Precomputed Search Trees: Planning for Interactive Goal-Driven Animation Manfred Lau and James Kuffner Carnegie Mellon University

Motion Planning approach InputsOutput

Behavior Planner Lau and Kuffner. “Behavior Planning for Character Animation.” SCA 05

Motivation Efficient algorithm for:  large number of characters  global planning  re-plan continuously in real- time  dynamic environment  complex motions including jump, crawl, duck, stop- and-wait

Main contribution Precomputed Search Tree

Traditional Planning ~50,000 μs for 1 s of motion

Precomputed Search Trees ~250 μs for 1 s of motion

Overview FSM Environment

Overview Precompute FSM Environment 1) Search Tree

Overview FSM Environment Precompute 2) Gridmaps

Overview FSM Environment Precompute 1) Search Tree 2) Gridmaps Runtime

Overview FSM Environment Precompute 1) Search Tree 2) Gridmaps Runtime 1) Map Obstacles

Overview FSM Environment Precompute 1) Search Tree 2) Gridmaps Runtime 1) Map Obstacles 2) Path Finding

Overview – Distant Goal Coarse-Level Planner

Overview – Distant Goal Coarse-Level PlannerRepeatedly select sub-goal and run each sub-case

Related Work Motion Planning Kuffner 98 Shiller et al. 01 Bayazit et al. 02 Choi et al. 03 Pettre et al. 03 Sung et al. 05 Koga et al. 94 Kalisiak and van de Panne 01 Yamane et al. 04 Choi et al. 03 Global Navigation Manipulation and whole-body motions

Related Work Precomputation Lee and Lee 04 Reitsma and Pollard 04 Re-playing original motion capture data Arikan and Forsyth 02 Kovar et al. 02 Lee et al. 02 Pullen and Bregler 02 Gleicher et al. 03 Lee et al. 06 Lee and Lee 04 Kovar et al. 02

Related Work Motion Vector Fields / Steering Approaches Brogan and Hodgins 97 Menache 99 Reynolds 99 Mizuguchi et al. 01 Treuille et al. 06 Treuille et al. 06

Advantages of our approach Precomputed Search Trees:  many characters re-plan continuously in real-time  global planning – as opposed to local policy methods  complex motions – jump, crawl, duck, stop-and-wait  one tree – can be used for all characters, and different environments

Environment Representation Obstacle Growth in Robot Path Planning Udupa 77 Lozano-Pérez and Wesley 83 Special regions for crawl/jump

Behavior Finite-State Machine

Precompute 1) Search Tree 2 levels, 3 behavior states

Precompute 1) Search Tree

Precompute 1) Search Tree represents all states reachable from current state 5 levels, 7 behavior states

Precompute 1) Search Tree – Pruned to ~10 MB exhaustivepruned

Precompute 2) Environment Gridmap used to identify the tree nodes that are blocked by obstacles

Precompute 2) Goal Gridmap used to efficiently extract all paths that reach goal from start state

Runtime 1) Map obstacles to Environment Gridmap

Runtime 1) Map obstacles to Environment Gridmap

Runtime 2) Path Finding – reverse path lookup (vs. forward search)

Runtime 2) Path Finding – take shortest path that reaches goal root obstacle

Runtime 2) Path Finding – take shortest path that reaches goal

Runtime 2) Path Finding – take shortest path that reaches goal

Motion Generation / Blending Sequence of behaviors  converted to actual motion Blending at frames near transition points Linearly interpolate root positions Smooth-in, smooth-out slerp interpolation for joint rotations

Planning to distant goals Only up to specific level

Intermediate goal points Apply precomputed tree repeatedly

Intermediate goal points Apply precomputed tree repeatedly

Intermediate goal points Apply precomputed tree repeatedly

Distant goal example Run coarse bitmap planner first

Distant goal example Find sub-goalRun sub-case

Distant goal example Find sub-goalRun sub-case

Distant goal example Final solution

Distant goal example Final solution

Result – speedup Precomputed Trees A*-search Avg. runtime or 3, ,591 search time (μs) 176 times faster Avg μs per frame ,445 Avg pathcost Avg time of synthesized 13,123,333 12,700,000 motion (μs) Real-time speedup 4,191 times 23 times

Tradeoff: Motion Quality vs. Memory exhaustive tree

Single Character Mode  complete solution path for one character continuously re-generated, as the user changes environment  large environment (70 by 70 meters), takes 6 ms to generate full path

Multiple Character Mode  execute “runtime path finding” phase only after we start rendering the first frame from the previous partial path  precompute blend frames (~20 motion clips), precompute all pairs  separate gridmaps for collision avoidance between characters  same precomputed tree for all characters

Summary Advantages of our approach:  large number of characters  global planning  re-plan continuously in real-time  complex environment  complex motions Precomputed Search Tree

Summary Advantages of our approach:  large number of characters  global planning  re-plan continuously in real-time  complex environment  complex motions Precomputed Search Tree Thank you! Questions.