Tham khảo tài liệu 'control of redundant robot manipulators - . patel and f. shadpey part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 36 3 Collision Avoidance for a 7-DOF Redundant Manipulator represent the arm and its environment. Colbaugh et al. 14 addressed this problem for a planar manipulator. The obstacles were represented by circles surrounded by a Surface of Influence SOI and the links were modeled by straight lines. A redundancy-resolution scheme was proposed to achieve obstacle avoidance. This approach was extended to the 3-D workspace of a 7-DOF manipulator in 75 71 24 . In 75 and 71 the manipulator links are represented by spheres and cylinders and the objects by spheres. Although this method is convenient for spherical or bulky objects it results in major reduction of the workspace when dealing with slender objects. Moreover the method is not capable of dealing with tasks involving passing through an opening. Glass et al. 24 proposed a scheme that considered an application to remote surface inspection. This application requires the robot to pass through circular or rectangular openings for inspection of a space structure such as the International Space Station. However they made the restrictive assumption of having an infinite surface with one opening which reduces the workspace of the robot. For instance this scheme does not permit an elbow to back into another opening. Moreover the arm used in their experiment the Robotics Research Corporation 7-DOF arm RRC is modeled as a series of four straight lines connecting joints one three and five. The thickness of the links is considered via a buffer region in the openings. This simplified model would not be appropriate for an arm with a more complex geometry such as the one used in the research described in this paper. A simplified geometrical model for links of industrial manipulators relevant to the study of collisions either with each other or with objects in the workspace is the cylinder. Also the cylinder is a very appropriate primitive for modelling many objects in the workspace such as rods mesh structures openings etc. without .