operating conditions and parametric uncertainties. A mathematical model considering the dynamics of the test vehicle and the steering actuator was used for controller design. The estimate of the unknown part of dynamics, called the total disturbance, obtained from the Extended State Observer (ESO) was used by Sliding Mode Controller (SMC) to compensate the actual total disturbance. It was observed that the lower bound on the SMC switching gain depends on the ratio of total disturbance estimation error and assumed known part of the system dynamics. This allows the choice of a low value of SMC switching gain, which in turn resulted in reduced chattering amplitude. Further attenuation in chattering was achieved using a saturation function.
After simulating the designed controller in MATLAB-SIMULINK environment, the controller was validated in IPG: CarMaker® simulation platform over a large operating range by changing the mass distribution of the vehicle, speed of the vehicle, cornering stiffness of the tire and terrain friction coefficient. A look-up table was formulated for the maximum achievable yaw rate at different speeds, i.e., from 5 to 20 m/s, given the maximum steering angle input considering rollover and slip threshold while the terrain friction coefficient was also varied from 0.2 to 0.8. It was observed that the designed controller was robust to changes in operating conditions, parametric uncertainties and unmodeled dynamics.
Even if there are many software and mathematical models available in the literature to analyze the dynamic performance of Unmanned Ground Vehicles (UGVs), it is always difficult to identify or collect the required vehicle parameters from the vehicle manufacturer for simulation. In analyzing the vehicle handling performance, a difficult and complex task is to use an appropriate tire model that can accurately characterize the ground-wheel interaction. Though, the well-known ‘Magic Formula’ is widely used for this purpose, it requires expensive test equipment to estimate the Magic Formula coefficients.
The design of longitudinal and lateral controllers plays a significant role in path tracking of an UGV. Though the speed of the vehicle may remain almost constant in most of the maneuvers such as lane change, Double Lane Change (DLC), step steer, cornering, etc., design of the lateral controller is always a challenging task as it depends on the vehicle parameters, road information and also on the steering actuator dynamics. Although a mathematical model is an abstraction of the actual system, the controller is designed based on this model and then deployed on the real system.
In this paper, a realistic mathematical model of the vehicle considering the steering actuator dynamics has been developed by calculating the cornering stiffnesses from the basic tire information and the vertical load on each tire. A heading angle controller of the UGV has been considered using the Point-to-Point navigation algorithm. Then, these controllers have been implemented on a test platform equipped with an Inertial Measurement Unit (IMU) and a Global Positioning System (GPS).
A wide range of experiments such as J-Turn, lane change and DLC have also been conducted for comparison with the simulation results. Sensitivity analysis has been carried out to check the robustness and stability of the controller by varying the cornering stiffness of tires, the most uncertain parameter. The longitudinal speed of the vehicle is assumed to vary between a minimum value of 1.4 m/s and a maximum value of 20 m/s. It has been found that when the vehicle is moving at a constant velocity of 3.2 m/s, a heading angle change of 20 degrees can be achieved within 3 seconds with 2% steady state error using a proportional controller. It was observed that at lower speeds, the controller is more sensitive to the steering actuator dynamics and at higher speeds, the controller is more sensitive to the cornering stiffness of tires.
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