1. Multi-Arm Manipulation Planning (1994) Yoshihito Koga Jean-Claude Latombe

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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)

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. Simple Example

17. 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

18. Limitations/Extensions  Take advantage of stable configurations on the floor or some obstacle  Multiple movable objects  More realistic models of dynamics and torques