A Collision-Free Motion Planning for Two Robot Arms using Minimum Distance Functions

SummaryThis paper presents a collision-free motion planning method of two articulated robot arms in a three dimensional common work space. Each link of a robot arm is modeled by a cylinder ended by two hemispheres, and the remaining wrist and hand is modeled by a sphere. To describe the danger of collision between two modeled objects, minimum distance functions, which are defined by the Euclidean norm, are used. These minimum distance functions are used to describe the constraints that guarantee no collision between two robot arms. The collision-free motion planning problem is formulated as a pointwise constrained nonlinear minimization problem, and solved by a conjugate gradient method with barrier functions. To improve the minimization process, a simple grid technique is incorporated. Finally, a simulation study is presented to show the significance of the proposed method.

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Obstacle Avoidance Influence Coefficients for Manipulator Motion Planning

Volume 7: 29th Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2005-84223 ◽

2005 ◽

Cited By ~ 4

Author(s):

Troy Harden ◽

Chetan Kapoor ◽

Delbert Tesar

Keyword(s):

Motion Planning ◽

Obstacle Avoidance ◽

Minimum Distance ◽

Higher Order ◽

Second Order ◽

Distance Functions ◽

Cluttered Environments ◽

Finite Difference Approximations ◽

Planning Decisions ◽

Influence Coefficients

Motion planning in cluttered environments is a weakness of current robotic technology. While research addressing this issue has been conducted, few efforts have attempted to use minimum distance rates of change in motion planning. Geometric influence coefficients provide extraordinary insight into the interactions between a robot and its environment. They isolate the geometry of distance functions from system inputs and make the higher-order properties of minimum distance magnitudes directly available. Knowledge of the higher order properties of minimum distance magnitudes can be used to predict the future obstacle avoidance, path planning, and/or target acquisition state of a manipulator system and aid in making intelligent motion planning decisions. Here, first and second order geometric influence coefficients for minimum distance magnitudes are rigorously developed for several simple modeling primitives. A general method for similar derivations using new primitives and an evaluation of finite difference approximations versus analytical second order coefficient calculations are presented. Two application examples demonstrate the utility of minimum distance magnitude influence coefficients in motion planning.

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