Motion Planning CS121 – Winter 2003 Motion Planning
Basic Problem Are two given points connected by a path? Motion Planning
From Robotics … Motion Planning
… to Graphic Animation … Motion Planning
… to Biology Motion Planning
… to Biology Motion Planning
How Do You Get There? ? Motion Planning
Approximate the free space Configuration Space Approximate the free space by random sampling Problems: Geometric complexity Number of dimensions of space How to discretize the free space? Motion Planning
Digital Character q q Q(t) Parts DOF L 19 68 H 51 118 1 2 n 3 4 n 4 q 2 Parts DOF L 19 68 H 51 118 Joint variables are avars for primary motions. A Motion clip is a curve parameterized by time in the joint space (C-space). MPEG4-SNHC standard body description each hand = 25 DOF lower body = 21 upper body = 62 global hip position & orientation = 6 Q(t) Motion Planning
Approximate the free space Configuration Space Approximate the free space by random sampling Problems: Geometric complexity Number of dimensions of space How to discretize the free space? Motion Planning
Hierarchical Collision Checking Motion Planning
Example in 3D Motion Planning
Hierarchical Collision Checking Motion Planning
Hierarchical Collision Checking Motion Planning
Performance Evaluation Collision checking takes between 0.0001 and .002 seconds for 2 objects of 500,000 triangles each on a 1-GHz Pentium III Collision checking is faster when objects collide or are far apart, and gets slower when they get closer without colliding Overall collision checking time grows roughly as the log of the number of triangles Motion Planning
Probabilistic Roadmap (PRM) local path free space milestone mb mg Motion Planning
Why It Works Motion Planning
Narrow Passage Issue Easy Difficult Motion Planning
Probabilistic Completeness Under the generally satisfied assumption that the free space is expansive, the probability that a PRM finds a path when one exists goes to 1 exponentially in the number of milestones (~ running time). Motion Planning
Multi-Query Sampling Strategies Motion Planning
Multi-Query Sampling Strategies Multi-stage strategies Obstacle-sensitive strategies Narrow-passage strategies Motion Planning
Single-Query Sampling Strategies mb mg Motion Planning
Single-Query Sampling Strategies mb mg Diffusion strategies Adaptive-step strategies Lazy collision checking Motion Planning
Examples Nrobot = 3,000; Nobst = 50,000 Nrobot = 5,000; Nobst = 83,000 Tav = 0.17 s Nrobot = 5,000; Nobst = 83,000 Tav = 4.42 s Motion Planning
Design for Manufacturing/Servicing General Motors General Motors General Electric [Hsu, 2000] Motion Planning
Modular Reconfigurable Robots Casal and Yim, 1999 Xerox, Parc Motion Planning
Motion Planning
[Kuffner and Inoue, 2000] (U. Tokyo) Humanoid Robot [Kuffner and Inoue, 2000] (U. Tokyo) Motion Planning Stability constraints
Space Robotics robot obstacles air thrusters gas tank air bearing [Kindel, 2000] Dynamic constraints Motion Planning
Single-Query Sampling Strategies mb mg Motion Planning
Total duration : 40 sec Motion Planning
Autonomous Helicopter [Feron, 2000] (AA Dept., MIT) Motion Planning
Other goals The goal may not be to attain a given position, but to achieve a certain condition, e.g.: - Irradiate a tumor - Build a map of an environment - Sweep an environment to find a target Motion Planning
Radiosurgery: Irradiate a Tumor Motion Planning
Mobile Robots: Map Building Motion Planning
Next-Best View Motion Planning
Example Motion Planning
Information State Example of an information state = (1,1,0) 0 : the target does not hide beyond the edge 1 : the target may hide beyond the edge Example of an information state = (1,1,0) Motion Planning
Critical Curve Motion Planning
More Complex Example Motion Planning
Example with Two Robots (Greedy algorithm) Motion Planning
Surgical Planning Motion Planning
Half-Dome, NW Face, Summer of 2010 … Motion Planning Tim Bretl
Motion Planning
Rock-Climbing Robot Motion Planning
Motion Planning
Motion Planning
Motion Planning