煤炭是中国最主要的一次能源，在中国经济发展中处于托底保障的决定性地位。但由于开采和掘进智能化水平差异，导致了煤炭行业存在“采掘失衡”问题，严重制约着煤炭产能提升的潜力。随着矿山开采规模的增加，为保证矿井掘进、运输、通风等大型井下设备的安装和运行，煤矿巷道的断面有逐渐扩大的趋势。传统的单悬臂掘进机因工作空间有限，在大断面快速成形时无法一次完成，工序繁复且效率低下。因此，本文提出了双悬臂截割机器人，旨在为大断面快速成型和巷道掘进提供理论依据和指导。本文的主要研究工作如下：
(1) 双悬臂截割机器人相对运动学建模：针对双悬臂截割机器人难以建立统一描述双臂运动的模型问题，基于D-H方法和机器人广义连杆坐标系建立了双悬臂截割机器人的运动学模型，通过运动学方程求导法和微分变换法相结合，计算得到单截割臂的雅可比矩阵。进一步地，通过相对旋转变换和相对旋转平移复合变换，建立了两种运动学的传播路径，并基于两种传播路径构建两臂的运动等式，最终建立双悬臂截割机器人的相对运动学模型，并基于机器人的运动学模型提出了机器人的双臂联合工作空间。对机器人的相对运动学建模表明，相对运动学模型能通过两末端截割头的相对运动作为唯一变量同时描述两截割臂的运动状态，将两臂独立的运动学整合为一个整体进行表达。对机器人的联合工作空间的仿真表明，相比于单臂掘进机，双悬臂截割机器人拥有更大的工作空间，其联合工作空间能够包络更大尺寸的断面，能够一次性完成大断面的成形工作，简化了单臂掘进机在开挖大断面时繁复的工序。
(2) 双悬臂截割机器人相对动力学建模：针对双悬臂截割机器人难以建立统一描述双臂动力学特性的模型问题，基于拉格朗日动力学方程求得机器人独立的单臂的动力学模型，再将机器人的动力学模型与虚位移与虚功原理结合，基于相对雅可比矩阵求得双悬臂截割机器人的相对动力学模型，由此求解了双臂末端相对力和机器人关节变量的映射关系。对机器人建立的相对动力学模型表明，以相对力作为唯一变量，相对动力学模型能够同时描述两臂的力学与动力学特性，将两臂独立的动力学整合为一个整体进行表达，为后续研究该机器人的控制算法提供了参考。
(3) 双悬臂截割机器人控制方法研究：针对双悬臂截割机器人存在多自由度导致统一控制困难的问题，基于机器人相对运动学模型设计了闭环的误差反馈控制器，通过末端相对位置误差实现同时控制双臂的运动。同时，基于机器人的相对动力学模型设计了闭环的相对力/位置混合控制器，最后搭建机器人虚拟样机进行了模型验证。对相对运动学反馈控制器的仿真表明，双悬臂截割机器人能够仅通过两截割头的相对运动这一唯一变量实现同时控制双臂的运动，使双臂末端截割头在笛卡尔空间中的轨迹逐渐收敛至期望位置。对相对力/位置控制器的仿真结果表明，该控制器能够在位置层通过唯一变量相对位置同时控制两截割头的运动，并在力层通过唯一变量相对力同时控制两截割头的输出力，为该机器人的控制提供了理论依据和有益参考。

Coal plays a crucial role as the primary non-renewable energy source in China, providing essential support for China’s economic development. However, due to disparities in the level of automation between coal mining and roadway excavation, the coal industry faces a problem of “mining imbalance”, which severely constrains the potential for increasing coal production capacity. With the increase in the scale of mining operations, there is a trend of gradually expanding the cross-section of coal mine tunnels to ensure the installation and operation of large underground equipment for mine driving, transportation, ventilation, and other purposes. The traditional single-arm mining machine, due to its limited working space, cannot complete large-section rapid formation in a single operation. The process is complex and inefficient. Therefore, this research proposes a dual-arm cutting robot, aiming to provide theoretical basis and guidance for large-section rapid formation and tunnel excavation. The main research is as follows: (1) Relative kinematic modeling of the dual-arm cutting robot: To address the difficulty in establishing a unified description of the dual-arm motion for a dual-arm cutting robot, a kinematic model of the robot is developed based on the Denavit-Hartenberg (D-H) method and the robot’s generalized link coordinate system. By combining the methods of kinematic equation differentiation and differential transformation, the Jacobian matrix for a single cutting arm is calculated. Furthermore, two kinematic propagation paths are established through relative rotational transformation and composite relative rotational-translational transformation. Based on these two propagation paths, the motion equations for the two arms are derived, ultimately leading to the development of the relative kinematic model for the dual-arm cutting robot. Based on the kinematic model, the dual-arm cooperative workspace of the robot is proposed. The relative kinematic modeling of the robot shows that the relative kinematic model can describe the motion states of both cutting arms simultaneously, using the relative motion of the two end cutting heads as the sole variable, integrating the independent kinematics of both arms into a unified expression. Simulation of the robot’s cooperative workspace indicates that, compared to a single-arm mining machine, the dual-arm cutting robot has a larger workspace. Its cooperative workspace can envelop larger cross-sections, enabling the robot to complete large-section formation in one operation, thus simplifying the complex procedures involved in large-section excavation with a single-arm mining machine. (2) Relative dynamic modeling of the dual-arm cutting robot: To address the difficulty in establishing a unified description of the dynamic characteristics of the two arms of a dual-arm cutting robot, the dynamic model of the independent single arm is first derived using the Lagrangian dynamics equation. Then, the dynamics model of the single arm is combined with the principles of virtual displacement and virtual work. Based on the relative Jacobian matrix, the relative dynamics model of the dual-arm cutting robot is obtained, which allows for solving the mapping relationship between the relative forces at the end-effector and the robot’s joint variables. The relative dynamics model established for the robot shows that, using the relative force as the sole variable, the relative dynamics model can simultaneously describe the mechanical and dynamic characteristics of both arms. This approach integrates the independent dynamics of the two arms into a unified expression, providing a reference for the subsequent development of control algorithms for the robot. (3) Research on the control of the dual-arm cutting robot: To address the issue of unified control difficulty caused by the dual end-effector outputs of the dual-arm cutting robot, a closed-loop error feedback controller is designed based on the robot’s relative kinematics model. The controller enables simultaneous control of the dual arms’ movement by using the relative position error of the end-effectors. Additionally, a closed-loop hybrid control system combining relative force/position is designed based on the robot’s relative dynamics model. Finally, a virtual prototype of the robot was built to validate the model. Simulation results of the relative kinematics feedback controller show that the dual-arm cutting robot can achieve simultaneous control of both arms’ movements using the relative motion between the two cutting heads as the sole variable. This enables the cutting heads’ trajectories in Cartesian space to gradually converge to the desired position. Simulation results of the relative force/position controller demonstrate that this controller can control the motion of both cutting heads simultaneously in the position layer through the relative position, and control the output forces of both cutting heads simultaneously in the force layer through the relative force. This provides a theoretical foundation and valuable reference for the control of the robot.

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