Sensor Based-Robotics: An Autonomous Observer Rafael Murrieta-Cid - - PowerPoint PPT Presentation

Sensor Based-Robotics: An Autonomous Observer

Rafael Murrieta-Cid ITESM – Estado de M´ exico Campus, Mechatronics Center

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Researchers involved in this work

• Professor Seth Hutchinson, U. of Illinois.
• Professor Jean Claude Latombe, Stanford U.
• Professor Steven LaValle, U. of Illinois.
• Dr. Hector Gonzalez, Honda Fundamental Research Labs.
• Dr. Alejandro Sarmiento, Intel.
• Sourabh Bhattacharya, Master Student U. of Illinois.
• Claudia Esteves PhD Student LAAS/CNRS.
• Teja Muppirala, Master Student U. of Illinois.
• Benjamin Tovar, PhD Student U. of Illinois.

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Problem Definition

• Our ideas are centered on the development of

mobile robotic systems that perform sophisticated visibility-based tasks.

Map Building Optimal Navigation Target Finding and Tracking

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Planning Exploration Strategies for SLAM

• A mobile sensor (the observer) must define a

motion strategy to efficiently build a map of an indoor environment.

• We have developed a randomized motion planner

that selects the next best view from a set based on maximizing a utility function.

• The final result of the exploration is a

multi-representational map consisting of polygons, landmarks and a road map.

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Planning Exploration Strategies for SLAM

e

e

Length of the closest free edge s Distance from the robot to the next possible position

Distance from the next possible position to the closest free edge

Orientation change to reach the next robot’s configuration

Cumulative uncertainty

Object identification probability

Number of landmarks inside a visibility region

Number of corners inside a visibility region

A function that penalizes configurations that like near an obstacle.

Minimum distance from a full edge

Table 1:

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Planning Exploration Strategies for SLAM

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Planning Exploration Strategies for SLAM

• Given two sets of points

and

, the Hausdorff distance is used to find the matching and update robot localization

• ❍

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Planning Exploration Strategies for SLAM (a) (b) (a) Laser data (b) Model matching

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Experiments

Omnidirectional and infinite range sensor 180 degrees field of view and limited range Fxperiments in Real Robot

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Planning Exploration Strategies for SLAM

• The crux of our method is a sampling-based

motion planner algorithm that, given a partial map

• f the environment, selects where to move the

robot next.

• We balance the desire to see as much of the

as-yet-unseen environment as possible, while at the same time having enough overlap and landmark information with the scanned part of the building to guarantee good registration and robot localization.

• Visibility is used to bias the sampling generation.

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Planning Exploration Strategies for SLAM

• Benjamín Tovar, Rafael Murrieta-Cid, Claudia

Esteves, Robot Motion Planning for Map Building.

in proc IEEE/RSJ International Conference on Intelligent Robots and Systems 2002.

• Benjamin Tovar, Rafael Murrieta-Cid, Claudia

Esteves, Robot Motion Planning for Model Building Under Perception Constraints. in proc 9th International

Symposium on Intelligent Robotic System 2001.

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Optimal Navigation

• We propose a sensor feedback motion strategy for

robot navigation.

• We developed a data structure and algorithm that

captures the topology of the environment and enables a robot to navigate optimally.

• This data structure is a dynamic tree that encodes

enough information to generate optimal paths, although only information of gap critical events is used.

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Optimal Navigation

The robot view of the environment

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Optimal Navigation

Reduced visibility graph Visibility tree at point q T(q) Visibility region Measurement of the gap sensor

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Optimal Navigation

Learning Tg

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Optimal Navigation

Experiments with real robots

Experiments

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Optimal Navigation

• We have presented a data structure and algorithm

that captures the topology of the environment and enables a robot to navigate optimally.

• We want to study what other capabilities should be

added to the robot to relax the requirements of

• mnidirectional, unbounded-range sensing.

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Optimal Navigation

• Benjamín Tovar, Steven M. LaValle and Rafael

Murrieta-Cid, Optimal Navigation and Object Finding without Geometric Maps or Localization. in

IEEE proc International Conference on Robotics and Automation 2003.

• Benjamín Tovar, Steven M. LaValle and Rafael

Murrieta-Cid, Locally-optimal Navigation in Multiply-connected Environments without Geometric Maps. in proc IEEE/RSJ International

Conference on Intelligent Robots and Systems 2003.

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Optimal Navigation II

Problem Definition: Path Planning for a Differential Robot (Minimal Length Paths).

• A mobile robot navigates in an obstacle-free

workspace while maintaining view of a fixed landmark

• The robot has sensing constraints namely, limited

range and angle of view

• Our goal is to find the path that is optimal in sense
• f distance between a given start and a goal

position

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Optimal Navigation II

Y X y x b

b

ψ θ φ

r=r r=r max

min

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Optimal Navigation II

I IV T T P T T T T III I’ III’ C D II’ IV’ V VI B A II Q T 1 2 2 2 1 1 P P P’ 1Q T1P’ T2P’ P P P’’ T2P’’ T1P’’ G G G G

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Optimal Navigation II

Conclusions

• Formulation of the problem of tracking a static

target with sensing constraints

• Proposed a constructive proof for the controllability
• f the system
• Proposed the nature of optimal paths
• Presented the partition of the workspace based on

the nature of the optimal paths

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Optimal Navigation II

• Sourabh Bhattacharya, Rafael Murrieta-Cid and

Seth Hutchinson, Path Planning for a Differential Drive Robot: Minimal Length Paths-A Geometric Approach, in proc IEEE/RSJ Conference on Intelligent

Robots and Systems 2004.

Proposed Research Directions

• Determine the optimal paths in the sense of time
• Investigate the case of a robot with area and mass.

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Generating Expected-Time Efficient Trajectories for Rapidly Finding an Object

Problem Definition

• Use one or more mobile robots to find an object as

quickly as possible on average.

• robots with omni-directional, infinite range sensors

moving in a known environment.

• Robots start moving from an initial position

at

along trajectories

.

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Object Finding

Expected Value vs. Worst Case:

• Route 1:

• ❯

• Worst case time

• Route 2:

• ❯

• Worst case time

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Object Finding

Different Versions of the Problem:

• Sensing at specific locations
• Polygonal environment
• If the object PDF is uniform,

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Object Finding

Different Versions of the Problem: Continuous sensing

• Polygonal environment
• Robot senses the environment as it moves

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Object Finding

Different Versions of the Problem:

• Simulation of a 3-D environment
• Robot has finite volume
• Robot is a redundant mobile manipulator

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Object Finding

Two-Layered Approach

• Partition the environment into regions bounded by

critical curves

• Find an ordering of visiting these regions
• Showed the discrete problem to be NP-hard by

reduction

• Solve each region independently and concatenate

the resulting sub-paths

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Calculus of Variations

• Find stationary values of integrals of the form

• Integral has a stationary value if and only if the Euler-Lagrange equation is

satisfied

• Minimize unseen area
• Second order non-linear differential equation

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Object Finding

Simulation Result

Locally Optimal Straight Line

Expected time: 115.3 Expected time: 136.9

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Object Finding

• Simulation of a 3-D environment

Sample−Based Convex Covering Path for finding an object in a 3D environment

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Object Finding

• Alejandro Sarmiento, Rafael Murrieta-Cid and Seth Hutchinson, A Sample-based

Convex Cover for Rapidly Finding an Object in a 3-D environment, Accepted in IEEE International Conference on Robotics and Automation 2005.

• Alejandro Sarmiento, Rafael Murrieta-Cid and Seth Hutchinson, Planning

Expected-time Optimal Paths for Searching Known Environments, in proc IEEE/RSJ

International Conference on Intelligent Robots and Systems 2004.

• Alejandro Sarmiento, Rafael Murrieta-Cid and Seth Hutchinson, An Efficient

Strategy for Rapidly Finding an Object in a Polygonal World. in proc IEEE/RSJ

International Conference on Intelligent Robots and Systems 2003.

• Alejandro Sarmiento, Rafael Murrieta-Cid and Seth Hutchinson, A Multi-robot

Strategy for Rapidly Searching a Polygonal Environment. in proc 9th Ibero-American

Conference on Artificial Intelligence 2004, Best conference paper award

• Alejandro Sarmiento, Rafael Murrieta-Cid and Seth Hutchinson, A Strategy for

Searching an Object with a Mobile Robot. in proc International Conference on Advanced

Robotics 2003.

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Pursuit-Evasion

Problem definition:

• A mobile robot must maintain visibility of a moving

evader at a fixed distance.

• The geometry of the environment is known a priori.
• We are assuming a feedback control scheme

where the instantaneous target velocity is measured or reported.

• The observer speed is bounded.
• Decision problem: can the evader escape?
• Planning problem: the motion strategy.

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Pursuit-Evasion

• The shortest distance to escape: Our algorithm computes a motion strategy by

maximizing the shortest distance to escape —the shortest distance the target must move to escape an observer’s visibility region.

O T

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Pursuit-Evasion

Experiments real robot Simulation two-pursuers/two-evaders

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Pursuit-Evasion

Problem Modeling: Critical curves

• Partition the environment into a set of non-critical regions separated by critical

curves.

• While the evader remains in a specific non-critical region, the obstacles that can

violate surveillance constraints are constant.

Curve type 0 (obstacle) Curve type 3 Curves type 2 Curve type 4 Curve type 5 Curve type 1 The Rod L L L L L L L L MOVIE 2005 – p.37/42

Pursuit-Evasion

• Examples

E4 R0 R5 R12 R14 E3 R2 R6 R3 R4 R1 R7 R15 R16 R8 R9 R10 R11 R17 E1 E2 R18 R13 (R1,E4,E1) (R1,E1,E4) (R2,E1,E1) (R4,E1,E2) (R5,E3,E1) (R3,E1,E2) (R3,E2,E1) (R6,E4,E3) (R0,E4,E1) (R6,E3,E1) (R15,E3,E4) (R12,E3,E1) (R14,E3,E4) (R11,E1,E3) (R16,E3,E3) (R17,E2,E3) (R7,E3,E1) (R5,E3,E1)

R8 GONE

(R6,E3,E1) (R9,E1,E3) (R10,E1,E3) (R13,E1,E3) (R2,E1,E1) (R1,E4,E1) (R0,E4,E1) (R3,E1,E2) (R18,E2,E3) (R4,E1,E2) (R13,E1,E3) (R13,E2,E1) (R12,E3,E1) (R12,E1,E4) (R11,E1,E3) (R10,E1,E3) (R10,E3,E2) (R9,E1,E3) (R9,E3,E2) (R8,E3,E1) (R9,E2,E1) (R8,E1,E3) (R7,E3,E1) (R7,E4,E3) (R7,E1,E4) (R15,E3,E4) (R15,E4,E3) (R16,E3,E3) (R17,E2,E3) (R17,E3,E2) (R18,E2,E3) (R14,E3,E4) Rod

(R0, Ω Ω ) (R1,E1,E1) (R2,E2,E2) (R3,E1,E2) (R3,E2,E1) (R4,V1,E1) (R5,V1,E2) (R5,E2,E1) (R6,V1,V2) (R6,E2,E1) (R20,V2,E4) (R18, E3,E4) (R18,E2,E1) (R16,V2,E4) (R17,E3,E4) (R19,E3,E4) (R19,V2,E1) (R21,E3,E3) (R22,E4,E4) (R7,E1,V2) (R7,E2,E1) (R8,E2,V2) (R10,V2,E4) (R11,E3,V1) (R12,E3,V2) (R12,E2,V1) (R13,E3,V2) (R13,E2,E1) (R14,V1,E4) (R14,E2,E1) (R15,V1,E4) (R15,V2,E1) (R9,E3,V1) Ω Ω (R23, , ) (R2,E2,E2) (R13,E3,V2) (R6,V1,V2) (R8,E2,V2) ) Ω Ω (R0, (R17,E3,E4) (R4,V1,E1) (R3,E1,E2) (R5,V1,E2) (R7,E1,V2) (R14,V1,E4) (R12,E3,V2) (R15,V1,E4) (R11,E3,V1) (R16,V2,E4) (R18,E3,E2) (R19,E3,E4) (R20,V2,E4) Ω (R23, , ) Ω (R21,E3,E3) (R22,E4,E4) (R1,E1,E1) (R9,E3,V1) (R10,V2,E4) R0 R6 R4 R5 R3 R7 R10 R9 R11 R14 R15 R16 R18R19 R20 R21 R22 E1 E2 E3 E4 V2 V1 R1 R2 R8 R17 R12 R13 R23 O T

Cells The graph

Rectangle Two convex corner

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Pursuit-Evasion

Triggers

• Definition :

is the minimal distance from an escape point such that, if the evader is farther than

from the escape point, the observer will have sufficient time to react and prevent escape.

• Properties of the observer motion strategy:
• The observer must be at the required fixed

distance from the evader.

• The observer must move with bounded speed.
• To minimize the time to change the rod

configuration, the observer moves with saturated speed.

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Pursuit-Evasion

Optimal evader path

• The optimal evader path to escape is not a straight

line.

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Pursuit-Evasion

• Teja Muppirala, Rafael Murrieta-Cid and Seth Hutchinson, Optimal Motion

Strategies Based on Critical Events to Maintain Visibility of a Moving Target, Accepted in IEEE International Conference on Robotics and Automation 2005.

• Rafael Murrieta-Cid, Alejandro Sarmiento, Sourabh Bhattacharya and Seth

Hutchinson, Maintaining Visibility of a Moving Target at a Fixed Distance: The Case of Observer Bounded Speed, in proc IEEE International Conference on Robotics and

Automation 2004.

• Rafael Murrieta-Cid, Héctor González and Benjamín Tovar, A Reactive Motion

Planner to Maintain Visibility of Unpredictable Targets. in IEEE proc International

Conference on Robotics and Automation 2002.

• Rafael Murrieta-Cid, Alejandro Sarmiento and Seth Hutchinson, On the Existence
• f a Strategy to Maintain a Moving Target within the Sensing Range of an

Observer Reacting with Delay. in proc IEEE/RSJ International Conference on Intelligent

Robots and Systems 2003.

• Rafael Murrieta-Cid, Alejandro Sarmiento and Seth Hutchinson, A Motion Planning

Strategy to Maintain Visibility of a Moving Target at a Fixed Distance in a Polygon.

in proc International Conference on Advanced Robotics 2003.

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Conclusion and Future Work

• Motion planning with visibility constraints raises

various problems combining geometry and control, ranging from theoretical to applied and experimental.

• Relations with art-gallery problems, but with

moving guards.

• Important theoritical issues: Optimality,

completness, complexity.

• Important future extensions: 3D models, outdoor

environments, information spaces, Nonholonomic and dynamic constraints.

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