Manipulator path planning by decomposition: algorithm and analysis

Abstract

Path planning is achieved by a special decomposition of the robot manipulator, an off-line preprocessing stage, and a three phase on-line path planning scheme. The decomposition consists of separating the robot into several chains where a chain is a combination of several consecutive links and joints. Preprocessing is performed by defining a set of postures for each chain and setting up a collision table which re-integrates the chains into the full robot and stores the collision states of various discretized robot configurations with the obstacles. Path planning using a local search is performed independently in joint subspaces associated with robot chains. The paths found for the chains are synthesized to obtain a collision-free path for the robot. This decomposition reduces the exponential growth of computation with robot degrees of freedom (DOF) to that of the much lower chain DOF. As a result, it is possible to achieve short planning times for practical robots operating in three-dimensional work spaces. Analysis of computation time and space of the proposed method are presented. Results supporting the analysis are provided for a large number of path-planning trials with two practical robots operating in relatively cluttered environments.

Inverse Kinematics of 7-DOF Robots and Limbs by Decomposition and Approximation

“…The swivel angle in (2) is a function of the first four joint angles and arm lengths and offsets. For the zero-offset anthropomorphic arm, (2) simplifies to = a tan2 s 2 s 3 s 4 ; d 5 s 4 (c 2 s 4 + s 2 c 3 (1 + c 4 )) =d (3) where d = d 2 3 + d 2 5 + 2d 3 d 5 c 4 . It is noted that the position x; y; z and the swivel angle are functions of the first four joint angles only.…”

“…Swivel angle can be used to constrain a selected point on the limb, to perform aiming of the hand towards a target point, to keep the figure balanced [6], or to avoid collision with an obstacle. The equation for the swivel angle in the general case of the arm with offset is given by [10] = a tan2 v T 1 (v2 2 v3); v T 2 v3 (2) where v 1 ; v 2 ; and v 3 are vectors defined in [10] that are drawn using the origins of the wrist, shoulder, and elbow frames. The swivel angle in (2) is a function of the first four joint angles and arm lengths and offsets.…”

“…The IK mapping is in general one to many, involves complex inverse trigonometric functions, and, for most manipulators and animation figures, has no closed-form solutions. Extremely fast IK computation is required in computer animation [1] and for real-time applications in fast moving manipulators, e.g., path planning (see, for example, [2] and references therein).…”

Trajectory planning for surface following with a manipulator under RGB-D visual guidance

“…Similarly, several approaches have been proposed to solve the path planning problem, including cell decomposition techniques, skeletons, and potential fields [8,9]. In addition, soft computing approaches, such as neural networks [10], fuzzy logic [11], and evolutionary algorithms [12], have been developed.…”

Global path planning and navigation of an omnidirectional Mecanum mobile robot

“…These global path planning problems have been solved using many existing approaches, such as cell decomposition [2][3], skeleton and potential field [4]. In addition, soft computing approaches, such as fuzzy logics [5], neural networks [6], and evolutionary algorithm [7], have been widely used to solve the global path planning problems.…”