柔性关节机械臂控制策略的研究
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摘要
目前,构建和维护空间在轨部件主要是通过宇航员冒着一定的风险进行舱外作业完成。在这些任务中,空间机器人的使用将会提供很多的便利,既能增加宇航员的安全性又能节省地面费用。由于空间机器人具有操作空间大和质量轻的特点,使得在轨机器人不可避免的具有柔性,这不仅限制了其操作灵巧性和末端速度,而且给控制带来更大的复杂度。由于空间机器人多层次的任务需求,对其进行精确的位置控制和具有柔顺性的阻抗控制将是两种比较引人注目的控制策略。本文在“卫星在轨自维护及遥操作关键技术的研究”项目的支持下,研究了对具有柔性关节的机器人如何进行位置控制和笛卡尔阻抗控制及其相关问题。
本文首先基于拉格朗日能量法建立了柔性关节机器人的动力学模型,并基于柔性关节机器人的简化模型,研究了柔性关节机器人的位置控制、笛卡尔阻抗控制以及具有时延影响的机器人系统控制。
从理论研究上看,对柔性关节机器人的控制主要有级联系统法、反馈线性化法和奇异摄动法等。传统的奇异摄动控制方法仅适用于关节柔性较小的机器人。针对这一问题,设计了关节柔性补偿器,提高了关节的等效刚度,消除了关节柔性对该方法的限制,将奇异摄动方法推广应用于具有一般关节柔性的机器人系统中。此外,设计了自适应控制规律完成对慢子系统的控制,保证了轨迹误差的渐近跟踪。该控制策略不限制关节柔性大小,并且不需要连杆加速度及其微分信号,便于工程应用。实验研究表明,不论慢子系统采用PD、计算力矩还是自适应控制方法,文中的控制策略都比传统的奇异摄动方案更有效。
与传统的基于机器人末端六维力/力矩信息的笛卡尔阻抗控制方案不同,针对只具有关节力矩传感器的机器人,文中分别研究了笛卡尔空间/关节空间基于力、笛卡尔空间/关节空间基于位置和刚度控制五种不同的笛卡尔阻抗控制策略。其中,利用无源性理论,重点分析了关节空间基于力的阻抗控制策略。在这种方法中,内部的力矩反馈环被视作对电机惯量的整形。基于这种对力矩反馈的物理解释,闭环系统动力学可以表示为两个无源子系统的反馈联接形式,保证了系统对参数不确定性的鲁棒性。此外,针对实际系统中的传感器信号,分析了延时和滤波环节对系统无源性的影响。对于由于算法和低通滤波引起的延时,引入了基于观测器(卡尔曼滤波或H∞滤波)的控制策略加以解决。而对于阻抗控制的一大应用领域,即具有本质延时的系统——机器人双向力反馈遥操作系统,基于鲁棒控制理论,利用线性矩阵不等式(LMI)处理方法给出了该问题的一般解法,解法的推导过程保证了系统的渐近稳定和相应的性能指标。
最后,通过相关实验和应用对所研究的控制算法及理论进行验证。正如理论分析所期望的那样,关节空间基于力的阻抗控制策略对模型参数的不确定性具有很好的鲁棒性;而基于观测器的控制策略能很好的克服速度计算中的延时,大大提高系统带宽及控制性能。
Construction and maintenance of on-orbit components is currently done primarily by extra-vehicular astronauts at great risk. Use of space robotics for these tasks provides the opportunity for both increased safety for the astronauts and major ground-crew cost savings. Owing to the characteristics such as large workspace and light weight, space robot will necessarily be quite flexible, which not only limits the dexterity and speed of the end-point, but also brings more complexity for the robot control. Due to the space robot’s multilayer-task demands, precise position control and impedance control with much compliance are the promising control schemes. The dissertation is under supporting of the project“Study on the key technologies of satellite on-orbit self-servicing and its tele-operation”, which aims to develop the research on how to perform the position control and the Cartesian impedance control and some associate issues for the robot with flexible joint.
In this thesis the dynamical model of the flexible joint robot is built firstly which is based on the Lagrange energy method. The position control, Cartesian impedance control and some control issues with time-delay influence are investigated in detail based on the reduced model of the flexible joint robot.
In view of the theoretical meaning, control methods for the flexible joint robot mainly consist of the cascaded system method, feedback linearization and singular perturbation technique, etc. The traditional singular perturbation approach can only be used in the robot system with weak joint flexibility. In order to solve this problem, a joint flexibility compensator is designed, which can increase the equivalent joint stiffness. So the limitation for the singular perturbation approach is removed and it can be extended to the robot system with normal joint flexibility. Besides these, an adaptive control law is designed for the slow subsystem, which can guarantee the trajectory error asymptotical tracking. The proposed control strategy can be applied to the engineering systems conveniently without any joint flexibility limitation and does not need the link acceleration or jerk information. The experimental results verify that whatever the PD, computed torque or adaptive control is used in the slow subsystem, the proposed singular perturbation strategy is more valid than the traditional one.
Different from the traditional Cartesian impedance control schemes which are mostly based on the robot end’s force/torque information, five Cartesian impedance control schemes including the force-based in Cartesian/joint space schemes, the position-based in Cartesian/joint space ones and the stiffness control scheme are considered, aiming at the robot with joint torque sensors in each joint. Among these, the force-based in joint space control scheme is analyzed in detail by using the passivity theory. In this approach an inner torque feedback loop is interpreted as a scaling of the motor inertia. Based on this physical interpretation of the joint torque feedback, the closed loop system can be regarded as a feedback interconnection of two passive subsystems, which guarantees the robustness against uncertainties in the model parameters. Besides these, aiming at the sensor signals in the practical system, the effect on the system’s passivity owing to time delay is analyzed. Observer(Kalman filter or H∞filter) based control schemes are introduced in order to deal with the time delay influence caused by algorithms and low filter. But to other system, that is to say, an extensive application of the impedance control, such as the bilateral teleoperation system, the LMI based approach gives the problem a general solution, which assures the closed loop system’s asymptotical stability and corresponding performance indexes during the derivation of the solution.
Finally, corresponding experiments and applications are presented for evaluating the control method and theory. As expected from the analysis, the force-based in joint space control scheme turns out to be very robust against uncertainties in the model parameters and the observer based control scheme can overcome the time delay in the velocity computation, which enlarges the system’s bandwidth and improves the control performance.
本文首先基于拉格朗日能量法建立了柔性关节机器人的动力学模型,并基于柔性关节机器人的简化模型,研究了柔性关节机器人的位置控制、笛卡尔阻抗控制以及具有时延影响的机器人系统控制。
从理论研究上看,对柔性关节机器人的控制主要有级联系统法、反馈线性化法和奇异摄动法等。传统的奇异摄动控制方法仅适用于关节柔性较小的机器人。针对这一问题,设计了关节柔性补偿器,提高了关节的等效刚度,消除了关节柔性对该方法的限制,将奇异摄动方法推广应用于具有一般关节柔性的机器人系统中。此外,设计了自适应控制规律完成对慢子系统的控制,保证了轨迹误差的渐近跟踪。该控制策略不限制关节柔性大小,并且不需要连杆加速度及其微分信号,便于工程应用。实验研究表明,不论慢子系统采用PD、计算力矩还是自适应控制方法,文中的控制策略都比传统的奇异摄动方案更有效。
与传统的基于机器人末端六维力/力矩信息的笛卡尔阻抗控制方案不同,针对只具有关节力矩传感器的机器人,文中分别研究了笛卡尔空间/关节空间基于力、笛卡尔空间/关节空间基于位置和刚度控制五种不同的笛卡尔阻抗控制策略。其中,利用无源性理论,重点分析了关节空间基于力的阻抗控制策略。在这种方法中,内部的力矩反馈环被视作对电机惯量的整形。基于这种对力矩反馈的物理解释,闭环系统动力学可以表示为两个无源子系统的反馈联接形式,保证了系统对参数不确定性的鲁棒性。此外,针对实际系统中的传感器信号,分析了延时和滤波环节对系统无源性的影响。对于由于算法和低通滤波引起的延时,引入了基于观测器(卡尔曼滤波或H∞滤波)的控制策略加以解决。而对于阻抗控制的一大应用领域,即具有本质延时的系统——机器人双向力反馈遥操作系统,基于鲁棒控制理论,利用线性矩阵不等式(LMI)处理方法给出了该问题的一般解法,解法的推导过程保证了系统的渐近稳定和相应的性能指标。
最后,通过相关实验和应用对所研究的控制算法及理论进行验证。正如理论分析所期望的那样,关节空间基于力的阻抗控制策略对模型参数的不确定性具有很好的鲁棒性;而基于观测器的控制策略能很好的克服速度计算中的延时,大大提高系统带宽及控制性能。
Construction and maintenance of on-orbit components is currently done primarily by extra-vehicular astronauts at great risk. Use of space robotics for these tasks provides the opportunity for both increased safety for the astronauts and major ground-crew cost savings. Owing to the characteristics such as large workspace and light weight, space robot will necessarily be quite flexible, which not only limits the dexterity and speed of the end-point, but also brings more complexity for the robot control. Due to the space robot’s multilayer-task demands, precise position control and impedance control with much compliance are the promising control schemes. The dissertation is under supporting of the project“Study on the key technologies of satellite on-orbit self-servicing and its tele-operation”, which aims to develop the research on how to perform the position control and the Cartesian impedance control and some associate issues for the robot with flexible joint.
In this thesis the dynamical model of the flexible joint robot is built firstly which is based on the Lagrange energy method. The position control, Cartesian impedance control and some control issues with time-delay influence are investigated in detail based on the reduced model of the flexible joint robot.
In view of the theoretical meaning, control methods for the flexible joint robot mainly consist of the cascaded system method, feedback linearization and singular perturbation technique, etc. The traditional singular perturbation approach can only be used in the robot system with weak joint flexibility. In order to solve this problem, a joint flexibility compensator is designed, which can increase the equivalent joint stiffness. So the limitation for the singular perturbation approach is removed and it can be extended to the robot system with normal joint flexibility. Besides these, an adaptive control law is designed for the slow subsystem, which can guarantee the trajectory error asymptotical tracking. The proposed control strategy can be applied to the engineering systems conveniently without any joint flexibility limitation and does not need the link acceleration or jerk information. The experimental results verify that whatever the PD, computed torque or adaptive control is used in the slow subsystem, the proposed singular perturbation strategy is more valid than the traditional one.
Different from the traditional Cartesian impedance control schemes which are mostly based on the robot end’s force/torque information, five Cartesian impedance control schemes including the force-based in Cartesian/joint space schemes, the position-based in Cartesian/joint space ones and the stiffness control scheme are considered, aiming at the robot with joint torque sensors in each joint. Among these, the force-based in joint space control scheme is analyzed in detail by using the passivity theory. In this approach an inner torque feedback loop is interpreted as a scaling of the motor inertia. Based on this physical interpretation of the joint torque feedback, the closed loop system can be regarded as a feedback interconnection of two passive subsystems, which guarantees the robustness against uncertainties in the model parameters. Besides these, aiming at the sensor signals in the practical system, the effect on the system’s passivity owing to time delay is analyzed. Observer(Kalman filter or H∞filter) based control schemes are introduced in order to deal with the time delay influence caused by algorithms and low filter. But to other system, that is to say, an extensive application of the impedance control, such as the bilateral teleoperation system, the LMI based approach gives the problem a general solution, which assures the closed loop system’s asymptotical stability and corresponding performance indexes during the derivation of the solution.
Finally, corresponding experiments and applications are presented for evaluating the control method and theory. As expected from the analysis, the force-based in joint space control scheme turns out to be very robust against uncertainties in the model parameters and the observer based control scheme can overcome the time delay in the velocity computation, which enlarges the system’s bandwidth and improves the control performance.
引文
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