康复步行训练机器人位置和速度跟踪误差同时约束的安全预测控制
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摘要
康复步行训练机器人通过跟踪医生指定的运动轨迹,帮助患者步行训练,针对运动过程中位置和速度跟踪误差过大,影响康复者的安全问题,提出一种预测控制方法,目的是使康复步行训练机器人从任意位置出发同时实现轨迹和速度跟踪,并将跟踪误差约束在指定范围内,提高系统的安全性。通过离散化康复步行训练机器人的动力学模型,建立了具有控制增量形式的预测模型。在预测时域内,设计轨迹跟踪误差性能优化指标,并构建运动位置和速度跟踪误差约束条件,通过设计辅助运动轨迹并求解控制增量形式的二次规划问题,获得了时域内满足误差约束条件的预测控制。通过仿真和实验研究,结果表明了所提控制方法同时约束位置和速度跟踪误差的有效性和优越性。
A rehabilitative training walker needs to track trajectory which is prescribed by doctors so that it can help rehabilitee train. Considering the safety of rehabilitees,a safety predictive controller is proposed to solve the problem of extensive motion position and velocity tracking errors during training. The ultimate aim is to realize robot's trajectory tracking and velocity tracking simultaneously for arbitrary initial position,and restrict tracing errors within prescribed range in order to increase the safety of the system. The predictive model with incremental control was established by discretizing kinetics model of the rehabilitative training walker. In predictive time-domain,the performance index of trajectory tracking errors was designed and the constraint conditions of tracking errors were structured. The predictive control of satisfying the constraint conditions of tracking errors was obtained by designing auxiliary motion trajectory and solving quadratic program with incremental control. The simulation and experiment results show the feasibility and superiority of the proposed control method with simultaneous constraints on position and velocity tracking errors.
A rehabilitative training walker needs to track trajectory which is prescribed by doctors so that it can help rehabilitee train. Considering the safety of rehabilitees,a safety predictive controller is proposed to solve the problem of extensive motion position and velocity tracking errors during training. The ultimate aim is to realize robot's trajectory tracking and velocity tracking simultaneously for arbitrary initial position,and restrict tracing errors within prescribed range in order to increase the safety of the system. The predictive model with incremental control was established by discretizing kinetics model of the rehabilitative training walker. In predictive time-domain,the performance index of trajectory tracking errors was designed and the constraint conditions of tracking errors were structured. The predictive control of satisfying the constraint conditions of tracking errors was obtained by designing auxiliary motion trajectory and solving quadratic program with incremental control. The simulation and experiment results show the feasibility and superiority of the proposed control method with simultaneous constraints on position and velocity tracking errors.
引文
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[17] KARL W,MOHANED W,MEHRE Z,ea al. Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs[J]. IEEE Transactions on Control Systems Technology,2016,24(4):1394.
[18]王永宾,林辉,计宏.多约束永磁同步电机稳定模型预测控制策略[J].电机与控制学报,2011,15(12):7.WANG Yongbin,LIN Hui,JI Hong. Stabilizing model predictive control strategy for permanent magnet synchronous motor with multi-variable constraints[J]. Electric Machines and Control,2011,15(12):7.
[19] CHANG Hongbin,SUN Ping,WANG Shuoyu. A robust adaptive tracking control method for a rehabilitative walker using random parameters[J]. International Journal of Control,2017,90(7):1446.
[20]曾志文,卢惠民,张辉,等.基于模型预测控制的移动机器人轨迹跟踪[J].控制工程,2011(18):80.ZENG Zhiwen,LU Huimin,ZHANG Hui,et al. Trajectory tracking based on model predictive control for omnidirectional mobile robot[J]. Control Engineering of China,2011(18):80.
[2] SAN M D,CESTARI M,AREVALO J C,et al. Generation and control of adaptive gaits in lower limb exoskeletons for motion assistance[J]. Advanced Robotics,2014,28(5):329.
[3] GUO Zhao,YU Haoyong,YUE H Y. Developing a mobile lower limb robotic exoskeletons for gait rehabilitation[J]. Journal of Medical Devices,2014,8(12):044503-1.
[4] JIANG Yinlai,WANG Shuoyu,ISHIDA K,et al. Directional control of an omnidirectional walking support walker:adaptation to individual differences with fuzzy learning[J]. Advanced Robotics,2014,28(7):479.
[5] SUN Ping,WANG Shuoyu. Redundant input safety tracking control for omnidirectional rehabilitative training walker with control constraints[J]. Asian Journal of Control,2017,19(1):116.
[6] TAN Renpeng,WANG Shuoyu,JIANG Yinlai. Adaptive control method for path-tracking control of an omnidirectional walker compensating for center-of-gravity shifts and load changes[J]. International Journal of Innovative Computing,Information and Control,2011,7(7):4423.
[7] LIU Quan,LIU Dong,MENG Wei,et al. Fuzzy sliding mode control of a multi-DOF robot in rehabilitation environment[J]. International Journal of Humanoid Robotics,2014,11(1):1.
[8] LI Yongming,TONG Shaocheng,LI Tieshan. Adaptive fuzzy output-feedback control for output constrained nonlinear systems in the presence of input saturation[J]. Fuzzy Sets and Systems,2014(248):138.
[9] HAN S I,LEE J M. Output tracking error constrained robust positioning control for a nonsmooth nonlinear dynamic system[J]. IEEE Transactions on Industrial Electronics,2014,61(12):6882.
[10]孙平.速度受限的全方向康复步行训练机器人Backstepping补偿跟踪控制[J].信息与控制,2015,44(3):309.SUN Ping. Backstepping compensation tracking control for omnidirectional rehabilitative training walker with velocity constraints[J]. Information and Control,2015,44(3):309.
[11] SUN Ping,WANG Shuoyu. Guaranteed cost non-fragile tracking control for omnidirectional rehabilitative training walker with velocity constraints[J]. International Journal of Control,Automation and Systems,2016,4(5):1340.
[12] NIU Ben,ZHAO Jun. Output tracking control for a class of switched nonlinear systems with partial state constraints[J]. IET Control Theory and Applications,2013,7(4):623.
[13] NIU Ben,ZHAO Jun. Tracking control for output-constrained nonlinear switched systems with a barrier Lyapunov function[J]. International Journal of System Science,2013,44(5):978.
[14] YUCELEN T,TORRE G D,JOHNSON E N. Improving transient performance of adaptive control architectures usingfrequency-limited system error dynamics[J]. International Journal of Control,2014,87(11):2383.
[15] ZHANG Zhengqiang,SHEN Hao,LI Ze,et al. Zero-error tracking control of uncertain nonlinear system in the presence of actuator hysteresis[J]. International Journal of System Science,2015,46(15):2853.
[16] WEI Guoliang,WANG Zidong,SHEN Bo. Error-constrained finite-horizon tracking control with incomplete measurements and bounded noises[J]. International Journal of Robust and Nonlinear Control,2012(22):223.
[17] KARL W,MOHANED W,MEHRE Z,ea al. Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs[J]. IEEE Transactions on Control Systems Technology,2016,24(4):1394.
[18]王永宾,林辉,计宏.多约束永磁同步电机稳定模型预测控制策略[J].电机与控制学报,2011,15(12):7.WANG Yongbin,LIN Hui,JI Hong. Stabilizing model predictive control strategy for permanent magnet synchronous motor with multi-variable constraints[J]. Electric Machines and Control,2011,15(12):7.
[19] CHANG Hongbin,SUN Ping,WANG Shuoyu. A robust adaptive tracking control method for a rehabilitative walker using random parameters[J]. International Journal of Control,2017,90(7):1446.
[20]曾志文,卢惠民,张辉,等.基于模型预测控制的移动机器人轨迹跟踪[J].控制工程,2011(18):80.ZENG Zhiwen,LU Huimin,ZHANG Hui,et al. Trajectory tracking based on model predictive control for omnidirectional mobile robot[J]. Control Engineering of China,2011(18):80.