Motion Planning A Journey of Robots Digital Actors

Motion Planning: A Journey of Robots, Digital Actors, Surgical Instruments, Molecules and Other Artifacts Jean-Claude Latombe Computer Science Department Stanford University

Goal of Motion Planning u Compute motion strategies, e. g. : – – – u geometric paths time-parameterized trajectories sequence of sensor-based motion commands To achieve high-level goals, e. g. : – – go from A to B without colliding with obstacles assemble product P build map of environment E find object O

Basic Problem

Extensions to the Basic Problem u Moving obstacles u Dynamic constraints u Multiple robots u Optimal planning u Movable objects u u Assembly planning u u Goal is to acquire information by sensing u – Model building – Object finding/tracking Nonholonomic constraints u u Uncertainty in control and sensing Exploiting task mechanics (sensorless motions) Physical models and deformable objects Integration of planning and control

Outline u Some historical steps and achievements u Applications u Computational approaches: – Criticality-based motion planning – Random-sampling motion planning u Some challenging problems ahead

Early Work Shakey (Nilsson, 1969): Visibility graph

Mathematical Foundations Lozano-Perez, 1980: Configuration Space C = S 1 x S 1

Computational Analysis Reif, 1979: Hardness (lower-bound results)

Exact General-Purpose Path Planners - Schwarz and Sharir, 1983: Exact cell decomposition based on Collins technique - Canny, 1987: Silhouette method

Heuristic Planners Khatib, 1986: Potential Fields

Nonholonomic Robots Laumond, 1986

Underactuated Robots Lynch, Shiroma, Arai, and Tanie, 1998

Part Orientation Godlberg, 1993

Assembly Sequence Planning Wilson, 1994: Non-Directional Blocking Graphs

Manipulation Planning Tsai-Yen Li, 1994

Deformable Objects Kavraki, Lamiraux, and Holleman 1998

Target Finding Guibas, Latombe, La. Valle, Lin, and Motwani, 1997

Integration of Planning and Control Brock and Khatib, 1999

Outline u Some historical steps and achievements u Applications u Computational approaches: – Criticality-based motion planning – Random-sampling motion planning u Some challenging problems ahead

Robot Programming and Placement David Hsu, 1999

Design for Manufacturing and Servicing General Electric General Motors

Design of Large Facilities EDF and LAAS-CNRS (MOLOG project), 1999

Verification of Building Code Charles Han, 1998

Graphic Animation of Digital Actors The Motion Factory Koga, Kondo, Kuffner, and Latombe, 1994

Graphic Animation of Digital Actors Digital Actor = Virtual Robot! Plan Sense Act Kuffner, 1999

Graphic Animation of Digital Actors Simulated Vision u Segment environment u Render false-color scene offscreen u Scan pixels & record IDs Actor camera image Vision module image

Graphic Animation of Digital Actors

Surgical Planning Cyberknife System (Accuray, Inc. ) CARABEAMER Planner Tombropoulos, 1997

Prediction of Molecular Motions Amit Singh, 1999

Outline u Some historical steps and achievements u Applications u Computational approaches: – Criticality-based motion planning – Random-sampling motion planning u Some challenging problems ahead

Approaches to Motion Planning u Goal: Answer queries about the connectivity of a certain space (e. g. , the collision-free subset of configuration space)

Approaches to Motion Planning u Old view (Latombe, 1991): – Roadmaps – Cell decomposition – Potential field

Approaches to Motion Planning u Old view (Latombe, 1991): – Roadmaps – Cell decomposition – Potential field u New View (Latombe, 2000): – Finding criticalities – Random sampling

Criticality-Based Motion Planning Retraction on Voronoi Diagram (O’Dunlaing and Yap, 1982)

Criticality-Based Motion Planning Part orientation (Goldberg, 1993)

Criticality-Based Motion Planning Non-Directional Blocking Graphs for assembly planning (Wilson, 1994)

Criticality-Based Motion Planning Non-Directional Preimage for landmark-based navigation (Lazanas, 1995)

Criticality-Based Motion Planning Target finding (Guibas, Latombe, La. Valle, Lin, and Motwani, 1997)

Criticality-Based Motion Planning Target finding (Guibas, Latombe, La. Valle, Lin, and Motwani, 1997) 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)

Criticality-Based Motion Planning Target finding (Guibas, Latombe, La. Valle, Lin, and Motwani, 1997) Recontaminated area

Criticality-Based Motion Planning u Advantage: – Completeness u Drawbacks: – Computational complexity – Difficult to implement

Outline u Some historical steps and achievements u Applications u Computational approaches: – Criticality-based motion planning – Random-sampling motion planning u Some challenging problems ahead

Random-Sampling Planning (Probabilistic Roadmap) admissible space milestone qg qb [Kavraki, Svetska, Latombe, Overmars, 95]

Motivation Computing an explicit representation of the admissible space is hard, but checking that a point lies in the admissible space is fast

Why Does it Work? Relation with Art-Gallery problems [Kavraki, Latombe, Motwani, Raghavan, 95]

In Theory, Random-Sampling Planning… u u Is probabilistically complete, i. e. , whenever a solution exists, the probability that it finds one tends toward 1 as the number N of milestones increases Under general hypotheses, the rate of convergence is exponential in N, i. e. : Prob[failure] = K exp(-N) u Computational gain is obtained against a “small” loss of completeness

Expansiveness of Admissible Space

Expansiveness of Admissible Space The admissible space is expansive if each of its subsets has a large lookout Lookout of F 1 Prob[failure] = K exp(-N)

In practice, Random-Sampling Planners… u Are fast u Deal effectively with many-dof robots u Deal well with complex admissibility constraints u Are easy to implement u Have solved complex problems

Real-Time Planning with Dynamic Constraints robot obstacles air thrusters gaz tank air bearing (Kindel, Hsu, Latombe, and Rock, 2000)

Total duration : 40 sec

Interactive Planning of Manipulation Motions Transfer Reach Return Kuffner, 1999 Grab Release

Random-Sampling Radiosurgical Planning Cyberknife (Neurosurgery Dept. , Stanford, Accuray) CARABEAMER Planner Tombropoulos, 1997

Random-Sampling Radiosurgical Planning Dose to the Tumor Region Tumor Dose to the Critical Region Critical Fall-off of Dose Around the Tumor Fall-off of Dose in the Critical Region

Random-Sampling Radiosurgical Planning

Random-Sampling Radiosurgical Planning • 2000 < Tumor < 2200 T B 1 B 2 2000 < B 2 + B 4 < 2200 2000 < B 3 < 2200 2000 < B 1 + B 3 + B 4 < 2200 2000 < B 1 + B 2 < 2200 C B 3 B 4 • 0 < Critical < 500 0 < B 2 < 500

Sample Case 50% Isodose Surface 80% Isodose Surface Conventional system’s plan CARABEAMER’s plan

Randomized Next-Best View Planning (Gonzalez, 2000)

Outline u Some historical steps and achievements u Applications u Computational approaches: – Criticality-based motion planning – Random-sampling motion planning u Some challenging problems ahead

Reconfiguration Planning for Modular Robots Mark Yim, 1999 Xerox, Parc

Planning Minimally Invasive Surgery Procedures Amidst Soft Tissue Structures

Truly Autonomous Interactive Digital Actors with Nice-Looking Motions A Bug’s Life (Pixar/Disney) Tomb Raider 3 (Eidos Interactive) Toy Story (Pixar/Disney) The Legend of Zelda (Nintendo) Antz (Dreamworks) Final Fantasy VIII (Square. One)

Generating Energetically Plausible Docking and Folding Motions of Proteins

Conclusion u u u Over the last decade there has been tremendous progress in motion planning and its application Though motion planning originated in robotics, applications are now very diverse: design, manufacturing, graphic animation, video games, surgery, biology, etc… Most future problems in motion planning are likely to be motivated by applications that are regarded today as non-robotics applications