独轮自平衡机器人建模与控制研究
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摘要
人或其他智慧生物需要经过一定的训练和学习才能骑行独轮自行车。独轮自平衡机器人是模拟人类骑行独轮车的行为构建的一种自平衡机器人系统,属于原理性仿生机器人。与一般移动机器人相比,独轮自平衡机器人与地面接触点数目降到最小,是一种典型的非完整、非线性、静不平衡系统。其建模和运动控制问题是控制科学及机器人学研究的重要问题。
本文设计了具有竖直飞轮和下行走轮结构的独轮自平衡机器人系统,建立了相应的运动学和动力学模型,并在系统特性分析的基础上,进行了运动平衡控制问题的研究,取得了以下主要研究成果:
1、独轮自平衡机器人系统
本文设计了一种独轮自平衡机器人系统,其最重要的结构特征是竖直惯性飞轮和下行走轮相互配合:竖直惯性飞轮调节横滚自由度平衡;行走轮调节俯仰自由度平衡。此结构模拟了人类骑行独轮车的特征,动力学特性较为复杂,其建模与控制问题具有一定难度。所设计独轮自平衡机器人的电气系统为分层递阶结构:组织级以嵌入式PC为核心,辅以各种人机接口,负责监测、获取信息,决策和下达运动控制指令;协调级以DSP为核心,辅以状态感知传感器,主要负责运动平衡控制;执行级为电机伺服系统,负责控制双轮电机完成指定运动。整个控制结构构成一种仿生的姿态感觉运动系统。
2、独轮自平衡机器人的动力学建模与分析
本文运用拉格朗日法建立了独轮自平衡机器人的动力学模型,并对其进行了实验验证。实验结果符合物理事实,验证了所建模型正确;其次,分析了独轮自平衡机器人的系统特性,证明独轮自平衡机器人在直立平衡点不稳定和局部可控;再次,分析了独轮自平衡机器人各设计参数:质量、重心高度、飞轮惯量等,对运动平衡控制系统的影响规律;最后,利用虚拟样机技术建立了独轮自平衡机器人的三维模型,并与数学模型相互验证正确性。本文建立的模型及相关分析为独轮自平衡机器人的设计和控制提供了一定理论依据。
3、基于非线性PD控制方法的独轮自平衡机器人运动平衡控制
本文针对独轮自平衡机器人的运动平衡控制问题,提出一种基于非线性PD的三环控制方法。该方法包括电机伺服驱动内环、姿态平衡控制中环和运动位移控制外环,其中,电机伺服驱动内环通过两个PID控制器分别实现上、下电机转矩伺服,控制器输入为姿态平衡控制器的输出转矩;姿态平衡控制中环为一种非线性PD控制器(PDNLB),控制机器人稳定平衡,PDNLB采用tan(θ)作为非线性比为非线性微分环节,PDNLB输入为由机器人运动控制器提供的期望姿态;外环为直线位移PD控制器,输入为期望的直线位移,输出经耦合转化为期望俯仰和横滚倾角。通过仿真实验对比分析了PDNLB与线性PD姿态平衡控制器的动态性能和鲁棒性,结果表明在相同参数下,PDNLB的动态性能指标、抗扰动和对象参数变化的适应能力均优于线性PD和LQR控制器。进行了独轮自平衡机器人静止平衡和运动位移控制的仿真以及物理系统实验,实验结果验证了本文提出的控制方法是一种解决独轮自平衡机器人运动平衡控制问题的有效方法。
4、基于非线性动态逆控制方法的独轮自平衡机器人平衡控制
针对独轮自平衡机器人的非线性控制问题,根据多变量非线性控制的理论—逆系统方法,设计了独轮自平衡机器人伪动态逆控制器,给出了具体实现方法。针对独轮自平衡机器人系统为最小相位系统,逆系统不存在的问题,通过时标分离的方法构建系统的伪逆,构成独轮自平衡机器人伪动态逆控制系统。针对动态逆系统精确模型难于获得、动态逆方法设计控制系统不便、伪动态逆控制性能难于保障的问题,利用神经网络具有逼近任意连续的n输入m输出映射的能力,提出基于神经网络的独轮自平衡机器人动态逆控制方法。该方法利用BP神经网络逼近系统的动态逆模型,构成参考模型神经网络动态逆控制系统。实验结果表明:该方案能够利用BP神经网络逼近系统的逆系统,可有效解决独轮自平衡机器人系统建模不精确、逆系统精确解析解难于求得等问题,并实现机器人的姿态平衡控制;但是该方法用于独轮自平衡机器人控制时,超调量、调节时间等控制性能并不理想,并且鲁棒性较差。
5、基于迭代学习控制方法的独轮自平衡机器人运动平衡控制
本文针对独轮自平衡机器人的姿态平衡控制问题,提出了基于神经网络反演方法的迭代学习控制方法。迭代学习控制方法,是在线性控制的基础上引入基于跟踪误差的指数型能量函数作为评价机制,通过迭代学习不断修正控制量以克服机器人系统的未知参数和干扰带来的不确定性,类似于人类的条件反射的学习过程。而神经网络反演控制是通过RBF神经网络进行反演迭代学习。并从理论上证明其跟踪误差的渐进收敛性。这种方案既具有线性控制系统思想简单、方法明确的优点,又能够利用在线学习过程动态补偿系统不确定性、非线性、耦合性、建模误差等因素对控制器的影响。计算机仿真实验表明,所提出的独轮自平衡机器人神经网络反演迭代学习控制方法在一定范围内是有效的。通过仿真实验对比分析了神经网络反演迭代学习控制、非线性PD三闭环控制、层叠结构伪非线性动态逆控制、神经网络动态逆控制与线性姿态平衡控制的动态性能和鲁棒性,结果表明在相同对象参数下,神经网络反演迭代学习控制的动态性能指和鲁棒性较好,非线性PD控制和非线性动态逆控制次之,线性控制方法和神经网络动态逆控制性能较差。
课题获得国家863计划项目(2007AA04Z226);国家自然科学基金项目(61075110);北京市教委重点项目(KZ200810005002);北京市自然科学基金项目(4102011)的资助。取得的科研成果,对于优化独轮自平衡机器人的系统结构,分析独轮自平衡机器人的运动规律和内在特性,研究自平衡机器人的运动平衡控制问题具有积极意义和一定的参考价值。课题研制的样机已获得多项国家专利,在机器人技术和控制科学的研究、教学领域,以及服务机器人、娱乐机器人领域有一定的应用价值。
Unicycle riding is a kind of senior motor skills of human beings or other intelligent animals after training. Single-wheeled Self-Balancing Robot (SWSBR, SWR) is a kind of intelligent mimetic systems imitating human behavior of riding an unicycle.
Different from other mobile robot with multiple wheels, the unicycle riding robot system or SWSBR has only one wheel to touch the ground. And it is a statically instable, coupled and highly nonlinear plant in three dimensions. Modeling and control of flexible self-balancing robot are important issues in the fields of control science and robotic engineering. This dissertation studies and designs a Single-Wheeled Self-Balancing Robot (SWSBR), develops the kinematics model and dynamic model of the robot, and on the basis of system characters analyzing, the research on the robot’s motion and balancing control is carried out. The main contributions are as follows:
(1) Single-Wheeled Self-Balancing Robot System
This dissertation illustrates the design of a single-wheeled self-balancing robot system (SWSBR System), whose the most important structure character imitates the overall structure of the unicycle: the vertical flywheel to tune the roll DOF and the walk wheel to adjust the pitch DOF, with robot frame for all modules fixed on. There is only one walk wheel contacting with the ground. Its dynamic feature is complex, and its modeling and control are difficult. The electronic system of the robot is hierarchical architecture: the organization layer has an embedded PC as the center, supplemented by a variety of human-machine interface. It is responsible for monitoring, acquiring information, decision-making and movement control instructions issued; the coordination layer has a DSP as the core, supplemented by state sensors, is mainly responsible for balance and motion control; the execution layer is the motor servo system, and responsible for controlling the torques of wheels. The control system structure of the studied robot constitutes a bionic sensory-motor system.
(2) Dynamic Modeling and Analysis of SWSBR
In this dissertation, the dynamic model of SWSBR is derived by applying the Lagrange method. Based on the proposed model, firstly, the dynamic characters of SWSBR is analyzed, zero input response and zero states response simulation are carried out, the outcome is in compliance with the physical fact, which examines the validity of the model. Secondly, the system characters of SWSBR is analyzed, it is proved that SWSBR is not stable and locally controllable on its upright equilibrium point. Thirdly, the analysis of the SWSBR design parameters is carried out: quality, center of gravity, inertia flywheel and so on. Finally, the three-dimensional model of SWSBR consistent with the dynamic model and physical fact is built by virtual prototyping technology. The model and the analysis described in this dissertation provide some theoretical basis for the modeling and control of SWSBR.
(3)Motion Balancing Control for SWSBR Based on Nonlinear Control Method
This dissertation proposes a three-loop control method based on nonlinear PD for the posture balancing and motion control of SWSBR. The nonlinear PD three closed-loop control method includes driven inner loop, posture balancing control mid loop and motion control outer loop. The input of the motor controllers is the output torques of posture balancing controller. The input of posture balancing controller is the output of motion controller. In the posture control mid loop, the stable equilibrium of SWSBR is controlled by 2 nonlinear PD controllers, in which tan (θ) is the nonlinear aspect ratio, used as the nonlinear differential link. The inputs of motion controller are desired position. The simulation and real system experiments in static balancing control and motion control are carried out. The results prove that the control method proposed by this dissertation is effective for single-wheeled self-balancing robot. The simulation results are compared with linear PD or LQR controller. They show that with the same parameters, PDNLB dynamic performance and robustness are much better than linear PD and LQR controllers.
(4) Dynamic Inversion Control Method for SWSBR
For nonlinear control problems of single-wheeled self-balancing robot, inverse system method is proposed and pseudo-dynamic inversion controller is designed. Single-wheeled self-balancing robot system is a minimum phase system, inverse system does not exist. To constitute single-wheeled self-balancing robot dynamic pseudo-inverse control system, the time scale separation method is used in building the system pseudo-inverse. But this method has such problems as: accurate model for dynamic inverse system is difficult to obtain, construction of dynamic inversion control system is inconvenient, performance of pseudo-dynamic inversion control is difficult to maintain. And the neural network has capability of the approximate any continuous input-output mapping. So the dynamic inversion control based on neural network is proposed. The method uses BP neural network to approach the dynamic inverse model, constitutes a reference model of neural network dynamic inversion control system. The results show that the method can take advantage of BP neural network to approximate the inverse system, effectively solve problems that the exact analytical model is difficult to obtain, and achieve posture control; but the overshoot, settling time and other control performance are not satisfactory, and the robustness is poor.
(6) Iterative Learning Control Method for SWSBR
In this dissertation, an iterative learning control method of neural network backstepping control method for SWSBR's posture and position control is proposed. The iterative learning control is introduced based on the energy function of tracking error to overcome the uncertainty caused by the robot system parameters and disturbances. The neural network backstepping control method is the tool for iterative learning. It is based on the linear control and approximation of ideal control law by the neural network. The iterative learning control method not only has a simple and clear form, but also can compensate uncertainty, nonlinearity, coupling, modeling error and other factors through the online learning process. Simulation results show that the iterative learning control of neural network backstepping method for SWSBR's posture and position control are effective within a certain range and have better performance than linear control. Comparative results of experiments show that with the same parameters, the performance of iterative learning control of neural network backstepping method, adaptive neural network dynamic inversion control are the best; nonlinear PD three closed-loop control and dynamic inversion control are the second; linear control method, neural network dynamic inversion control and dynamic inversion control are the worst.
This subject is supported by the National Natural Foundation (60774077) and the High Technology Development Plan (863) (2007AA04Z226). The research results have significance for optimizing the system structure of flexible robots, the analysis of the Single-Wheeled Self-Balancing Robot’s motion pattern and identity, and the study of motion and balancing control problem. Several patents have been granted to the proposed robot, which has application value in the fields of research and education for robotic technology and control science, and service/entertainment robot development.
本文设计了具有竖直飞轮和下行走轮结构的独轮自平衡机器人系统,建立了相应的运动学和动力学模型,并在系统特性分析的基础上,进行了运动平衡控制问题的研究,取得了以下主要研究成果:
1、独轮自平衡机器人系统
本文设计了一种独轮自平衡机器人系统,其最重要的结构特征是竖直惯性飞轮和下行走轮相互配合:竖直惯性飞轮调节横滚自由度平衡;行走轮调节俯仰自由度平衡。此结构模拟了人类骑行独轮车的特征,动力学特性较为复杂,其建模与控制问题具有一定难度。所设计独轮自平衡机器人的电气系统为分层递阶结构:组织级以嵌入式PC为核心,辅以各种人机接口,负责监测、获取信息,决策和下达运动控制指令;协调级以DSP为核心,辅以状态感知传感器,主要负责运动平衡控制;执行级为电机伺服系统,负责控制双轮电机完成指定运动。整个控制结构构成一种仿生的姿态感觉运动系统。
2、独轮自平衡机器人的动力学建模与分析
本文运用拉格朗日法建立了独轮自平衡机器人的动力学模型,并对其进行了实验验证。实验结果符合物理事实,验证了所建模型正确;其次,分析了独轮自平衡机器人的系统特性,证明独轮自平衡机器人在直立平衡点不稳定和局部可控;再次,分析了独轮自平衡机器人各设计参数:质量、重心高度、飞轮惯量等,对运动平衡控制系统的影响规律;最后,利用虚拟样机技术建立了独轮自平衡机器人的三维模型,并与数学模型相互验证正确性。本文建立的模型及相关分析为独轮自平衡机器人的设计和控制提供了一定理论依据。
3、基于非线性PD控制方法的独轮自平衡机器人运动平衡控制
本文针对独轮自平衡机器人的运动平衡控制问题,提出一种基于非线性PD的三环控制方法。该方法包括电机伺服驱动内环、姿态平衡控制中环和运动位移控制外环,其中,电机伺服驱动内环通过两个PID控制器分别实现上、下电机转矩伺服,控制器输入为姿态平衡控制器的输出转矩;姿态平衡控制中环为一种非线性PD控制器(PDNLB),控制机器人稳定平衡,PDNLB采用tan(θ)作为非线性比为非线性微分环节,PDNLB输入为由机器人运动控制器提供的期望姿态;外环为直线位移PD控制器,输入为期望的直线位移,输出经耦合转化为期望俯仰和横滚倾角。通过仿真实验对比分析了PDNLB与线性PD姿态平衡控制器的动态性能和鲁棒性,结果表明在相同参数下,PDNLB的动态性能指标、抗扰动和对象参数变化的适应能力均优于线性PD和LQR控制器。进行了独轮自平衡机器人静止平衡和运动位移控制的仿真以及物理系统实验,实验结果验证了本文提出的控制方法是一种解决独轮自平衡机器人运动平衡控制问题的有效方法。
4、基于非线性动态逆控制方法的独轮自平衡机器人平衡控制
针对独轮自平衡机器人的非线性控制问题,根据多变量非线性控制的理论—逆系统方法,设计了独轮自平衡机器人伪动态逆控制器,给出了具体实现方法。针对独轮自平衡机器人系统为最小相位系统,逆系统不存在的问题,通过时标分离的方法构建系统的伪逆,构成独轮自平衡机器人伪动态逆控制系统。针对动态逆系统精确模型难于获得、动态逆方法设计控制系统不便、伪动态逆控制性能难于保障的问题,利用神经网络具有逼近任意连续的n输入m输出映射的能力,提出基于神经网络的独轮自平衡机器人动态逆控制方法。该方法利用BP神经网络逼近系统的动态逆模型,构成参考模型神经网络动态逆控制系统。实验结果表明:该方案能够利用BP神经网络逼近系统的逆系统,可有效解决独轮自平衡机器人系统建模不精确、逆系统精确解析解难于求得等问题,并实现机器人的姿态平衡控制;但是该方法用于独轮自平衡机器人控制时,超调量、调节时间等控制性能并不理想,并且鲁棒性较差。
5、基于迭代学习控制方法的独轮自平衡机器人运动平衡控制
本文针对独轮自平衡机器人的姿态平衡控制问题,提出了基于神经网络反演方法的迭代学习控制方法。迭代学习控制方法,是在线性控制的基础上引入基于跟踪误差的指数型能量函数作为评价机制,通过迭代学习不断修正控制量以克服机器人系统的未知参数和干扰带来的不确定性,类似于人类的条件反射的学习过程。而神经网络反演控制是通过RBF神经网络进行反演迭代学习。并从理论上证明其跟踪误差的渐进收敛性。这种方案既具有线性控制系统思想简单、方法明确的优点,又能够利用在线学习过程动态补偿系统不确定性、非线性、耦合性、建模误差等因素对控制器的影响。计算机仿真实验表明,所提出的独轮自平衡机器人神经网络反演迭代学习控制方法在一定范围内是有效的。通过仿真实验对比分析了神经网络反演迭代学习控制、非线性PD三闭环控制、层叠结构伪非线性动态逆控制、神经网络动态逆控制与线性姿态平衡控制的动态性能和鲁棒性,结果表明在相同对象参数下,神经网络反演迭代学习控制的动态性能指和鲁棒性较好,非线性PD控制和非线性动态逆控制次之,线性控制方法和神经网络动态逆控制性能较差。
课题获得国家863计划项目(2007AA04Z226);国家自然科学基金项目(61075110);北京市教委重点项目(KZ200810005002);北京市自然科学基金项目(4102011)的资助。取得的科研成果,对于优化独轮自平衡机器人的系统结构,分析独轮自平衡机器人的运动规律和内在特性,研究自平衡机器人的运动平衡控制问题具有积极意义和一定的参考价值。课题研制的样机已获得多项国家专利,在机器人技术和控制科学的研究、教学领域,以及服务机器人、娱乐机器人领域有一定的应用价值。
Unicycle riding is a kind of senior motor skills of human beings or other intelligent animals after training. Single-wheeled Self-Balancing Robot (SWSBR, SWR) is a kind of intelligent mimetic systems imitating human behavior of riding an unicycle.
Different from other mobile robot with multiple wheels, the unicycle riding robot system or SWSBR has only one wheel to touch the ground. And it is a statically instable, coupled and highly nonlinear plant in three dimensions. Modeling and control of flexible self-balancing robot are important issues in the fields of control science and robotic engineering. This dissertation studies and designs a Single-Wheeled Self-Balancing Robot (SWSBR), develops the kinematics model and dynamic model of the robot, and on the basis of system characters analyzing, the research on the robot’s motion and balancing control is carried out. The main contributions are as follows:
(1) Single-Wheeled Self-Balancing Robot System
This dissertation illustrates the design of a single-wheeled self-balancing robot system (SWSBR System), whose the most important structure character imitates the overall structure of the unicycle: the vertical flywheel to tune the roll DOF and the walk wheel to adjust the pitch DOF, with robot frame for all modules fixed on. There is only one walk wheel contacting with the ground. Its dynamic feature is complex, and its modeling and control are difficult. The electronic system of the robot is hierarchical architecture: the organization layer has an embedded PC as the center, supplemented by a variety of human-machine interface. It is responsible for monitoring, acquiring information, decision-making and movement control instructions issued; the coordination layer has a DSP as the core, supplemented by state sensors, is mainly responsible for balance and motion control; the execution layer is the motor servo system, and responsible for controlling the torques of wheels. The control system structure of the studied robot constitutes a bionic sensory-motor system.
(2) Dynamic Modeling and Analysis of SWSBR
In this dissertation, the dynamic model of SWSBR is derived by applying the Lagrange method. Based on the proposed model, firstly, the dynamic characters of SWSBR is analyzed, zero input response and zero states response simulation are carried out, the outcome is in compliance with the physical fact, which examines the validity of the model. Secondly, the system characters of SWSBR is analyzed, it is proved that SWSBR is not stable and locally controllable on its upright equilibrium point. Thirdly, the analysis of the SWSBR design parameters is carried out: quality, center of gravity, inertia flywheel and so on. Finally, the three-dimensional model of SWSBR consistent with the dynamic model and physical fact is built by virtual prototyping technology. The model and the analysis described in this dissertation provide some theoretical basis for the modeling and control of SWSBR.
(3)Motion Balancing Control for SWSBR Based on Nonlinear Control Method
This dissertation proposes a three-loop control method based on nonlinear PD for the posture balancing and motion control of SWSBR. The nonlinear PD three closed-loop control method includes driven inner loop, posture balancing control mid loop and motion control outer loop. The input of the motor controllers is the output torques of posture balancing controller. The input of posture balancing controller is the output of motion controller. In the posture control mid loop, the stable equilibrium of SWSBR is controlled by 2 nonlinear PD controllers, in which tan (θ) is the nonlinear aspect ratio, used as the nonlinear differential link. The inputs of motion controller are desired position. The simulation and real system experiments in static balancing control and motion control are carried out. The results prove that the control method proposed by this dissertation is effective for single-wheeled self-balancing robot. The simulation results are compared with linear PD or LQR controller. They show that with the same parameters, PDNLB dynamic performance and robustness are much better than linear PD and LQR controllers.
(4) Dynamic Inversion Control Method for SWSBR
For nonlinear control problems of single-wheeled self-balancing robot, inverse system method is proposed and pseudo-dynamic inversion controller is designed. Single-wheeled self-balancing robot system is a minimum phase system, inverse system does not exist. To constitute single-wheeled self-balancing robot dynamic pseudo-inverse control system, the time scale separation method is used in building the system pseudo-inverse. But this method has such problems as: accurate model for dynamic inverse system is difficult to obtain, construction of dynamic inversion control system is inconvenient, performance of pseudo-dynamic inversion control is difficult to maintain. And the neural network has capability of the approximate any continuous input-output mapping. So the dynamic inversion control based on neural network is proposed. The method uses BP neural network to approach the dynamic inverse model, constitutes a reference model of neural network dynamic inversion control system. The results show that the method can take advantage of BP neural network to approximate the inverse system, effectively solve problems that the exact analytical model is difficult to obtain, and achieve posture control; but the overshoot, settling time and other control performance are not satisfactory, and the robustness is poor.
(6) Iterative Learning Control Method for SWSBR
In this dissertation, an iterative learning control method of neural network backstepping control method for SWSBR's posture and position control is proposed. The iterative learning control is introduced based on the energy function of tracking error to overcome the uncertainty caused by the robot system parameters and disturbances. The neural network backstepping control method is the tool for iterative learning. It is based on the linear control and approximation of ideal control law by the neural network. The iterative learning control method not only has a simple and clear form, but also can compensate uncertainty, nonlinearity, coupling, modeling error and other factors through the online learning process. Simulation results show that the iterative learning control of neural network backstepping method for SWSBR's posture and position control are effective within a certain range and have better performance than linear control. Comparative results of experiments show that with the same parameters, the performance of iterative learning control of neural network backstepping method, adaptive neural network dynamic inversion control are the best; nonlinear PD three closed-loop control and dynamic inversion control are the second; linear control method, neural network dynamic inversion control and dynamic inversion control are the worst.
This subject is supported by the National Natural Foundation (60774077) and the High Technology Development Plan (863) (2007AA04Z226). The research results have significance for optimizing the system structure of flexible robots, the analysis of the Single-Wheeled Self-Balancing Robot’s motion pattern and identity, and the study of motion and balancing control problem. Several patents have been granted to the proposed robot, which has application value in the fields of research and education for robotic technology and control science, and service/entertainment robot development.
引文
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