移动型模块化机器人的高效重构规划方法

doi:10.13973/j.cnki.robot.2016.0467

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胡亚南, 马书根, 李斌, 王明辉, 王越超. 移动型模块化机器人的高效重构规划方法[J]. 机器人, 2016, 38(4): 467-474,485.DOI: 10.13973/j.cnki.robot.2016.0467. HU Yanan, MA Shugen, LI Bin, WANG Minghui, WANG Yuechao. An Efficient Reconfiguration Planning Method for Mobile Type Modular Robots. ROBOT, 2016, 38(4): 467-474,485. DOI: 10.13973/j.cnki.robot.2016.0467.

摘要基于穷举思想的模块化机器人重构规划方法的计算复杂度与模块数呈阶乘关系，难以适用于模块较多的场合．为此，本文提出一种与模块数呈线性复杂度的高效重构规划方法．将重构规划问题视为最优控制问题，通过求解Hamilton-Jacobi-Bellman方程得到定义在状态空间上的值函数和最优控制律．值函数的吸引域决定了各模块对应的最优目标，而应用控制律能够得到不同状态到达最优目标的最优运动轨迹．这样既避免了考虑不同构形模块间的多种对应关系所产生的组合爆炸，同时也能得到各模块的满足运动学约束的最优轨迹．仿真试验验证了方法的可行性和计算效率．

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关键词 ：重构规划, 运动学, 最优控制, HJB方程, 模块化机器人

Abstract：The reconfiguration planning methods for modular robots based on the exhaustion idea have factorial time complexity with respect to the number of modules, which are difficult to be applied to the cases containing large numbers of modules. To solve this problem, an efficient reconfiguration planning method is proposed, which has linear time complexity with respect to the number of modules. The reconfiguration planning problem is viewed as an optimal control problem. By solving the Hamilton-Jacobi-Bellman equation, the value function and optimal control law defined on the state space are obtained. The domain of attraction of the value function determines the optimal goal for the individual modules, and the optimal trajectories to the optimal goals at different states can be obtained by applying the optimal control law. Thus, the combination explosion caused by calculating the corresponding relations between modules of two configurations can be avoided, and the optimal trajectories of the individual modules that satisfy their kinematic constraints can be obtained at the same time. Simulation results validate the feasibility and efficiency of the proposed method.

Key words： modular robot reconfiguration planning kinematics optimal control Hamilton-Jacobi-Bellman equation

收稿日期: 2016-01-18 录用日期: 2016-05-16

TP242

基金资助:“十二五”国家科技支撑计划（2014BAK12B01）

通讯作者: 王明辉，mhwang@sia.cn E-mail: mhwang@sia.cn

作者简介: 胡亚南（1986-），男，博士生．研究领域：模块化机器人，动力学，运动规划．
马书根（1963-），男，博士，教授．研究领域：仿生机器人，机器人机构．
李斌（1963-），硕士，研究员．研究领域：仿生机器人，救援机器人．

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https://robot.sia.cn/CN/10.13973/j.cnki.robot.2016.0467 或 https://robot.sia.cn/CN/Y2016/V38/I4/467

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