二自由度冗余驱动并联机器人的动力学建模及控制研究
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摘要
与传统的串联机器人相比,并联机器人具有刚度大、精度高、承载力强等优点。冗余驱动并联机器人能够利用冗余特性完全或部分消除奇异性,优化分配驱动力,提高并联机器人的速度和加速度能力。然而,并联机器人存在多条支链的特点给运动学性能分析带来了困难。同时,它又是一个复杂的多输入多输出的非线性系统,具有时变、强耦合和非线性动力学特性,增加了控制的难度。本文针对平面二自由度冗余驱动并联机器人,从运动学分析、机电耦合动力学模型的建立、控制器设计以及实验方面对并联机器人系统进行了深入地研究。
研究了并联机器人的速度性能和加速度性能与装配构型之间的关系。利用位置分析得到了并联机器人的全部装配构型,引入速度性能和加速度性能评价指标对各种装配构型进行性能分析。推导出基于机构一阶Jacobian影响系数矩阵和二阶Hessian影响系数矩阵的运动学性能指标,并将抽象的性能指标用曲线的形式描绘在平面上形成直观的性能图谱。结合并联机器人的工作空间分析、奇异位形分析,得出了具有最优机构运动学性能的装配构型。避免了并联机器人设计过程中的盲目性,有利于实现并联机器人高精度的轨迹跟踪。
建立了交流伺服电机冗余驱动并联机器人的机电耦合动力学模型。首先利用拉格朗日方程得到三个开链机构的动力学方程,在末端执行器处施加约束得到并联机构的动力学模型。用这种方法简化了建模过程,可以利用已经研究成熟的二杆开链机构的动力学模型,从而实现并联机构的快速建模。其次,利用矢量控制技术,建立了交流永磁同步伺服电机的动力学模型。然后,根据力矩匹配的原则,联立并联机构和交流伺服电机的动力学模型,得到整个并联机器人系统的机电耦合动力学模型。最后,通过对并联机器人系统进行的动力学分析,得到了并联机器人末端执行器的轨迹跟踪效果图、三个主动关节的角位移和交流伺服电机q轴电流的变化规律。
利用非线性PID的大范围稳定和对角递归神经网络的非线性逼近能力,设计了非线性PID控制与对角递归神经网络控制相结合的新型智能复合控制器。通过比较三种不同控制策略,即PID控制、神经网络自整定PID控制和新型智能复合控制对并联机器人轨迹跟踪控制效果的影响,说明所设计的新型智能复合控制器无论是对存在初始位置误差的圆轨迹进行跟踪,还是对梯形速度规划下的直线轨迹进行跟踪,都具有较好的控制效果。研究发现,新型智能复合控制器能够克服单一控制方法的不足,鲁棒性强,从而有利于提高轨迹跟踪的精度。
针对并联机器人运行过程中的外部扰动,提出了两种用于机器人轨迹跟踪的滑模变结构控制策略,即Terminal滑模控制和神经滑模控制。Terminal滑模控制对外界扰动具有较强的抑制能力,而且通过设定不同的Terminal时间可以实现不同的收敛速度。神经滑模控制有效抑制了常规滑模控制的抖振,即使存在系统参数误差和外界扰动等非线性不确定性因素的影响,仍能实现对期望轨迹的理想跟踪。
对平面二自由度冗余驱动并联机器人进行了动力学性能及轨迹跟踪控制实验。进行了并联机器人振动及频率特性测试,验证了考虑交流永磁同步伺服电动机和并联机构的相互作用所建立的机电耦合动力学模型的正确性。通过在PID控制的基础上引入速度前馈和加速度前馈,提高了轨迹跟踪的精度。
本文的工作为冗余驱动并联机器人系统的进一步应用研究奠定了基础,也为其它类型并联机器人的理论和应用研究提供了借鉴,有助于实现并联机器人高质量的运行。
In comparison with serial robots, parallel robots have very good performances in terms of rigidity, accuracy and ability to manipulate large loads. In order to avoid or reduce singularity, and optimize motor torques, actuation redundancy is introduced into parallel robots. However, due to the closed-loop existing in parallel robots, the motions of these mechanisms are rather complex. Meanwhile, it is hard to control parallel robots, because of the MIMO system with time-varying, strong coupling and nonlinear dynamic properties. In this paper, a 2-DOF redundantly actuated parallel robot was taken as the object of study. The study contents mostly included kinematic analysis, electromechanical coupling dynamic modeling, control system design, and experimental test.
The effects of assembly configuration on the velocity and acceleration performance were studied. All types of assembly configuration were found by the forward position analysis and the inverse position analysis. Then the velocity performance index and acceleration performance index were introduced into the performance analysis of the configuration. The Jacobian matrix and the Hessian matrix were established by adopting the influence coefficient matrix. According to the given velocity and acceleration performance index, the corresponding performance atlas was plotted. Considering the workspace analysis, the singular configuration, the velocity performance and the acceleration performance, the optimal type of assembly configuration was pointed out. So the blindness of mechanism design can be reduced and the efficiency of optimization can be raised. And it is beneficial to realize high precision trajectory tracking control of parallel robots.
Dynamic deals with the relationship between the input torque of motors and the displacements, velocities, and accelerations of the parts of the system. In order to develop an effective controller for optimal trajectory tracking performance, the dynamics of a mechanism must be thoroughly analyzed. The steps of establishing the electromechanical coupling dynamic model were as follows:Firstly, by using the Lagrange method we got three open-loop two-bar mechanisms, by loading constraints we got the dynamic model of the parallel mechanism. The modeling process was simplified and the practical performance of the models was enhanced by using the mature dynamic model of the open-loop two-bar mechanism. Secondly, the dynamic model of the permanent-magnet AC servomotor was formulated using the field orient control principle. Thirdly, two dynamic models were integrated via torque pass, so we got the electromechanical coupling dynamic model. Lastly, through dynamic analysis, we got the trajectory tracking results of the end-effector, the angular displacement of the three active joints, and the motors'current.
The nonlinear proportional integral differential (PID) is insensitive to the change of system parameters, and the diagonal recurrent neural network (DRNN) control has the nonlinear approach ability. So considering both of the advantages of the nonlinear PID and DRNN, we designed a new compound intelligent controller. Comparing the new compound intelligent controller with the traditional PID controller and the diagonal recurrent neural network self-tunning PID controller, we found that the new compound intelligent controller had the best performance not only for the circular trajectory with initial errors, but also for the symmetric trapezoidal trajectory. The new compound intelligent controller overcomes deficiency of the traditional single controller, and has a good robustness, so it is helpful to improve the tracking performance.
In order to deal with external disturbance, sliding mode control schemes were introduced into trajectory tracking control of the parallel robot. The terminal sliding mode control not only guarantees the existence of the sliding phase of the closed-loop system, but also guarantees that the tracking error converges to zero under limit time. In order to deal with modeling error and external disturbance, the neuro-sliding mode control was derived. The RBF neural networks were used to approximate the discontinuous part of control gain in a classical sliding mode controller. Through the numerical simulation, the effectiveness of the sliding mode control methods was verified.
The experiments on the dynamic properties and trajectory tracking control of the 2-DOF redundantly actuated parallel robots were carried out. Tests of vibration and frequency characteristic were finished. The electromechanical coupling dynamic model was verified by the symmetric trapezoidal trajectory tracking control experiment. On the basis of traditional PID controller, velocity and acceleration feed-forward control was introduced to improve the trajectory tracking performance.
The work of this dissertation will lay a solid foundation for further application study of redundantly actuated parallel robots, and will give reference to theory and application study of other types of parallel robots. This will help parallel robots operate with high quality.
研究了并联机器人的速度性能和加速度性能与装配构型之间的关系。利用位置分析得到了并联机器人的全部装配构型,引入速度性能和加速度性能评价指标对各种装配构型进行性能分析。推导出基于机构一阶Jacobian影响系数矩阵和二阶Hessian影响系数矩阵的运动学性能指标,并将抽象的性能指标用曲线的形式描绘在平面上形成直观的性能图谱。结合并联机器人的工作空间分析、奇异位形分析,得出了具有最优机构运动学性能的装配构型。避免了并联机器人设计过程中的盲目性,有利于实现并联机器人高精度的轨迹跟踪。
建立了交流伺服电机冗余驱动并联机器人的机电耦合动力学模型。首先利用拉格朗日方程得到三个开链机构的动力学方程,在末端执行器处施加约束得到并联机构的动力学模型。用这种方法简化了建模过程,可以利用已经研究成熟的二杆开链机构的动力学模型,从而实现并联机构的快速建模。其次,利用矢量控制技术,建立了交流永磁同步伺服电机的动力学模型。然后,根据力矩匹配的原则,联立并联机构和交流伺服电机的动力学模型,得到整个并联机器人系统的机电耦合动力学模型。最后,通过对并联机器人系统进行的动力学分析,得到了并联机器人末端执行器的轨迹跟踪效果图、三个主动关节的角位移和交流伺服电机q轴电流的变化规律。
利用非线性PID的大范围稳定和对角递归神经网络的非线性逼近能力,设计了非线性PID控制与对角递归神经网络控制相结合的新型智能复合控制器。通过比较三种不同控制策略,即PID控制、神经网络自整定PID控制和新型智能复合控制对并联机器人轨迹跟踪控制效果的影响,说明所设计的新型智能复合控制器无论是对存在初始位置误差的圆轨迹进行跟踪,还是对梯形速度规划下的直线轨迹进行跟踪,都具有较好的控制效果。研究发现,新型智能复合控制器能够克服单一控制方法的不足,鲁棒性强,从而有利于提高轨迹跟踪的精度。
针对并联机器人运行过程中的外部扰动,提出了两种用于机器人轨迹跟踪的滑模变结构控制策略,即Terminal滑模控制和神经滑模控制。Terminal滑模控制对外界扰动具有较强的抑制能力,而且通过设定不同的Terminal时间可以实现不同的收敛速度。神经滑模控制有效抑制了常规滑模控制的抖振,即使存在系统参数误差和外界扰动等非线性不确定性因素的影响,仍能实现对期望轨迹的理想跟踪。
对平面二自由度冗余驱动并联机器人进行了动力学性能及轨迹跟踪控制实验。进行了并联机器人振动及频率特性测试,验证了考虑交流永磁同步伺服电动机和并联机构的相互作用所建立的机电耦合动力学模型的正确性。通过在PID控制的基础上引入速度前馈和加速度前馈,提高了轨迹跟踪的精度。
本文的工作为冗余驱动并联机器人系统的进一步应用研究奠定了基础,也为其它类型并联机器人的理论和应用研究提供了借鉴,有助于实现并联机器人高质量的运行。
In comparison with serial robots, parallel robots have very good performances in terms of rigidity, accuracy and ability to manipulate large loads. In order to avoid or reduce singularity, and optimize motor torques, actuation redundancy is introduced into parallel robots. However, due to the closed-loop existing in parallel robots, the motions of these mechanisms are rather complex. Meanwhile, it is hard to control parallel robots, because of the MIMO system with time-varying, strong coupling and nonlinear dynamic properties. In this paper, a 2-DOF redundantly actuated parallel robot was taken as the object of study. The study contents mostly included kinematic analysis, electromechanical coupling dynamic modeling, control system design, and experimental test.
The effects of assembly configuration on the velocity and acceleration performance were studied. All types of assembly configuration were found by the forward position analysis and the inverse position analysis. Then the velocity performance index and acceleration performance index were introduced into the performance analysis of the configuration. The Jacobian matrix and the Hessian matrix were established by adopting the influence coefficient matrix. According to the given velocity and acceleration performance index, the corresponding performance atlas was plotted. Considering the workspace analysis, the singular configuration, the velocity performance and the acceleration performance, the optimal type of assembly configuration was pointed out. So the blindness of mechanism design can be reduced and the efficiency of optimization can be raised. And it is beneficial to realize high precision trajectory tracking control of parallel robots.
Dynamic deals with the relationship between the input torque of motors and the displacements, velocities, and accelerations of the parts of the system. In order to develop an effective controller for optimal trajectory tracking performance, the dynamics of a mechanism must be thoroughly analyzed. The steps of establishing the electromechanical coupling dynamic model were as follows:Firstly, by using the Lagrange method we got three open-loop two-bar mechanisms, by loading constraints we got the dynamic model of the parallel mechanism. The modeling process was simplified and the practical performance of the models was enhanced by using the mature dynamic model of the open-loop two-bar mechanism. Secondly, the dynamic model of the permanent-magnet AC servomotor was formulated using the field orient control principle. Thirdly, two dynamic models were integrated via torque pass, so we got the electromechanical coupling dynamic model. Lastly, through dynamic analysis, we got the trajectory tracking results of the end-effector, the angular displacement of the three active joints, and the motors'current.
The nonlinear proportional integral differential (PID) is insensitive to the change of system parameters, and the diagonal recurrent neural network (DRNN) control has the nonlinear approach ability. So considering both of the advantages of the nonlinear PID and DRNN, we designed a new compound intelligent controller. Comparing the new compound intelligent controller with the traditional PID controller and the diagonal recurrent neural network self-tunning PID controller, we found that the new compound intelligent controller had the best performance not only for the circular trajectory with initial errors, but also for the symmetric trapezoidal trajectory. The new compound intelligent controller overcomes deficiency of the traditional single controller, and has a good robustness, so it is helpful to improve the tracking performance.
In order to deal with external disturbance, sliding mode control schemes were introduced into trajectory tracking control of the parallel robot. The terminal sliding mode control not only guarantees the existence of the sliding phase of the closed-loop system, but also guarantees that the tracking error converges to zero under limit time. In order to deal with modeling error and external disturbance, the neuro-sliding mode control was derived. The RBF neural networks were used to approximate the discontinuous part of control gain in a classical sliding mode controller. Through the numerical simulation, the effectiveness of the sliding mode control methods was verified.
The experiments on the dynamic properties and trajectory tracking control of the 2-DOF redundantly actuated parallel robots were carried out. Tests of vibration and frequency characteristic were finished. The electromechanical coupling dynamic model was verified by the symmetric trapezoidal trajectory tracking control experiment. On the basis of traditional PID controller, velocity and acceleration feed-forward control was introduced to improve the trajectory tracking performance.
The work of this dissertation will lay a solid foundation for further application study of redundantly actuated parallel robots, and will give reference to theory and application study of other types of parallel robots. This will help parallel robots operate with high quality.
引文
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