Multi-Arm Manipulation Planning (1994)

Yoshihito Koga

Jean-Claude Latombe

Motivation For Multi-Arm Planning

Improved efficiency through simultaneous motion Cooperate to move heavy/bulky objects Increased workspace of the moving objects by

passing the object from one arm to the other

Problem Overview

3D Workspace

Movable object M, with 6 degrees of freedom

Multiple robot arms working together to move M from initial to goal configuration

Grasping

A grasp is a rigid attachment of the last link in an arm to M

Predefined finite grasp set set associated with M

2 Types of movable objects considered:• Those that can be moved by a single grasping robot

• Those that can be moved by 2 grasping robots

Algorithm Overview

Particularly designed for problems of a complexity found in manufacturing (assembling, welding, etc.)

Problems of this type are so complicated with so many degrees of freedom that it is not feasible to search the whole configuration space

Sacrifice completeness in nasty cases by making reasonable assumptions for these types of problems

Decompose path planning process into smaller pieces

Space Types Stable space: set of all legal configurations where movable

object M is statically stable Grasp space: set of all legal configurations where at least

one robot is grasping M with sufficient torque to move it

Path Types Transit path: arm motions that do not change position of M Transfer path: arm motions that changes position of M Manipulation Path: alteration of transit and transfer paths

from initial configuration to goal configuration

Algorithm Intuition Stage 1: Plan all transfer tasks in sequence, defining exactly

when and where grasp transfers of M are made Stage 2: Fill in each transit path (start and goal

configurations were exactly defined by transfer tasks)

Algorithm Intuition This decomposition greatly reduces search time Makes assumption that some valid transit path must exist

between the 2 valid endpoint configurations defined in the transfer path phase; not unreasonable for arms in 3D space

Stage 1: Transfer Path Generation

Generation of a path obj that defines a path of M from start to goal such that the necessary number of arms are grasping M at all times

Might involve several changes changes of grasping arms

Uses a modified version of the RPP algorithm

Modified RPP

Iteratively moves M toward the goal in small steps determined by a potential field

At each step M cannot intersect with an obstacle, and there must be some legal grasping of M

Modified RPP

Maintain a set of possible grasp assignments first computed at the initial state

At each step of RPP, if any grasp in this set is no longer possible, remove it from the grasp set

If the grasp set becomes empty recompute all possible grasp assignments for that position of M; this represents a grasp change and a transit path will have to be planned

Modified RPP

Assume that each arm has some predefined non-obstructive position that it can move while other arms are involved in a transfer path

Stage 2: Transit Path Generation Transfer path planning phase defines several transit

path problems; assume each is solvable First and last transit paths are easy and can be

solved with a normal planning algorithm such as regular RPP

Middle transit paths (between 2 transfer paths) are harder because we must change grasps while maintaining M in a stable configuration

Stage 2: Transit Path Generation Transit task might require

several regrasps to solve Generate all grasping

assignments achievable from initial configuration

Generate successors of these grasping assignments until goal grasp is achieved

Simple Example

Conclusion Fast but not necessarily complete Planned paths are good in terms of distance traveled

by M and number of regrasps done in that path Parallel processing possible

Limitations/Extensions Take advantage of stable configurations on the

floor or some obstacle Multiple movable objects More realistic models of dynamics and torques