Relative dynamics modeling and force-position hybrid control of dual-arm cutting robot
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摘要: 双悬臂截割机器人可解决传统单臂掘进机在截割大尺寸断面时效率低下的难题，但其与煤岩的动态交互影响控制性能。现有研究以双臂接触同一对象形成运动闭链为前提，无法满足双悬臂截割机器人双臂运动及末端截割头输出力的控制要求。针对该问题，设计了一种基于机器人相对动力学模型的力位混合控制系统。建立双悬臂截割机器人运动学和动力学模型，基于机器人的相对雅可比矩阵及虚位移与虚功原理推导出机器人的相对动力学模型，通过单一变量同时描述机器人双臂的运动状态，将机器人双臂独立的动力学模型整合为一个整体。基于机器人的相对动力学模型，设计了机器人双臂力位混合控制系统，通过李雅普诺夫函数验证了系统的稳定性和可行性。仿真结果表明：双悬臂截割工艺较单悬臂截割拥有更大的工作空间，具有一次性实现大断面截割的能力；双悬臂截割机器人力位混合控制系统能够完成对期望相对位置和期望相对力的同步跟踪，对截割头期望位置跟踪的绝对误差在0.313 2 m以内，均方根误差为0.144 7 m。Abstract: The dual-arm cutting robot addresses the low efficiency of traditional single-arm roadheaders when cutting large cross-sections. However, its dynamic interaction with coal-rock affects control performance. In current studies, both arms of the dual-arm cutting robot interact with the same object, forming a closed kinematic chain, which fails to meet the control requirements for independent arm movement and the output force of each cutting head. To solve this issue, a force-position hybrid control system based on the robot’s relative dynamics model was designed. The kinematic and dynamics models of the dual-arm cutting robot were established, with the relative dynamics model derived using the robot’s relative Jacobian matrix and principles of virtual displacement and virtual work. This model used a single variable to describe the motion states of both arms, integrating their independent dynamics models into a unified one. Based on this relative dynamics model, a force-position hybrid control system was developed for the robot’s dual arms, with system stability and feasibility verified via the Lyapunov function. Simulation results indicated that the dual-arm cutting process had a larger workspace compared to single-arm cutting, allowing for efficient large cross-section cutting. The force-position hybrid control system enabled synchronized tracking of expected relative position and force, with the absolute error in tracking the target cutter position kept within 0.3132 m and a root mean square error of 0.1447 m.
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图 3 基于相对动力学模型的双悬臂截割机器人相对位置控制器
Figure 3. Relative position controller for dual-arm cutting robot based on relative dynamics model
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图 4 基于相对动力学模型的双悬臂截割机器人相对力控制器
Figure 4. Relative force controller for dual-arm cutting robot based on relative dynamics model
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图 5 基于相对动力学模型的双悬臂截割机器人力位混合控制系统
Figure 5. Force-position hybrid control system for dual-arm cutting robot based on relative dynamics model
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图 6 单悬臂与双悬臂截割工艺的工作空间
Figure 6. Workspace for single-arm cutting and dual-arm cutting processes
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图 7 双悬臂截割机器人截割头S形运动轨迹
Figure 7. S-shaped motion trajectories of cutting heads of dual-arm cutting robot
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图 8 双悬臂截割机器人两截割头的期望相对位置
Figure 8. Expected relative position for two cutting heads of dual-arm cutting robot
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图 10 力位混合控制系统对截割头相对位置的控制结果
Figure 10. Relative position tracking results of cutting head by force-position hybrid control system
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图 11 力位混合控制系统对截割头相对力的控制结果
Figure 11. Relative force tracking results of cutting heads by force-position hybrid control system
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图 12 初始相对位置存在误差时力位控制结果
Figure 12. Tracking results of force-position with errors in initial relative position
表 1 双悬臂截割机器人的D−H参数
Table 1 D-H parameters of dual-arm cutting robot
关节编号 θi/rad di/m ai/m αi/rad i=1 [0, π/2] 0 a1 0 i=2 [−π/2,0] 0 1 π/2 i=3 [0, π/2] 0 [4.18，4.73] 0 i=4 [−π/2,0] 0 a4 0 i=5 [0, π/2] 0 1 π/2 i=6 [0, π/2] 0 [4.18，4.73] 0 
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表 2 处于S形轨迹拐点处的双悬臂截割机器人关节变量
Table 2 Joint variables of dual-arm cutting robot at inflection points of S-shaped trajectories
端点
序号移动平台
推移量/mθ2/rad θ3/rad a3/m θ5/rad θ6/rad a6/m 1 1.0 0 π/3 4.73 0 π/3 4.73 2 1.1 −π/2 π/3 4.18 π/2 π/3 4.18 3 1.3 −π/2 2π/9 4.18 π/2 2π/9 4.18 4 1.5 0 2π/9 4.73 0 2π/9 4.73 5 1.7 0 π/9 4.18 0 π/9 4.18 6 1.9 −π/2 π/9 4.73 π/2 π/9 4.73 7 2.1 −π/2 0 4.18 π/2 0 4.18 8 2.3 0 0 4.73 0 0 4.73
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