两轮自平衡移动机器人建模与控制研究
摘要
轮式倒立摆是一类欠驱动结构,它被广泛地应用在自主移动机器人和智能小型交通工具上,其动力学模型具有不稳定、多变量、强耦合、非线性等特点,是检验控制方法有效性的重要平台。由于其结构简单、体积小,可以在狭小、危险以及人无法到达的环境运动,因此基于轮式倒立摆的移动机器人在民用、工业、军事、航天航空中都有广泛的应用前景。
本文研究了轮式倒立摆的结构,在非完整约束情况下建立其在平坦地面上运动时的动力学模型,并实现轮式倒立摆的平衡点控制和速度控制。在此基础上,提出一种基于轮式倒立摆的新型座椅自平衡两轮机器人,它本质上是一类两轮自平衡移动机器人。它的下体部分是由两个同轴、左右平行分布的车轮的传统轮式倒立摆构成；上体由直线电机驱动的可移动座椅组成。主体结构类似于轮式倒立摆系统,但它优于轮式倒立摆系统,具有更多的运动自由度。车体的重心在两个车轮的上方,通过可移动座椅运动实现自平衡。该移动机器人作为个人交通工具,具有体积小、质量轻、结构简单、能够与其他座椅自平衡两轮机器人共用一个车道或车位、低排放等特点,特别适合狭小空间的运载操作。与已有的基于轮式倒立摆的个人交通工具等相比,座椅自平衡两轮机器人增加的可移动座椅,解决了驾驶者在行驶过程中的疲劳问题。
本文在分析新型座椅自平衡两轮机器人的发展和特点的基础上,根据该机器人的机械结构,计算得到机器人各部分的动能、势能和耗散能,再采用拉格朗日运动方程的方法建立了座椅自平衡两轮机器人在平坦路面和不平坦路面上运动的二维动力学模型,进一步得到了其在平坦地面上运动的三维动力学模型。在这些模型的基础上,计算得到该机器人在运动过程中的平衡点,通过设计LQR控制器和滑模控制器,实现了其在直线运动和拐弯运动时的速度控制。为了改进速度控制的性能,进一步提出了一种改进的滑模控制方法,使座椅自平衡两轮机器人在速度控制过程中收敛到期望值的速度更快。
为了验证理论分析,本文分别在MATLAB和动态物理引擎ODE仿真环境中实现了轮式倒立摆和座椅自平衡两轮机器人的控制。ODE是一个典型的三维多物体动态仿真引擎,它通过在虚拟环境中搭建实物结构来仿真物体运动,模拟空间物体之间的动态关系,反映物体的动态特性,提供三维动态虚拟环境。通过两个仿真结果的比较,一定程度上证明了该动力学模型的正确性,仿真结果验证了所提控制器控制器的有效性。
Mobile Wheeled Inversed Pendulum (MWIP) system is a kind of underactuated mechanical system, which is widely used in the fired of autonomous robots and intelligent narrow vehicles. The dynamic model of MWIP is unstable, multivariable, strong coupling, and nonlinear. Therefore, an MWIP system is an important platform used to verify the effectiveness of various control methods. Because the robot is simple in mechanics and small in volume, it is applicable in narrow, dangerous places and in that where the people cannot arrive. Thus, the MWIP based mobile robots are widely used in civilian, industrial, military and aerospace fields.
In this dissertation, we studied the structure of an MWIP system and the dynamic model of MWIP running on the flat ground is derived considering nonoholonomic constraint. Based on the dynamic model, the equilibrium control and velocity control are discussed. Inspired by the MWIP system, we introduce a novel mobile robot, which is a kind of intelligent robot in essence and similar to MWIP. It has more degrees of freedom than the MWIP and is much superior to it. The novel structure includes a conventional MWIP system which is composed of two coaxial, parallel wheels driven by motors and a movable seat which can be driven by a linear motor along the straight moving direction. The centre of gravity of new robot system is above the two wheels. By adjusting the movement of the seat, the vehicle can be self-balanced. As the personal transportation, the character of the new mobile robot includes small volume, light quality, simple structure, low emission and can share a same lane and garage with other robots et al. It is especially suitable for working and moving in narrow space. Compare to the existed MWIP-based personal transport, such as Segway, the proposed new robot uses a moveable seat which can reduce the problem of driver fatigue while operation. But it is difficult to design control law to control the new robot system because of the inherent nonlinear and uncertain features.
Based on the research of the technology and development of the new robot and the analysis of the mechanism structure, the dynamic model of the underactuated system running on the flat ground is derived using Lagrange's motion equation in the 2-dimensional space on both flat ground and rough terrain ground. We also obtained the3-dimensional model of the new robot running on the flat ground by using Lagrange motion equations. Based on the models, equilibriums are derived. The LQR control and SMC (Sliding mode control) scheme are chosen to realize equilibrium control and velocity control of the new robot both in straightforward running and turning motion. In order to achieve better performance in velocity control, we proposed an improved sliding mode control strategy. As a result, the rate of convergence in velocity control becomes faster.
In order to verify the theoretical results, we realize the velocity control both in MATLAB and ODE (Open Dynamic Engine). ODE is a typical3-dimensional muti-body dynamic simulation engine, which builts physical structure in the virtual environment and simulates the dynamic relationship. The numerical simulations are provided to verify and illustrate the correctness of the dynamic model of our proposed new robot. The effectiveness of proposed approaches is also verified through the simulation results.
本文研究了轮式倒立摆的结构,在非完整约束情况下建立其在平坦地面上运动时的动力学模型,并实现轮式倒立摆的平衡点控制和速度控制。在此基础上,提出一种基于轮式倒立摆的新型座椅自平衡两轮机器人,它本质上是一类两轮自平衡移动机器人。它的下体部分是由两个同轴、左右平行分布的车轮的传统轮式倒立摆构成；上体由直线电机驱动的可移动座椅组成。主体结构类似于轮式倒立摆系统,但它优于轮式倒立摆系统,具有更多的运动自由度。车体的重心在两个车轮的上方,通过可移动座椅运动实现自平衡。该移动机器人作为个人交通工具,具有体积小、质量轻、结构简单、能够与其他座椅自平衡两轮机器人共用一个车道或车位、低排放等特点,特别适合狭小空间的运载操作。与已有的基于轮式倒立摆的个人交通工具等相比,座椅自平衡两轮机器人增加的可移动座椅,解决了驾驶者在行驶过程中的疲劳问题。
本文在分析新型座椅自平衡两轮机器人的发展和特点的基础上,根据该机器人的机械结构,计算得到机器人各部分的动能、势能和耗散能,再采用拉格朗日运动方程的方法建立了座椅自平衡两轮机器人在平坦路面和不平坦路面上运动的二维动力学模型,进一步得到了其在平坦地面上运动的三维动力学模型。在这些模型的基础上,计算得到该机器人在运动过程中的平衡点,通过设计LQR控制器和滑模控制器,实现了其在直线运动和拐弯运动时的速度控制。为了改进速度控制的性能,进一步提出了一种改进的滑模控制方法,使座椅自平衡两轮机器人在速度控制过程中收敛到期望值的速度更快。
为了验证理论分析,本文分别在MATLAB和动态物理引擎ODE仿真环境中实现了轮式倒立摆和座椅自平衡两轮机器人的控制。ODE是一个典型的三维多物体动态仿真引擎,它通过在虚拟环境中搭建实物结构来仿真物体运动,模拟空间物体之间的动态关系,反映物体的动态特性,提供三维动态虚拟环境。通过两个仿真结果的比较,一定程度上证明了该动力学模型的正确性,仿真结果验证了所提控制器控制器的有效性。
Mobile Wheeled Inversed Pendulum (MWIP) system is a kind of underactuated mechanical system, which is widely used in the fired of autonomous robots and intelligent narrow vehicles. The dynamic model of MWIP is unstable, multivariable, strong coupling, and nonlinear. Therefore, an MWIP system is an important platform used to verify the effectiveness of various control methods. Because the robot is simple in mechanics and small in volume, it is applicable in narrow, dangerous places and in that where the people cannot arrive. Thus, the MWIP based mobile robots are widely used in civilian, industrial, military and aerospace fields.
In this dissertation, we studied the structure of an MWIP system and the dynamic model of MWIP running on the flat ground is derived considering nonoholonomic constraint. Based on the dynamic model, the equilibrium control and velocity control are discussed. Inspired by the MWIP system, we introduce a novel mobile robot, which is a kind of intelligent robot in essence and similar to MWIP. It has more degrees of freedom than the MWIP and is much superior to it. The novel structure includes a conventional MWIP system which is composed of two coaxial, parallel wheels driven by motors and a movable seat which can be driven by a linear motor along the straight moving direction. The centre of gravity of new robot system is above the two wheels. By adjusting the movement of the seat, the vehicle can be self-balanced. As the personal transportation, the character of the new mobile robot includes small volume, light quality, simple structure, low emission and can share a same lane and garage with other robots et al. It is especially suitable for working and moving in narrow space. Compare to the existed MWIP-based personal transport, such as Segway, the proposed new robot uses a moveable seat which can reduce the problem of driver fatigue while operation. But it is difficult to design control law to control the new robot system because of the inherent nonlinear and uncertain features.
Based on the research of the technology and development of the new robot and the analysis of the mechanism structure, the dynamic model of the underactuated system running on the flat ground is derived using Lagrange's motion equation in the 2-dimensional space on both flat ground and rough terrain ground. We also obtained the3-dimensional model of the new robot running on the flat ground by using Lagrange motion equations. Based on the models, equilibriums are derived. The LQR control and SMC (Sliding mode control) scheme are chosen to realize equilibrium control and velocity control of the new robot both in straightforward running and turning motion. In order to achieve better performance in velocity control, we proposed an improved sliding mode control strategy. As a result, the rate of convergence in velocity control becomes faster.
In order to verify the theoretical results, we realize the velocity control both in MATLAB and ODE (Open Dynamic Engine). ODE is a typical3-dimensional muti-body dynamic simulation engine, which builts physical structure in the virtual environment and simulates the dynamic relationship. The numerical simulations are provided to verify and illustrate the correctness of the dynamic model of our proposed new robot. The effectiveness of proposed approaches is also verified through the simulation results.
引文
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