High-Order Sliding Mode-Based Synchronous Control of a Novel Stair-Climbing Wheelchair Robot

Hindawi Publishing Corporation Journal of Control Science and Engineering Volume 2015, Article ID 680809, 16 pages http://dx.doi.org/10.1155/2015/680809 Research Article High-Order Sliding Mode-Based Synchronous Control of a Novel Stair-Climbing Wheelchair Robot Juanxiu Liu, Yifei Wu, Jian Guo, and Qingwei Chen School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China Correspondence should be addressed to Yifei Wu; Received 27 April 2015; Revised 3 September 2015; Accepted 9 September 2015 Academic Editor: Hung-Yuan Chung Copyright © 2015 Juanxiu Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. For the attitude control of a novel stair-climbing wheelchair with inertial uncertainties and external disturbance torques, a new synchronous control method is proposed via combing high-order sliding mode control techniques with cross-coupling techniques. For this purpose, a proper controller is designed, which can improve the performance of the system under conditions of uncertainties and torque perturbations and also can guarantee the synchronization of the system. Firstly, a robust high-order sliding mode control law is designed to track the desired position trajectories effectively. Secondly, considering the coordination of the multiple joints, a high-order sliding mode synchronization controller is designed to reduce the synchronization errors and tracking errors based on the controller designed previously. Stability of the closed-loop system is proved by Lyapunov theory. The simulation is performed by MATLAB to verify the effectiveness of the proposed controller. By comparing the simulation results of two controllers, it is obvious that the proposed scheme has better performance and stronger robustness. 1. Introduction With the rapid increase of the elderly population over the age of 60, population aging will be an outstanding performance of global population trends in the 21st century. Aging society brings a lot of problems, such as nursing for the elderly and medical problems. At the same time, thousands of people lost the ability to walk each year caused by a variety of accidents, natural disasters, and diseases. With the development of the society and the improvement of human civilization, the people with disabilities need to use modern high-tech to improve their freedom and quality of life. Hence, wheelchair robot used to help the disabled or elderly people walking has become a hot research area in recent years. Although the barrier-free accessibility has been disseminated in recent years, stairs and other architectural barriers still exist in many cities and buildings. Since the standard wheelchair has no capability of crossing barriers, a number of stair-climbing wheelchairs which can help the disabled or elderly people overcoming obstacles have been researched. The common stair-climbing mechanisms used in the stair-climbing wheelchairs are tracks, wheels, and hybrid structures. Tracked stair-climbing wheelchair can guarantee the stability of the users in the process of ascending and descending stairs. Lawn et al. [1] designed a tracked wheelchair capable of negotiating large number of twisting and irregular stairs. In [2], a wheelchair using cluster wheels was developed. The wheelchair seat was kept stable during the stairs ascending process and the user needed not to face down the stairs. In [3], Wheelchair.q using triple cluster wheels was designed. The cluster wheels systems usually have complex mechanisms and the stability is lower than crawler systems. A stair-climbing robot with legs and wheels was designed in [4]. Chen and Pham [5] designed a prototype which was comprised of a pair of rotational multilimbed structures. There are some other design schemes adopting hybrid structures in [6–8]. Since the stair-climbing wheelchair is used in complex terrain, the first thing that should be considered is high precious position control for wheelchair system. In [2], PID control was used to provide appropriate torque during climbing process. A fuzzy controller was applied to correct the errors in direction and position misalignment, so that the final posture of the tracked mobile robot was corrected in [9]. In [10], an active tension control law combined with the computed torque method was obtained for wheelchair 2 robot during the stair-climbing process, which can track the reference input curve of homonymic constraint force when tracking reference input curve of each joint. Although the control strategies mentioned above can make some efforts for the control of stair-climbing wheelchair, various system uncertainties and torque perturbations were not taken into consideration. Since the sliding mode control has strong robustness for system disturbances and unmodeled dynamics, it has been widely used in robot control. Conventional sliding mode control can achieve the first-order sliding motion of the system states, which means the relative degree of the sliding variable 𝑠 is 1. When the system states slide along the preset manifold, only the sliding variable is guaranteed to converge to zero, and its derivative is nonsmooth, so the chattering phenomenon always comes up in the sliding mode control system. In order to solve the chattering which exists in conventional sliding mode control, a variety of methods were proposed such as state-dependent gain method, observerbased chattering suppression, and the high-order sliding model control (HOSMC) in [11, 12]. In [13], with the HOSMC used in attitude control of large-scale spacecraft, the robustness of the system with respect to uncertainties and external disturbances was improved, and the chattering phenomenon was attenuated. In [14], a HOSMC was designed for a flexible link space robotic arm with payload, which exploited the robustness properties of SMC, while also increasing accuracy by reducing chattering effects. Another important problem that should be considered is the coordination of the stair-climbing wheelchair system due to its characteristic of multiple joints. If the stair-climbing wheelchair works in a noncoordination manner, the assembly task will be failed, and a more serious consequence is that the users will be injured. In [15], a new control approach to position synchronization of multiple motion axes was developed, by incorporating cross-coupling technology into adaptive control architecture. A novel robust adaptive terminal sliding mode position synchronized control approach was proposed for the operation of multiple motion axes system and the convergence of position errors and synchronization errors could be guaranteed in [16]. In [17], the synchronous control of a dual linear motor servosystem was developed by a cross-coupled intelligent complementary sliding mode control system; a better (...truncated)