«上一篇
 文章快速检索 高级检索

 哈尔滨工程大学学报  2018, Vol. 39 Issue (9): 1546-1553  DOI: 10.11990/jheu.201703030 0

### 引用本文

LIU Weihui, CHEN Diansheng, ZHANG Lizhi. Learning from demonstration based obstacle avoidance algorithm to plan the trajectory of a mobile manipulator[J]. Journal of Harbin Engineering University, 2018, 39(9), 1546-1553. DOI: 10.11990/jheu.201703030.

### 文章历史

Learning from demonstration based obstacle avoidance algorithm to plan the trajectory of a mobile manipulator
LIU Weihui, CHEN Diansheng, ZHANG Lizhi
School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
Abstract: To improve the environmental adaptability of service robots and alleviate user loads, a trajectory amendment algorithm utilizing learning from demonstration is proposed in this paper. First, a new trajectory with a shape similar to that previously demonstrated was generated by utilizing the dynamic movement primitives model, after which an improved distance-weighted k-nearest neighbor algorithm was developed to realize local modification for the trajectory shape at the end of the mobile manipulator. An online updating method was designed to avoid loss of adjacent effective training data. Obstacle avoidance experiments and real-time tests were then implemented in the human-robot interaction system. The experimental results showed the adaptability of the proposed obstacle avoidance algorithm to the new task, the obstacle avoidance decision ability and the online modification ability, to ensure friendly and smooth human-robot interactions.
Keywords: service robot    learning from demonstration    human-robot interaction    mobile manipulator    obstacle avoidance for trajectory    online adjusting    k-nearest neighbor algorithm    dynamic movement primitives

1 基于DMP模型的轨迹生成

DMP[12-13]通过加有外部干扰项的线性弹簧阻尼系统实现对任意形状轨迹的动作表达。每个独立自由度上的动力学表达式如下

 $\tau \dot v = K\left( {g - x} \right) - Dv + f\left( s \right)$ (1)
 $\tau \dot x = v$ (2)

 $f\left( s \right) = \frac{{\mathop \sum \limits_i {\omega _i}{\psi _i}\left( s \right)s}}{{\mathop \sum \limits_i {\psi _i}\left( s \right)}}$ (3)

 Download: 图 1 基于DMP模型的轨迹生成方法 Fig. 1 Trajectory generation based on DMP model
2 基于距离加权k-NN算法的轨迹修正

2.1 基于距离加权k-NN的轨迹修正算法

 $T = {T_{{\rm{original}}}} + \Delta T$ (4)

1) 计算轨迹点Pi到每一个训练数据Pk的距离。本文采用欧式距离‖Pi-Pk‖；

2) 按照距离由小到大对训练数据进行排序；

3) 确定最近邻域个数K，本文暂定为10；

4) 按照反距离加权法计算轨迹点Pi的修正值ΔPi。其中，每个训练数据的权值与到该轨迹点的距离成反比。

 ${\omega _k} = {{\rm{e}}^{ - \lambda \left\| {{P_i} - {P_k}} \right\|}}/\left( {\sum\limits_{k = 1}^K {{{\rm{e}}^{ - \lambda \left\| {{P_i} - {P_k}} \right\|}}} } \right)$ (5)

 $\Delta {P_i} = \sum\limits_{k = 1}^K {({\omega _k}{d_k})}$ (6)

 Download: 图 4 y=exp(-λx)的函数关系曲线图 Fig. 4 The functional relationship graphic of y=exp(-λx)

 $\Delta {P_i} = \sum\limits_{k = 1}^K {\left( {\frac{1}{{1 + {{\rm{e}}^{\alpha (\left\| {{P_i} - {P_k}} \right\| - {P_{{\rm{threshold}}}})}}}}{\omega _k}{d_k}} \right)}$ (7)

 Download: 图 5 训练点到轨迹点距离与该训练点对轨迹修正值影响力的关系 Fig. 5 The relationship between the distance from training data to the trajectory point and the influence of the training data on the adjustment

 $\begin{array}{*{20}{c}} {\Delta {P_i} = }\\ {\sum\limits_{k = 1}^K {\left( {\frac{1}{{1 + {{\rm{e}}^{\beta (\left\| {{R_i} - {r_k}} \right\| - {R_{{\rm{threshold}}}})}}}}\frac{1}{{1 + {{\rm{e}}^{\alpha (\left\| {{P_i} - {P_k}} \right\| - {P_{{\rm{threshold}}}})}}}}{\omega _k}{d_k}} \right)} } \end{array}$ (8)

3 训练数据的更新

FOR k=1：1：M

data_new(k)=data(M-k+1)；

ENDFOR

num=M；   \\需要具有两个或两个以上训练数据

FOR i=1:1：num-1

FOR j=i+1:1：num

IF (‖ pj- pi‖ < δupdate )& (‖rj- ri‖ < δupdate )

DELETE data_new(j) \\删除该训练数据

ENDIF

ENDFOR

ENDFOR

4 避障能力实验 4.1 实验平台

4.2 避障能力测试

 Download: 图 10 机器人相对障碍物环境静止时，轨迹避障实验 Fig. 10 Obstacle avoidance experiment of the trajectory in the case that robot is relative static to the obstacle environment

 Download: 图 11 机器人跟随初始点移动时，轨迹避障实验 Fig. 11 Obstacle avoidance experiment of the trajectory in the case that robot is following the position of start point

 Download: 图 12 避障决策实验 Fig. 12 Experiment of making obstacle avoidance decision

 Download: 图 13 多障碍物场景的信息融合 Fig. 13 Information fusion of multiple obstacle scenarios
4.3 避障算法的实时性测试