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

Compute motion strategies, e.g.:
– 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
Goal of Motion Planning

Compute motion strategies, e.g.:
– 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
Goal of Motion Planning

Compute motion strategies, e.g.:
– 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

Moving obstacles

Dynamic constraints

Multiple robots

Optimal planning

Movable objects


Assembly planning
Uncertainty in control and
sensing

Goal is to acquire
information by sensing

Exploiting task mechanics
(sensorless motions)

Physical models and
deformable objects

Integration of planning
and control
– Model building
– Object finding/tracking

Nonholonomic constraints
Extensions to the Basic Problem

Moving obstacles

Dynamic constraints

Multiple robots

Optimal planning

Movable objects


Assembly planning
Uncertainty in control and
sensing

Goal is to acquire
information by sensing

Exploiting task mechanics
(sensorless motions)

Physical models and
deformable objects

Integration of planning
and control
– Model building
– Object finding/tracking

Nonholonomic constraints
Extensions to the Basic Problem

Moving obstacles

Dynamic constraints

Multiple robots

Optimal planning

Movable objects


Assembly planning
Uncertainty in control and
sensing

Goal is to acquire
information by sensing

Exploiting task mechanics
(sensorless motions)

Physical models and
deformable objects

Integration of planning
and control
– Model building
– Object finding/tracking

Nonholonomic constraints
Extensions to the Basic Problem

Moving obstacles

Dynamic constraints

Multiple robots

Optimal planning

Movable objects


Assembly planning
Uncertainty in control and
sensing

Goal is to acquire
information by sensing

Exploiting task mechanics
(sensorless motions)

Physical models and
deformable objects

Integration of planning
and control
– Model building
– Object finding/tracking

Nonholonomic constraints
Outline

Some historical steps and achievements

Applications

Computational approaches:
– Criticality-based motion planning
– Random-sampling motion planning
 Some challenging problems ahead
Early Work
Shakey (Nilsson, 1969): Visibility graph
Mathematical Foundations
Lozano-Perez, 1980: Configuration Space
C = S1 x S1
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
Goal
  1 1  1 
if   0 ,
    2
FObstacle      0   x

0
if    0

Go
al
F
orc
e
Robot
n
Mo tio
orc e
O bs tac le F
FGoal  k p ( x  xGoal )
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, LaValle,
Lin, and Motwani, 1997
Integration of Planning and Control
Brock and Khatib, 1999
Outline

Some historical steps and achievements

Applications

Computational approaches:
– Criticality-based motion planning
– Random-sampling motion planning
 Some challenging problems ahead
Robot Programming and Placement
David Hsu, 1999
Design for Manufacturing and Servicing
General Electric
General Motors
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

Segment environment

Render false-color scene offscreen

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

Some historical steps and achievements

Applications

Computational approaches:
– Criticality-based motion planning
– Random-sampling motion planning
 Some challenging problems ahead
Approaches to Motion Planning

Goal:
Answer queries about the connectivity of a
certain space (e.g., the collision-free subset of
configuration space)
Approaches to Motion Planning

Old view (Latombe, 1991):
– Roadmaps
– Cell decomposition
– Potential field
Approaches to Motion Planning

Old view (Latombe, 1991):
– Roadmaps
– Cell decomposition
– Potential field

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
Non-Directional Preimage for
landmark-based navigation (Lazanas, 1995)
Criticality-Based Motion Planning
Target finding (Guibas, Latombe, LaValle,
Lin, and Motwani, 1997)
Criticality-Based Motion Planning
Target finding (Guibas, Latombe, LaValle,
Lin, and Motwani, 1997)
Criticality-Based Motion Planning
Target finding (Guibas, Latombe, LaValle,
Lin, and Motwani, 1997)
Criticality-Based Motion Planning
Target finding (Guibas, Latombe, LaValle,
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, LaValle,
Lin, and Motwani, 1997)
Recontaminated area
Criticality-Based Motion Planning

Advantage:
– Completeness
 Drawbacks:
– Computational complexity
– Difficult to implement
Outline

Some historical steps and achievements

Applications

Computational approaches:
– Criticality-based motion planning
– Random-sampling motion planning
 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…

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)

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 F1
Prob[failure] = K exp(-N)
In practice, Random-Sampling Planners…

Are fast

Deal effectively with many-dof robots

Deal well with complex admissibility constraints

Are easy to implement

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
B1
B2
2000 < B2 + B4 < 2200
2000 < B4 < 2200
2000 < B3 + B4 < 2200
2000 < B3 < 2200
2000 < B1 + B3 + B4 < 2200
2000 < B1 + B4 < 2200
2000 < B1 + B2 + B4 < 2200
2000 < B1 < 2200
2000 < B1 + B2 < 2200
C
B4
B3
• 0 < Critical < 500
0 < B2 < 500
Sample Case
50% Isodose Surface
80% Isodose Surface
Conventional system’s plan
CARABEAMER’s plan
Randomized Next-Best View Planning
(Gonzalez, 2000)
Randomized Next-Best View Planning
(Gonzalez, 2000)
Randomized Next-Best View Planning
(Gonzalez, 2000)
Randomized Next-Best View Planning
(Gonzalez, 2000)
Randomized Next-Best View Planning
(Gonzalez, 2000)
Outline

Some historical steps and achievements

Applications

Computational approaches:
– Criticality-based motion planning
– Random-sampling motion planning
 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 (SquareOne)
Generating Energetically Plausible
Docking and Folding Motions of Proteins
Conclusion

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