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摘要: 为了控制机器人完成复杂的多臂协作任务, 提出了一种基于动态时间规整−高斯混合模型(Dynamic time warping-Gaussian mixture model, DTW-GMM)的机器人多机械臂多任务协同策略. 首先, 针对机器人示教时轨迹时间长短往往存在较大差异的问题, 采用动态时间规整方法来统一时间的变化; 其次, 基于动态时间规整的多机械臂示教轨迹, 采用高斯混合模型对轨迹的特征进行提取, 并以某一机械臂的位置空间矢量作为查询向量, 基于高斯混合回归泛化输出其余机械臂的执行轨迹; 最后, 在Pepper仿人机器人平台上验证了所提出的多机械臂协同策略, 基于DTW-GMM算法控制机器人完成了双臂协作搬运任务和汉字轨迹的书写任务. 提出的基于DTW-GMM算法的多任务协同策略简单有效, 可以利用反馈信息实时协调各机械臂的任务, 在线生成平滑的协同轨迹, 控制机器人完成复杂的协作操作.Abstract: To control robot to complete complex multi-arm cooperation tasks, a multi-task collaborative strategy based on dynamic time warping-Gaussian mixture model (DTW-GMM) is proposed in this paper. Firstly, in view of the problem that demonstration trajectories are shown to be largely different in the aspects of lasting time, the amic time warping algorithm is adopted to unify the variation of the time. Secondly, after the multi-arm demonstration trajectories are aligned by amic time warping algorithm, the Gaussian mixture model is used to extract the common features. And using the position space vector of a manipulator as the query vector, the Gaussian mixture regression algorithm is adopted to generically output the remaining manipulators＇ trajectory; Finally, the multi-task collaborative strategy proposed was verified on Pepper platform. Tasks for dual-arm to collaboratively move basket and write the Chinese character are completed based on the DTW-GMM algorithm. The multi-task collaborative strategy based on the DTW-GMM method proposed in this paper is effective. The feedback information can be introduced to coordinate the robot arms＇ task in real time, and the generated coordinated trajectories are smooth, which can control the robot to complete complex cooperative operations.
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图 6 基于微分逆运动学的机器人运动控制引擎设计框图
Fig. 6 Block diagram of the motion control engine based on differential inverse kinematics
图 12 搬运实验左右手臂轨迹泛化输出
Fig. 12 Generalized dual-arm trajectory output in moving experiment
图 14 基于DTW-GMM算法的汉字轨迹书写
Fig. 14 Chinese character trajectory generation based on DTW-GMM algorithm
表 1 算法的时间复杂度
Table 1 Time complexity of algorithms
轨迹规划算法 时间复杂度 DP ${n_x} {n_y}$ GCTW $2dl{{m} } + 8{{ {m^3} } }$ 
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表 2 DTW-GMM算法参数设置
Table 2 Parameter setting of the DTW-GMM algorithm
参数 参数值 $\delta$ $1 \times {10^{{\rm{ - 10}}}}$ ${i_{\max }}$ 10000 $\lambda$ 0.0001
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表 3 GMM表征协方差矩阵表
Table 3 Covariance matrix of GMM algorithm
变量 t x y z t 1 0.0814 −0.0074 0.0280 x 0.0814 1 −0.0003 0.0010 y −0.0074 −0.0003 1 −0.0001 z 0.0280 0.0010 −0.0001 1
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表 4 DTW-GMM表征协方差矩阵表
Table 4 Covariance matrix of DTW-GMM algorithm
变量 t x y z t 1 0.0078 −0.0063 0.0122 x 0.0078 1 −0.0001 0.0002 y −0.0063 −0.0001 1 0.0001 z 0.0122 0.0010 0.0001 1
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