Adaptive sliding mode control of trajectory tracking based on DC motor drive for agricultural tracked robot

Abstract: In order to improve the performance of trajectory tracking control for agricultural tracked robot (ATR) in which the geometrical center does not coincide with the centroid, this paper comparatively analyzes the performance of all kinds of control methods for ATR, such as PID (proportion, integral, derivative) control, sliding mode control (SMC), neural network control method. The ATR model is regarded as a cascade system consisting of the drive motor equations and the mobile ATR kinematics equations. Through analyzing both the kinematic model of ATR and the unique features of motor driven model, this paper establishes a motor driven model and a posture error model which is based on tracking coordinate system and inertial coordinate system. And then a sliding mode control module and an integral sliding mode switching function (ISMSF) are proposed as well. Furthermore, this paper develops an adaptive sliding mode control (ASMC) based on ISMSF, which is composed of equivalent control and nonlinear switch control. The ASMC can feed back the position and orientation error as well as the time-varying parameters of the driven equation to the controller, based on which it can calculate the expected angular velocities of the left and right driving wheels and drive ATR to smoothly run. The simulation results show that under adaptive sliding control, the angular velocity for drive wheel can reach the ideal value in 0.375 s, while the common sliding mode control requires 0.75 s to achieve a relatively stable state with chattering phenomenon. Besides, when the biggish pose error appears in the system, ASMC can limit the integral function to keep the system from too large overshoot; when the less pose error appears in the system on the other hand, ASMC will prevent the system from chattering. Especially, when ATR tracks the fold line path, the initial position for the target trajectory is 0, 0, π/4T, the velocity for ATR is 2 m/s, and the initial position for ATR starts from -2, -2, π/4T, the pose error for ATR can converge to 0 in a relatively short period of time, the tracking error for ATR ranges from 0 to 0.04 m along the distance error in the direction of motion, and from -0.07 to 0.07 m along the lateral distance error, and the heading error ranges from -0.02 to 0.045 rad; when ATR tracks the circular path (where the curvature is always changing), the initial position for target trajectory is 10, 0, π/2T, the initial position for ATR starts from 7, 0, π/2T, and both the left and right driving wheel angular velocities start from 0, ASMC can adjust the output control in time, and output the angular velocity of left and right driving wheels smoothly, which make the posture error for ATR approach to 0, and ensure that ATR can never become divorced from the reference trajectory. Through experiments in the field, the results show that: When ATR tracks the combination trajectory of curve and slash paths, ATR runs at speed of 1, 3, and 4 m/s, the tracking error for ATR ranges from -0.04 to 0.04 m along the distance error in the direction of motion, and from -0.09 to 0.07 m along the lateral distance error, and the heading error ranges from -0.03 to 0.05 rad, which enable the actual ATR trajectory to follow the desired route smoothly. Thus adaptive sliding mode control based on DC (direct current) motor drive for ATR can achieve promising tracking performance, and satisfy the requirements of the farmland works. All results verify the effectiveness and correctness of the control method.