非完整轮式移动机器人运动规划与控制研究
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摘要
近年来随着科技进步，通过利用移动机器人在复杂环境下进行探测和开发，人类的研究领域进一步扩展。将移动机器人作为实验平台，人们可以对人类思维模式进行探索，研究复杂智能体行为的产生。移动机器人的运动规划与运动控制问题涉及到认知科学、模式识别、非线性控制等领域，所得到的成果也将带动军事、交通、工业等机器人系统应用领域的发展。本文以轮式移动机器人作为研究对象，重点研究移动机器人的运动控制与运动规划问题，主要研究内容与创新点概括如下：
1.研究非完整轮式移动机器人的轨迹跟踪控制问题。不同于路径跟踪问题，轨迹跟踪控制不仅具有空间位置要求，同时具有时间要求，即在特定的时间到达特定的位置，使机器人跟踪一条以时间为参数的轨迹。本文提出一种不存在控制奇异点的轨迹跟踪方法。该方法并不是直接跟踪姿态角，而是根据当前的侧向误差设计一个引导角作为期望姿态，随着侧向误差的收敛该引导角也逐渐趋向于姿态角，以此实现位姿跟踪。将引导角作为虚拟输入，结合Backstepping方法设计了基于移动机器人运动学模型的轨迹跟踪控制律，并给出了参数选取条件，然后将基于运动学模型的控制律进行扩展，考虑到外部扰动的影响，设计了基于动力学模型的控制律。最后通过仿真验证了所设计的控制律的有效性。
2.研究非完整轮式移动机器人的路径跟踪控制问题。路径跟踪的目标是控制移动机器人跟踪一条几何曲线而无时间要求。提出一种跟踪参数曲线路径的方法。以路径上期望位置为原点建立路径坐标系，并在路径坐标系中计算跟踪误差，设计一个引导角作为期望的角度误差，可以使侧向误差随着角度误差一起收敛，结合Backstepping设计了路径跟踪控制律以及路径参数的更新律，并分析了参数选取应满足的条件，可以使跟踪误差收敛。最后通过仿真验证了所提出方法的有效性。
3.研究了包含模型不确定性的轮式移动机器人的运动控制问题。由于移动机器人的物理参数难以精确测定，因此首先假设除了车轮半径和和两驱动轮间距外，机器人其余的物理参数均为未知，基于模糊系统逼近非线性函数的能力解决模型不确定性带来的困难，并以移动机器人的轨迹跟踪控制为例，设计了控制律和模糊系统权值矩阵的更新律，通过仿真验证了所提出方法的有效性。然后进一步假设机器人所有物理参数均为未知，结合自适应Baskstepping和模糊系统设计了轨迹跟踪控制律、未知参数的自适应律和模糊系统权值矩阵的更新律，并通过仿真验证了所提出方法的有效性。
4．提出一种改进的考虑加速度限制的移动机器人运动规划方法。在移动机器人跟踪预先规划轨迹的过程中，不可避免会产生跟踪误差。导致误差产生的原因之一是规划路径的曲率不连续，产生跟踪误差的另一个原因是车轮的打滑和侧滑。在移动机器人运动过程中，车轮与地面间的最大摩擦力决定了机器人运动过程中的加速度限制。包括机器人加速减速运动时的切向加速度及曲线运动时的侧向加速度。当加速度超出限制时，轮胎与地面间发生滑移，产生跟踪误差。给定规划起止位姿和速度，首先基于三次Bezier曲线进行了路径的规划。然后根据受到的最大加速度限制规划时间最优的最大允许速度轨线。对于可能会出现的规划速度轨线在起点和终点处的速度低于规划目标值的情况，给出了进一步的规划方法。仿真结果验证了该方法的有效性和求解的快速性。
With recent advances in technology, the fields of human research have been furtherexpanded through the use of mobile robot in a complex environment. People can explore thehuman thinking mode and discuss the generation of complex agent behaviors by taking themobile robot as an experimental platform. The motion planning and motion control issues of themobile robot are related to cognitive science, pattern recognition, nonlinear control, and otherfields. The resulting outcomes will also promote the development of military, transportation andindustrial robot system applications. In this dissertation, the motion planning and control forwheeled mobile robots is considered. Major researches and innovations are summarized asfollows:
1. The trajectory tracking problem of nonholonomic wheeled mobile robots is considered.Unlike the path following problem, the trajectory tracking problem not only have the spatialposition requirements, but also have time requirements, i.e., to control the mobile robot reachesa specific location at a specific time. A novel trajectory tracking control method based on thedynamic model of a wheeled mobile robot is proposed. Tracking errors between the referenceand the real postures are calculated in the robot body coordinate system. Then the guidanceangle is designed by analyzing the relationship between lateral and angular errors. Thekinematics tracking controller is developed with the backstepping approach by taking theguidance angle as a virtual input. Parameter selection criterion for the controller is alsoinvestigated. By taking the external disturbances into account, a torque controller based on thedynamic model is derived. Simulation results verify the effectiveness of the proposed method.
2. The problem of path following of nonholonomic wheeled mobile robots is considered.The goal of path following is to control the mobile robot to follow a geometric curve withoutany time requirements. A control scheme is proposed for the following of parametric curves. Tracking errors between the actual and desired postures are first calculated in the pathcoordinate system. The origin of the path frame is fixed to the desired poison on the referencepath. The guidance angle is assigned by analyzing the relationship between lateral and angularerror in the path frame. The path following controller and the update law of the path parameterare designed by using the Lyapunov direct method and backstepping technique. Simulationresults following a Bezier curve path demonstrate the effectiveness of the method.
3. The control problem of wheeled mobile robots with model uncertainties is considered.Since the actual physical parameters of the mobile robot are difficult to determine accurately, itis first assumed that the physical parameters of the robot were assumed to be unknown exceptthe wheel radius and the distance between the two driving wheels. The problem is solved byusing the nonlinear approximation capacity of the fuzzy system. And by taking the trajectorytracking problem as an example, an integrated controller based on the dynamics model of themobile and the update law of fuzzy weight matrix are designed. Then it is further assumed thatall the physical parameters of the mobile robot are unknown. The control law is designed byusing the adaptive backstepping and the fuzzy approach. The adaptive law of unknownparameters and fuzzy weight matrix are also given.. The effectiveness of the proposed method isverified by simulation results.
4. Proposed an improved method for mobile robot motion planning without violatingacceleration limits. When a mobile robot tracking a trajectory planned in advance, willinevitably produce tracking errors. One of the causes of the tracking error is that the curvature ofthe planned path is not continuous. Another reason for the generation of tracking error is theslippage of the driving wheels. When the acceleration limits are exceeded, slippage occursbetween the tire and the ground, resulting in tracking error. The acceleration limits aredetermined by the friction between the wheels and the ground. The tangential acceleration isresponsible for the change in the robot’s velocity. The radical acceleration is due to the curvatureof the path. Given the terminal posture sand velocities, the cubic Bezier curve is employed forpath planning. Then the maximum allowable velocity profile can be calculated according to theacceleration limits while the acceleration limits can be determined by the surface frictionbetween the wheels and the ground. Simulation results show the effectiveness and quickness ofthe proposed algorithm.
1.研究非完整轮式移动机器人的轨迹跟踪控制问题。不同于路径跟踪问题，轨迹跟踪控制不仅具有空间位置要求，同时具有时间要求，即在特定的时间到达特定的位置，使机器人跟踪一条以时间为参数的轨迹。本文提出一种不存在控制奇异点的轨迹跟踪方法。该方法并不是直接跟踪姿态角，而是根据当前的侧向误差设计一个引导角作为期望姿态，随着侧向误差的收敛该引导角也逐渐趋向于姿态角，以此实现位姿跟踪。将引导角作为虚拟输入，结合Backstepping方法设计了基于移动机器人运动学模型的轨迹跟踪控制律，并给出了参数选取条件，然后将基于运动学模型的控制律进行扩展，考虑到外部扰动的影响，设计了基于动力学模型的控制律。最后通过仿真验证了所设计的控制律的有效性。
2.研究非完整轮式移动机器人的路径跟踪控制问题。路径跟踪的目标是控制移动机器人跟踪一条几何曲线而无时间要求。提出一种跟踪参数曲线路径的方法。以路径上期望位置为原点建立路径坐标系，并在路径坐标系中计算跟踪误差，设计一个引导角作为期望的角度误差，可以使侧向误差随着角度误差一起收敛，结合Backstepping设计了路径跟踪控制律以及路径参数的更新律，并分析了参数选取应满足的条件，可以使跟踪误差收敛。最后通过仿真验证了所提出方法的有效性。
3.研究了包含模型不确定性的轮式移动机器人的运动控制问题。由于移动机器人的物理参数难以精确测定，因此首先假设除了车轮半径和和两驱动轮间距外，机器人其余的物理参数均为未知，基于模糊系统逼近非线性函数的能力解决模型不确定性带来的困难，并以移动机器人的轨迹跟踪控制为例，设计了控制律和模糊系统权值矩阵的更新律，通过仿真验证了所提出方法的有效性。然后进一步假设机器人所有物理参数均为未知，结合自适应Baskstepping和模糊系统设计了轨迹跟踪控制律、未知参数的自适应律和模糊系统权值矩阵的更新律，并通过仿真验证了所提出方法的有效性。
4．提出一种改进的考虑加速度限制的移动机器人运动规划方法。在移动机器人跟踪预先规划轨迹的过程中，不可避免会产生跟踪误差。导致误差产生的原因之一是规划路径的曲率不连续，产生跟踪误差的另一个原因是车轮的打滑和侧滑。在移动机器人运动过程中，车轮与地面间的最大摩擦力决定了机器人运动过程中的加速度限制。包括机器人加速减速运动时的切向加速度及曲线运动时的侧向加速度。当加速度超出限制时，轮胎与地面间发生滑移，产生跟踪误差。给定规划起止位姿和速度，首先基于三次Bezier曲线进行了路径的规划。然后根据受到的最大加速度限制规划时间最优的最大允许速度轨线。对于可能会出现的规划速度轨线在起点和终点处的速度低于规划目标值的情况，给出了进一步的规划方法。仿真结果验证了该方法的有效性和求解的快速性。
With recent advances in technology, the fields of human research have been furtherexpanded through the use of mobile robot in a complex environment. People can explore thehuman thinking mode and discuss the generation of complex agent behaviors by taking themobile robot as an experimental platform. The motion planning and motion control issues of themobile robot are related to cognitive science, pattern recognition, nonlinear control, and otherfields. The resulting outcomes will also promote the development of military, transportation andindustrial robot system applications. In this dissertation, the motion planning and control forwheeled mobile robots is considered. Major researches and innovations are summarized asfollows:
1. The trajectory tracking problem of nonholonomic wheeled mobile robots is considered.Unlike the path following problem, the trajectory tracking problem not only have the spatialposition requirements, but also have time requirements, i.e., to control the mobile robot reachesa specific location at a specific time. A novel trajectory tracking control method based on thedynamic model of a wheeled mobile robot is proposed. Tracking errors between the referenceand the real postures are calculated in the robot body coordinate system. Then the guidanceangle is designed by analyzing the relationship between lateral and angular errors. Thekinematics tracking controller is developed with the backstepping approach by taking theguidance angle as a virtual input. Parameter selection criterion for the controller is alsoinvestigated. By taking the external disturbances into account, a torque controller based on thedynamic model is derived. Simulation results verify the effectiveness of the proposed method.
2. The problem of path following of nonholonomic wheeled mobile robots is considered.The goal of path following is to control the mobile robot to follow a geometric curve withoutany time requirements. A control scheme is proposed for the following of parametric curves. Tracking errors between the actual and desired postures are first calculated in the pathcoordinate system. The origin of the path frame is fixed to the desired poison on the referencepath. The guidance angle is assigned by analyzing the relationship between lateral and angularerror in the path frame. The path following controller and the update law of the path parameterare designed by using the Lyapunov direct method and backstepping technique. Simulationresults following a Bezier curve path demonstrate the effectiveness of the method.
3. The control problem of wheeled mobile robots with model uncertainties is considered.Since the actual physical parameters of the mobile robot are difficult to determine accurately, itis first assumed that the physical parameters of the robot were assumed to be unknown exceptthe wheel radius and the distance between the two driving wheels. The problem is solved byusing the nonlinear approximation capacity of the fuzzy system. And by taking the trajectorytracking problem as an example, an integrated controller based on the dynamics model of themobile and the update law of fuzzy weight matrix are designed. Then it is further assumed thatall the physical parameters of the mobile robot are unknown. The control law is designed byusing the adaptive backstepping and the fuzzy approach. The adaptive law of unknownparameters and fuzzy weight matrix are also given.. The effectiveness of the proposed method isverified by simulation results.
4. Proposed an improved method for mobile robot motion planning without violatingacceleration limits. When a mobile robot tracking a trajectory planned in advance, willinevitably produce tracking errors. One of the causes of the tracking error is that the curvature ofthe planned path is not continuous. Another reason for the generation of tracking error is theslippage of the driving wheels. When the acceleration limits are exceeded, slippage occursbetween the tire and the ground, resulting in tracking error. The acceleration limits aredetermined by the friction between the wheels and the ground. The tangential acceleration isresponsible for the change in the robot’s velocity. The radical acceleration is due to the curvatureof the path. Given the terminal posture sand velocities, the cubic Bezier curve is employed forpath planning. Then the maximum allowable velocity profile can be calculated according to theacceleration limits while the acceleration limits can be determined by the surface frictionbetween the wheels and the ground. Simulation results show the effectiveness and quickness ofthe proposed algorithm.
引文
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