Direction and Trajectory Tracking Control for Nonholonomic Spherical Robot by Combining Sliding Mode Controller and Model Prediction Controller

Abstract

Owing to uncertainties in both kinematics and dynamics, the current trajectory tracking framework for mobile robots like spherical robots cannot function effectively on multiple terrains, especially uneven and unknown ones. Since this is a prerequisite for robots to execute tasks in the wild, we enhance our previous hierarchical trajectory tracking framework to handle this issue. First, a modified adaptive RBF neural network (RBFNN) is proposed to represent all uncertainties in kinodynamics. Then the Lyapunov function is utilized to design its adaptive law, and a variable step-size algorithm is employed in the weights update procedure to accelerate convergence and improve stability. Hence, a new adaptive model prediction controlbased instruction planner (VAN-MPC) is proposed. Without modifying the bottom controllers, we finally develop the multi-terrain trajectory tracking framework by employing the new instruction planner VAN-MPC. The practical experiments demonstrate its effectiveness and robustness.

Spherical robot: A novel robot for exploration in harsh unknown environments

“…A fuzzy PID controller was tried in our earlier research [16], which was model-independent and exhibited high robustness to terrain changes but relatively low control accuracy. We also tried sliding mode controllers [23,25,26], which were model-based that improved control accuracy over fuzzy PID controllers, but free-chattering problem resulted in higher motor energy consumption and lower motor life. In the latest works, we started from the dynamic model of spherical robot, designed an offset-free linear MPC for velocity control in Ref.…”

“…An instruction planning controller is necessary to tell the spherical robot how to track the reference path given by the global path planning algorithm with minimum cost. We designed the controller based on the principle of MPC to find the optimal control strategy in our previous work [23], and we refine it in this paper. Cost function J (⋅) to be minimised is defined in the following equations, and meaning of symbols is shown in Table 6.…”

“…Dynamic model is built up by Euler-Lagrange method [23,27,28]. The definitions of the symbols are shown in Tables 1 and 7, and Euler-Lagrange equations can be written as Equation (16).…”

“…Assuming that the estimate of disturbance w* in Equation (23) is constant, the following operations in Equation ( 24) can be performed, in order to remove the disturbance from cost function (23) and transform it into a finite-horizon optimal control problem, which is only related to state x and control variable u.…”

Design and validation of a novel adaptive motion control for a pendulum spherical robot

“…In order to solve the problems of inaccurate dynamic modeling, parameter changes, and interference in the SR control that led to poor performance of traditional controllers, Cai Y. et al [12] proposed a speed control method combining fuzzy logic and SMC, while Kayacan E. et al [13] utilized the adaptive neuro-fuzzy controller and the learning algorithm of the SMC theory for the SR’s speed control. Liu Y. et al [14, 15] designed a hierarchical SMC (HSMC) for speed and orientation control of the SR, improving control efficiency and stability. Nevertheless, it is challenging to fit sensors in the limited space of the sphere to measure variables such as rolling speed in spherical robots.…”