Tham khảo tài liệu 'mobile robots -towards new applications 2008 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Safe Motion Planning for Human-Robot Interaction Design and Experiments 151 operational space. The potential field is used to generate forces to pull the robot away from any obstacles and the end effector towards the goal. This approach does not require extensive precomputation of the global path can operate on-line and can be easily adapted to sensor based planning and dynamic obstacles. When a redundant robot is used this approach can be extended to allow the robot to continue executing the task while avoiding obstacles Khatib 1995 . Maciejewski and Klein Maciejewski and Klein 1985 proposed a similar method for redundant manipulators and tasks where a goal trajectory is specified and not just a goal location. In this approach the force generated by the obstacle avoidance potential field is mapped to the null space of the redundant manipulator so that the robot can continue to execute the goal trajectory while using its redundant degrees of freedom to avoid obstacles. A major issue with these planning methods is that only local search is used so the robot can reach a local-minimum that is not at the goal location. A second issue is the formulation of the forces applied to the robot in the operational space. This requires the use of the robot Jacobian to translate these forces to joint torques and introduces position and velocity error near any robot singularities. Nokata et al. Nokata Ikuta et al. 2002 use a danger index based on the impact force between a human and the end effector. The danger index is the ratio of the actual force to the largest safe impact force an impact force that does not cause injury to the human . The danger index is calculated based on factors such as the distance and velocity between the human and the manipulator end effector. Two approaches are proposed for planning the motion of a planar robot end effector minimizing the greatest danger index along the path and minimizing the total amount integral of the danger index along the path. .