水平运动的欠驱动机器人运动规划与控制研究
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摘要
欠驱动机器人是指控制输入数目小于系统广义坐标数目的一类机器人,它在提高机器人灵活性、降低成本和能耗、增加结构紧凑性等方面的性能为人们提供了新思路,具有重要的理论意义和广阔的应用前景,尤其在能源日益紧缺的今天,越来越受到人们的关注,成为机器人研究的新热点。
本文以被动关节自由的水平运动欠驱动机器人为研究对象,致力于摸索这类欠驱动系统固有的内在品质,在对欠驱动系统特性分析的基础上对欠驱动机器人的运动规划、轨迹跟踪及位置控制等问题进行了理论及实验研究。
首先,利用凯恩方程建立了欠驱动机器人的动力学模型,对系统的可积性、可控性及精确线性化问题进行了分析,给出系统可积性及可控性判据,得到系统不满足精确状态反馈线性化条件的结论。根据欠驱动机器人的耦合特性,提出了欠驱动机器人操作空间可操作性及关节空间可操作性指标,分别用来衡量主动关节加速度对操作臂末端以及主动关节加速度对被动关节加速度的操作能力,这两个评价指标对欠驱动机器人结构设计及动力学控制具有重要意义。
其次,对欠驱动机器人的最优运动规划及避障规划问题进行了研究。针对最优运动规划问题,提出了一种利用遗传算法解决二阶非完整系统最优运动规划的新方法。针对避障规划问题,分别提出了虚拟弹簧—阻尼系统法及罚函数法两种新方法。对二自由度及三自由度欠驱动机器人进行了仿真,仿真结果表明上述方法有效,具有很好的稳定性,可以推广到多自由度欠驱动机器人的运动规划中。
再次,对欠驱动机器人的关节空间实时跟踪及操作空间几何路径跟踪问题进行了研究。对于实时跟踪问题,引入滑模变结构控制方法,精确实现了2R及3R欠驱动机器人关节空间的实时轨迹跟踪。对于欠驱动机器人几何路径轨迹跟踪问题,提出了路径坐标系下轨迹跟踪以及基于遗传算法的欠驱动机器人轨迹跟踪两种新方法,对这两种方法比较分析表明,基于遗传算法的欠驱动机器人轨迹跟踪方法对系统初始状态没有限制,具有更好的自适应性,更容易推广到多自由度欠驱动机器人的轨迹跟踪中。
然后,研究了欠驱动机器人的操作空间及关节空间位置控制问题。将智能控制方法与遗传算法相结合,提出了欠驱动机器人分层模糊控制及直接自适应模糊控制两种新方法。对二自由度及三自由度欠驱动机器人进行了控制仿真,仿真结果表明基于遗传算法的模糊控制器具有很好的自适应性和稳定性,为欠驱动机器人的智能运动控制提供了新思路。
最后,进行了欠驱动机器人的位置控制实验研究。搭建了欠驱动机器人软、硬件实验平台,分别对被动关节半自由及完全自由两种情况设计了控制器,从实验角度实现了2R及3R欠驱动机器人精确位置控制,实验结果与期望值相对误差保持在2%以内,说明了控制器的有效性。
Underactuated robots that have fewer control inputs than the generalizedcoordinates of the system provide a new way to improve the performances of robotsin terms of dexterity, low energy consumption and compactness. The underactuatedrobots have important theoretical significance and broad application prospects,especially for the growing shortage of energy, the underactuated system have attractedmore and more attention in nowadays and become the advanced topics of roboticresearch.
This dissertation is focused on underactuated robots. The main purpose is to findthe intrinsic characteristics of underactuated system. The motion planning, trajectorytracking and position control of underactuated robots are dealt with theoretically andexperimentally based on the characteristic analysis of underactuated system.
Firstly, the dynamic model of underactuated robot is developed based on Kanemethod. The integrability, controllability and exact linearization ability of theunderactuated system are analyzed. Criterions of integrability and controllability ofunderactuated system are proposed and the conclusion is made that the system doesnot satisfy the exact state feedback linearization condition. The manipulability indexesof underactuated robots in operation space and joint space that are used to measure theability of active joint acceleration to the endpoint acceleration and passive jointacceleration are proposed respectively for the first time. The manipulability indexesare of significance in the structural design and dynamic control of underactuatedrobots.
Secondly, the optimal motion planning and the collision-free motion planning ofunderactuated robots are studied. A new method that based on genetic algorithm isproposed to solve the optimal motion planning of second order nonholonomic system.The virtual spring-damper and penalty methods are proposed for the obstacleavoidance of underactuated robots. Simulation results of 2R and 3R underacutatedrobots indicate the effectiveness of psoposed methods. These methods can beextended to the motion planning of underactuated robots with more degree offreedoms.
Thirdly, the real time trajectory tracking in joint space and the geometric pathtracking in operation space of underactuated robots are investigated. The sliding modecontrol method is introduced to fulfill the exact real time trajectory tracking of 2R and3R underactuated robots. For the geometric path tracking, the path tracking under pathcoordinate and GA based tracking method for underactuated robots are proposed. Compare with path tracking under path coordinate method, GAbased tracking methodhas good adaptiability and has no restrictions to the initial status. It can be extended togeometric path tracking of underactuated robots with more degree of freedoms.
Fourthly, position control of underactuated robots in operation space and in jointspace is studied. Two new methods called hierarchical fuzzy control and direct fuzzycontrol are proposed respectively based on the combination of intelligent controlmethod and genetic algorithm. The simulation results of 2-DOF and 3-DOFunderacutated robots show the effiectiveness of the designed controllers. The GAbased fuzzy controllers have good adaptability and stability. It provides a new way forthe intelligent control of underactuated robots.
Finally, the experimental platform of underactuated system is developed and theexperimental study of underactuated robots is proposed. The motion controllers aredesigned and experiment study is carried out on 2R and 3R underactuated robots withand without brake. The relative control errors between the experiment results and thedesired values are less than 2%, which show the effectiveness of the designedcontrollers.
本文以被动关节自由的水平运动欠驱动机器人为研究对象,致力于摸索这类欠驱动系统固有的内在品质,在对欠驱动系统特性分析的基础上对欠驱动机器人的运动规划、轨迹跟踪及位置控制等问题进行了理论及实验研究。
首先,利用凯恩方程建立了欠驱动机器人的动力学模型,对系统的可积性、可控性及精确线性化问题进行了分析,给出系统可积性及可控性判据,得到系统不满足精确状态反馈线性化条件的结论。根据欠驱动机器人的耦合特性,提出了欠驱动机器人操作空间可操作性及关节空间可操作性指标,分别用来衡量主动关节加速度对操作臂末端以及主动关节加速度对被动关节加速度的操作能力,这两个评价指标对欠驱动机器人结构设计及动力学控制具有重要意义。
其次,对欠驱动机器人的最优运动规划及避障规划问题进行了研究。针对最优运动规划问题,提出了一种利用遗传算法解决二阶非完整系统最优运动规划的新方法。针对避障规划问题,分别提出了虚拟弹簧—阻尼系统法及罚函数法两种新方法。对二自由度及三自由度欠驱动机器人进行了仿真,仿真结果表明上述方法有效,具有很好的稳定性,可以推广到多自由度欠驱动机器人的运动规划中。
再次,对欠驱动机器人的关节空间实时跟踪及操作空间几何路径跟踪问题进行了研究。对于实时跟踪问题,引入滑模变结构控制方法,精确实现了2R及3R欠驱动机器人关节空间的实时轨迹跟踪。对于欠驱动机器人几何路径轨迹跟踪问题,提出了路径坐标系下轨迹跟踪以及基于遗传算法的欠驱动机器人轨迹跟踪两种新方法,对这两种方法比较分析表明,基于遗传算法的欠驱动机器人轨迹跟踪方法对系统初始状态没有限制,具有更好的自适应性,更容易推广到多自由度欠驱动机器人的轨迹跟踪中。
然后,研究了欠驱动机器人的操作空间及关节空间位置控制问题。将智能控制方法与遗传算法相结合,提出了欠驱动机器人分层模糊控制及直接自适应模糊控制两种新方法。对二自由度及三自由度欠驱动机器人进行了控制仿真,仿真结果表明基于遗传算法的模糊控制器具有很好的自适应性和稳定性,为欠驱动机器人的智能运动控制提供了新思路。
最后,进行了欠驱动机器人的位置控制实验研究。搭建了欠驱动机器人软、硬件实验平台,分别对被动关节半自由及完全自由两种情况设计了控制器,从实验角度实现了2R及3R欠驱动机器人精确位置控制,实验结果与期望值相对误差保持在2%以内,说明了控制器的有效性。
Underactuated robots that have fewer control inputs than the generalizedcoordinates of the system provide a new way to improve the performances of robotsin terms of dexterity, low energy consumption and compactness. The underactuatedrobots have important theoretical significance and broad application prospects,especially for the growing shortage of energy, the underactuated system have attractedmore and more attention in nowadays and become the advanced topics of roboticresearch.
This dissertation is focused on underactuated robots. The main purpose is to findthe intrinsic characteristics of underactuated system. The motion planning, trajectorytracking and position control of underactuated robots are dealt with theoretically andexperimentally based on the characteristic analysis of underactuated system.
Firstly, the dynamic model of underactuated robot is developed based on Kanemethod. The integrability, controllability and exact linearization ability of theunderactuated system are analyzed. Criterions of integrability and controllability ofunderactuated system are proposed and the conclusion is made that the system doesnot satisfy the exact state feedback linearization condition. The manipulability indexesof underactuated robots in operation space and joint space that are used to measure theability of active joint acceleration to the endpoint acceleration and passive jointacceleration are proposed respectively for the first time. The manipulability indexesare of significance in the structural design and dynamic control of underactuatedrobots.
Secondly, the optimal motion planning and the collision-free motion planning ofunderactuated robots are studied. A new method that based on genetic algorithm isproposed to solve the optimal motion planning of second order nonholonomic system.The virtual spring-damper and penalty methods are proposed for the obstacleavoidance of underactuated robots. Simulation results of 2R and 3R underacutatedrobots indicate the effectiveness of psoposed methods. These methods can beextended to the motion planning of underactuated robots with more degree offreedoms.
Thirdly, the real time trajectory tracking in joint space and the geometric pathtracking in operation space of underactuated robots are investigated. The sliding modecontrol method is introduced to fulfill the exact real time trajectory tracking of 2R and3R underactuated robots. For the geometric path tracking, the path tracking under pathcoordinate and GA based tracking method for underactuated robots are proposed. Compare with path tracking under path coordinate method, GAbased tracking methodhas good adaptiability and has no restrictions to the initial status. It can be extended togeometric path tracking of underactuated robots with more degree of freedoms.
Fourthly, position control of underactuated robots in operation space and in jointspace is studied. Two new methods called hierarchical fuzzy control and direct fuzzycontrol are proposed respectively based on the combination of intelligent controlmethod and genetic algorithm. The simulation results of 2-DOF and 3-DOFunderacutated robots show the effiectiveness of the designed controllers. The GAbased fuzzy controllers have good adaptability and stability. It provides a new way forthe intelligent control of underactuated robots.
Finally, the experimental platform of underactuated system is developed and theexperimental study of underactuated robots is proposed. The motion controllers aredesigned and experiment study is carried out on 2R and 3R underactuated robots withand without brake. The relative control errors between the experiment results and thedesired values are less than 2%, which show the effectiveness of the designedcontrollers.
引文
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