ANALYSIS ON PLANAR OBSTACLE AVOIDANCE LOCOMOTION OF VIBRATION-DRIVEN SYSTEM
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摘要: 近年来，工业机器人的应用领域日益广泛，可移动机器人的发展备受关注，为了在一些复杂环境中准确地完成作业，学者们提出并研究了振动驱动移动系统.本文研究了在各向异性黏性摩擦环境中一类有两个在平行轨道内做正弦运动的内部质量块的振动驱动移动系统的运动规律，提出了使系统完成包括避障等规定作业的驱动设计方法.首先利用第二类拉格朗日方程，建立了系统的动力学方程；然后，利用速度Verlet积分法分析了系统的运动规律，得到了内部驱动参数与系统运动轨迹、运动速度的关系；最后，结合振动驱动移动系统的运动规律，提出了使系统沿预设路径运动和实现避障运动的驱动设计方法.通过曲线离散得到了系统沿预设路径运动的移动轨迹，进而通过改变内部质量块的驱动参数，使系统沿预设路径运动.为了使移动系统在障碍物环境中达到目标位置，提出了结合栅格法，Floyd算法及最小顶点圆法的优化的路径规划计算方法，得到了振动驱动移动系统在障碍物环境中运动的最优路径，并通过改变内部质量块的驱动参数实现了移动系统的避障运动.Abstract: In recent years, with the wide application of the industrial robot, the development of the mobile robot has attracted more and more attention. In order to finish the work accurately in some complex environments, vibrationdriven system has been proposed and researched by scholars. At the presence of anisotropic viscous friction, this paper investigates the motion law of a vibration-driven locomotion system in which two internal masses vibrate sinusoidally in two parallel guides and puts forward a design method to conduct the tasks like obstacle avoiding. Firstly, by using the second-kind Lagrange's equation, dynamical equations of the system are established; then, the motion law is numerically analyzed, the relationship between the internal drive parameters and the system trajectory and the system velocity are obtained by using the velocity-verlet algorithm; finally, based on the motion law of the vibration-driven locomotion system, the drive design method is proposed to make the system move along a prescribed path and realize the obstacle avoidance. To make the mobile system move along a prescribed path, the motion trajectory of the system could be obtained by curve discretization. Then, by changing the driving parameters of the internal mass block, the system could move along the preset path. In order to make the mobile system reach the goal position in the obstacle environment, an optimized path planning method based on the grid method, Floyd algorithm and the minimum vertex circle method is proposed, and the optimal motion path of the vibration-driven mobile system is obtained. Finally, obstacle avoiding can be realized through changing the driving parameters of the internal mass block.
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图 2 支撑 $c_i \ (i=1,2,3,4)$ 处的黏性摩擦力模型
Figure 2. Model of the viscous frictional force at the i-th support
图 3 振动驱动系统与平面间的相互作用力和力矩
Figure 3. The interaction force and moment of force between vibration-driven system and ground
图 6 系统x方向速度 $\dot x_M$ 与时间t的关系
Figure 6. Relations between velocity $\dot x_M$ and time t
图 7 $\omega_1=100$ rad/s, n取不同值时系统轨迹
Figure 7. Trajectories of vibration-driven system under different n when $\omega_1=100$ rad/s
图 8 $\omega_1=100$ rad/s, $n < 1$ 时系统的转角 $\varphi$ 与时间t的关系
Figure 8. Relations between angular displacement $\varphi$ and time t when $n < 1$ and $\omega_1=100$ rad/s
图 9 $\omega_1=100$ rad/s, $n < 1$ 时系统路程s与时间t的关系
Figure 9. Relations between displacement s and time t when $n < 1$ and $\omega_1=100$ rad/s
图 10 $\omega_1=100$ rad/s, 系统曲率半径R与驱动频率比n的关系
Figure 10. Relations between radius R and n when $\omega_1=100$ rad/s
图 17 栅格地图模型 (红点:起始点，绿点:目标点)
Figure 17. Model of grid map (red: initial point, green: target point)
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