# A Path Optimization Technique with Obstacle Avoidance for an 8-DOF Robot in Bolt Looseness Detection Task

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## Abstract

In the bolt looseness detection task of the locomotive system, the robot could be used to highly improve the working efficiency and reliability, but faces the complex static obstacles while planning the path for the robotic motion. In this paper, a path optimization technique is proposed to obtain an optimal path with obstacle avoidance for a redundant robot in the static complicated environment. There are three main contributions in this technique. The first is the solving of the inverse kinematics problem for a redundant robot based on the screw theory and the geometric description, which is general to all robots with rotational joints. The second is the modeling of the spatial constraint, where the pseudo distance is defined based on the plane description of the obstacles and calculated using the spatial analytic geometry knowledge. The third is the presentation of the whole path-planning framework based on the above two contributions, which could largely improve the generality of the presented technique. In this framework, the minimum-time path could be obtained while guaranteeing both the motion stability and obstacle avoidance. Moreover, a real setting that includes an obstacle environment and an 8-DOF robot, is taken as an example to better present the technique. Finally, the simulation experiment was performed in Isight software to verify the effectiveness of the path optimization technique.

## Keywords

Redundant manipulator Path optimization Obstacle avoidance Inverse kinematics Motion stability## List of symbols

- \( {\text{a}},{\text{b}},{\text{c}} \)
Parameters used in spatial equation of the obstacle plane

- \( {\text{a}}_{1} , \ldots ,{\text{a}}_{6} \)
Parameters used in the quintic polynomial function

- \( {\text{A}} \)
Maximum absolute value of angular acceleration for one joint

- \( {\mathbf{c}} \)
Position vector of the intersection between the trajectory planes

- \( {\text{c}}0, \ldots ,{\text{c}}6 \)
Condition parameters used in pseudo distance modeling

- \( {\text{d}} \)
A distance taken for the reliable operation

- \( {\text{D}} \)
Pseudo distance

- \( {\text{Dt}} \)
Threshold value used for ensuring the reliable avoidance

- \( {\text{gst}} \)
Pose of the end effector

- \( {\mathbf{J}} \)
Position vector of the end of the robot-link centerline

- \( {\text{L}} \)
Dimension parameters used in the kinematic model

- \( {\text{N}}_{{\rm c}} \)
Number of the intersections between the projection and the obstacle boundaries

- \( {\mathbf{n}}_{{\rm o}} \)
Normal vector of one obstacle plane

- \( {\mathbf{O}} \)
Position vector of the vertex on the obstacle plane

- \( {\mathbf{P}} \)
Position vector of the real end effector

- \( {\mathbf{q}} \)
Positon vector of a point fixed on the axis

- \( {\text{R}} \)
Bottom radius of one robotic link

- \( {\mathbf{S}} \)
Position vector of the intersection between one projected line and one boundary line

- \( {\text{t}},{\text{T}} \)
Motion times of one trajectory and the total path

- \( {\text{V}} \)
Maximum absolute value of angular velocity for one joint

- \( {\text{x}},{\text{y}},{\text{z}} \)
Coordinate parameters for one point

- \( \upeta \)
Parameter used in the parametric equation of one line

- \( \uplambda \)
Criterion index used in the selection of the unique IK solution

- \( \uptheta,{\uptheta^{\prime}},{\uptheta^{\prime\prime}} \)
Angular displacement, angular velocity and angular acceleration of one joint

- \( {\varvec{\upomega}} \)
Initial unit vector of one rotational axis

- \( {\varvec{\upxi}} \)
Twist motion coordinate of one joint

- \( {\varvec{\Omega}}\,, \, {\varvec{\Omega}^{\prime}} \)
Target orientations of the real and nominal end effectors

- \( \Pi_{{\rm O}} \)
One obstacle plane

## Notes

### Acknowledgements

This work was supported by Beijing Municipal Science & Technology Commission (No: D17110400590000); National Natural Science Foundation (No. 51575009); BJTT united Grand scientific research program on intelligent manufacturing (No. 001000546317515) and Jing-Hua Talents Project of Beijing University of Technology.

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