CS 326 A: Coordination of Multiple Robots

1
CS 326 A Coordination of Multiple Robots

• Two main approaches
• Decoupled PlanningPlan for each robot
  independently of the others and coordinate them
  later
• Centralized PlanningPlan the motion of the
  robots in their composite configuration space

2
Planning with Moving Obstacles

• Moving obstacles require planning a trajectory
  t t1,t2 ? F i.e., a
  path indexed by time
• A trajectory is best represented configuration x
  time space CT. In this space a trajectory is a
  continuous curve whose tangent always projects
  positively onto the time axis
• Obstacles map as forbidden regions into CT.
  Constraints on velocity constrain tangents to t.
  Constraints on acceleration constrain curvature
  of t

(See class 9 on Kinodynamic Planning
Programming project)
3
Example
t
y
x
4
Coordination of Multiple Robots

• Does not require explicit introduction of time
  (except if there are moving obstacles)
• Only requires using the same parameter to index
  the paths of the coordinated robots
• Using the same indexing parameter corresponds to
  fixing the relative velocities of the robots

5
Decoupled Planning

• Pure velocity tuning(1) Separately plan the
  path of each robot to avoid collision with
  (static) obstacles(2) Compute the relative
  velocities of the robots to avoid inter-robot
  collision (e.g., coordination diagram)
• Robot prioritization- Plan path of a first
  robot in its configuration space- Iterate Plan
  trajectory of ith robot in its configuration x
  time space assuming that robots 1,,i-1 are
  obstacles moving at some velocities

6
Centralized Planning

• Plan a collision-free path in the composite
  configuration C1 x C2 xx Cp space of the robots
• Forbidden regions in the composite configuration
  space are all configurations where either a robot
  collide with an obstacle or two robots collide
  with one another
• The projection of this path into Ci is the path
  of the ith robot

7
Pros and Cons

• Assume p robots with n degrees of freedom each.
• Worst-case complexity of centralized planning
  ison the order of enp
• Worst-case complexity of decoupled planning ison
  the order of pen ltlt enp
• But decoupled planning is incomplete