A spherical robot is a nonlinear, nonholonomic, and unstable system which increases the difficulty of the direction and trajectory tracking problem. In this study, we propose a new direction controller Hierarchical Terminal Sliding Mode Controller (HTSMC), an instruction planning controller called Model Prediction Control-based Planner (MPCBP), and a trajectory tracking framework named MPCBP-HTSMC-HSMC (MHH). The HTSMC is designed by integrating a fast terminal algorithm, a hierarchical method, the motion features of a spherical robot, and its dynamics. In addition, the new direction controller has an excellent control effect with a quick response speed and strong stability. MPCBP can obtain optimal commands that are then transmitted to the velocity and direction controller. Since the two torque controllers in MHH are all Lyapunov-based sliding mode controllers, the MHH framework may achieve optimal control performance while assuring stability. Finally, the two controllers eliminate the requirement for MPCBP's stability and dynamic constraints. Finally, hardware experiments demonstrate the efficacy of the HTSMC, MPCBP, and MHH.

One controller cannot work on multiple and unknown terrains in the velocity control of the spherical robot, because the dynamic models of the robot vary on different terrains, and unmodeled dynamics and uncertainties exist in estimated dynamic models. Based on the above problem, a new velocity controller for spherical robot is designed. This controller combines a hierarchical sliding mode controller (HSMC), an adaptive RBF neural network (RBFNN) and a variable step-size algorithm. The RBFNN is used to online estimate the uncertainties, and the Lyapunov function is utilized to design the adaptive law for the RBFNN. In order to learn the uncertainties faster, while minimizing overshoot and preventing velocity oscillations, a variable step-size algorithm is proposed. The practical experiments demonstrate that, this controller of the spherical robot achieves velocity tracking on multiple and complex terrains, while eliminating steady-state error, having a good control effect, and maintaining high stability.

In this letter, a general robust reference path selection method (RPSM) that can be integrated into current existing motion planning algorithms is proposed to improve the mobile performance of autonomous patrol robots. The proposed RPSM maintains a dynamic array of path candidates that contains newly found paths, optimal historical paths, and hybrid paths that incorporate local trajectories. All these candidates will be evaluated in a unified criterion, and the best path with the minimal cost will be presented for trajectory tracking, ensuring the consistency and smoothness of the actual motion. Experiments with two different kinds of robots in various scenarios confirm that RPSM enriches the diversity and robustness of reference paths, and improves the execution efficiency by significantly reducing the average actual trajectory distance, orientation change, and total execution time, with an acceptable extra computational cost in comparison to the corresponding original hybrid A* algorithm.

The authors propose a complete software and hardware framework for a novel spherical robot to cope with exploration in harsh and unknown environments. The proposed robot is driven by a heavy pendulum covered by a fully enclosed spherical shell, which is strongly protected, amphibious, anti‐overturn and has a long‐battery‐life. Algorithms for location and perception, planning and motion control are comprehensively designed. On the one hand, the authors fully consider the kinematic model of a spherical robot, propose a positioning algorithm that fuses data from inertial measurement units, motor encoder and Global Navigation Satellite System, improve global path planning algorithm based on Hybrid A* and design an instruction planning controller based on model predictive control (MPC). On the other hand, the dynamic model is built, linear MPC and robust servo linear quadratic regulator algorithm is improved, and a speed controller and a direction controller are designed. In addition, based on the pose and motion characteristics of a spherical robot, a visual obstacle perception algorithm and an electronic image stabilisation algorithm are designed. Finally, the authors build physical systems to verify the effectiveness of the above algorithms through experiments.

There are few studies on the lateral motion of spherical robots. In this article, a new algorithm is proposed to solve the problem of low control accuracy of the lateral motion. A single lateral motion model is established, and the optimal solution of the linear quadratic regulator in infinite time domain is obtained. Aiming at the problems of longitudinal velocity and lateral angle coupling and low control precision, state compensation and velocity feedforward are carried out, and an improved robust servo linear quadratic regulator control algorithm is proposed. Experiments show that the proposed lateral control algorithm has strong adaptability and robustness to changing speeds and lateral angles, and the control effect is stable and reliable.

Multi-terrain trajectory tracking control is a prerequisite for robots to execute tasks in the wild and unknown environments. However, due to the uncertainties in both kinematics and dynamics, the current trajectory tracking framework for mobile robots, such as spherical robots cannot function effectively on multiple terrains, especially uneven and unknown ones. Thus, an efficient online adaptive algorithm that can rapidly obtain uncertainties online and assist the robot in adapting to multiple terrains is required. In this article, we propose an adaptive model predictive control-based instruction planner (VAN-MPC) and a multi-terrain trajectory tracking framework (VANMHH). The VAN-MPC is composed of three components as follows. 1) An adaptive dual-RBF neural network that online estimates all uncertainties based on the adaptive law and composite error. 2) A model predictive controller with a control Lyapunov function constraint. 3) The variable step-size algorithm for the adaptive controller to accelerate convergence and enhance stability. Without modifying the bottom velocity and direction controllers, we finally develop the multi-terrain trajectory tracking framework VANMHH just by employing the new instruction planner VAN-MPC. The practical experiments on multiple terrains demonstrate its effectiveness and robustness.