autonomous robotics team autonomous robotics lab: cooperative control of a three-robot formation...

Autonomous Robotics Team

Autonomous Robotics Lab:Cooperative Control of a Three-Robot Formation

Texas A&M University, College Station, TX

Fall Presentations

21 November 2008

Outline

• Motivation

• Autonomous Robotics Lab

• Project Objectives

• Cooperative Control Laws

• Implementation Challenges

• Project Results

• Conclusions

Motivation• NASA’s Vision for Space Exploration includes

returning manned missions to the moon by 2020.

• Robots are expected to be an integral part of lunar and Martian exploration.

• The robots can have varying levels of autonomy:– Teleoperation from Earth (Mars Rovers)– Teleoperation from the lunar surface (Chariot)– Fully autonomous

Motivation• Possible autonomous tasks include:

– Transporting materials from point A to point B• Moving materials from landing sites to building sites

• Cooperative manipulation of large objects by n robots

– Terrain mapping– Search and rescue

• The SEI Autonomous Robotics Team’s Mission is to address and understand some of the challenges encountered in the development of autonomous robotics.

Outline

• Motivation





• Project Results

• Conclusions

Autonomous Robotics Lab• The Autonomous Robotics Lab has been

developed to enable hardware testing of autonomous robotics theory and concepts.

• The lab includes:– Three iRobot Create platforms

– A global-positioning system to measure robot states.

– A wireless communications network.

– A central PC that manages functions including:• Sequences of autonomous tasks• Trajectory planning• Trajectory-tracking control laws

Autonomous Robotics Lab• The global-positioning system is an overhead camera

integrated with image processing software to measure robot states (inertial position and orientation).

• On the moon or Mars, satellites or star-tracking systems may provide global positioning information.

Project Objectives• The semester goals are:

1. A hardware demonstration of cooperative control laws for a three-robot formation.

2. Investigation of time-delay effects on formation stability.

• Primary Tasks:1. Development and testing of formation control laws in

a MATLAB environment.

2. Integrating control-law code with the central-PC software for a three-robot formation.

3. Hardware demonstrations of the formation control laws.

Outline

• Motivation





• Project Results

• Conclusions

Cooperative Control Laws

• Cooperative control involves the control of a group of entities that are working collectively to meet a common objective.

• Decentralized cooperative controllers use state information from other vehicles in order to determine control inputs.

• Decentralized systems are more efficient for large numbers of vehicles.

• Formation control laws used here were developed by Weitz, Hurtado, and Sinclair.

Cooperative Control Laws• The robot equations of motion:

• The kinematic vehicle model can be written as:

Exact linear representation becomes design space

Transformation from design space to robot controls

Cooperative Control Laws• Cooperative control laws were designed to drive

three robots to a desired formation (drive errors between vehicles to zero). ― Robot 1 tracks a Reference Trajectory.― Robot 2 follows Robot 1 (and reference trajectory).― Robot 3 follows Robot 2 (and reference trajectory).

• General control form:

Position error wrt lead vehicle

Velocity error wrt lead vehicle Position error wrt

reference trajectory

Velocity error wrt reference trajectory

Cooperative Control Laws• If a leader-tracking scheme is preferred set cp, cv = 0.

• If a reference-trajectory-tracking scheme is preferred set kp, kv = 0.

Position error wrt lead vehicle

Velocity error wrt lead vehicle Position error wrt

reference trajectory

Velocity error wrt reference trajectory

Cooperative Control Laws• Three control schemes were investigated:

– Full-State Measurement Control Law

– Rate-Estimate Control Law: rates are estimated using an additional state, .

– Rate-Free Control Law: a different control law is developed that only requires position information relative to the reference trajectory.

Commanded Velocity vs.

Actual Velocity


• MATLAB Simulations of control laws were used to:1. Select control gains that meet robot performance

criteria (acceleration and angular turn rate).

2. Design reference trajectories that fit within the lab space.

Full-State Control Law Rate-Estimate Control Law Rate-Free Control Law


Full-State Control Law Rate-Estimate Control Law Rate-Free Control Law

Outline

• Motivation





• Project Results

• Conclusions

Implementation Challenges• Due to lack of computational power onboard the robots, the

central PC computes control inputs based upon state information received from the camera (centralized vs. decentralized).

Measurement Class

Camera Data

10 Hz

Kalman FilterPosition & Orientation

Robot Class Velocity Commands

State Estimation

Control Laws

Zigbee Class

Packet Communication

Robot 1

Camera PC

Firewire

Image Processing

PC

UDP Communication

Class

Position & Orientation

Camera Data

Central PC

Controls Algorithms

Robot 2

UDP Communication

Class

Robot 3

8 Hz

Delays are introduced in the process flow due to both computational time and planned delays when sending velocity commands to the robot.

Largest delays occur when sending velocity commands to each robot. Delays must be introduced to allow the robots’ onboard microcontrollers to parse data packets.

Implementation Challenges

• The control laws command and , but the robot inputs are and .

• There are two approaches to implementing the control laws:1. Send and commands to the robot, and the

onboard microcontroller finds the velocity using a first-order approximation.

2. Send and commands to the robot, which are held constant until the next update from the camera.

Implementation Challenges

Outline

• Motivation





• Project Results

• Conclusions

Project Results

• Tests run for two trajectories:– Piece-wise trajectory

• Tracking both lead vehicle and reference trajectory• Reference trajectory tracking only• Lead vehicle tracking only

– Circular trajectory• Tracking both lead vehicle and reference trajectory• Reference trajectory tracking only• Lead vehicle tracking only

Project Results

Piece-wise trajectory• 4 constant-velocity

trajectories

• Some aggressive velocity changes

0 500 1000 1500 2000 2500 30000

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x (mm)y

(mm

)

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v (m

m/s

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Project Results• Lead-vehicle and reference-trajectory tracking (kp=kv=cp=cv = 0.5).

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x (mm)

y (m

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Reference TrajectoryRobot 1Robot 2Robot 3

0 5 10 15 20 25 300

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time (sec)

err

ors

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Robot 1Robot 2Robot 3

Project Results• Piece-wise Trajectory Test Results

• Lead-vehicle tracking only was unstable for the following cases:– Gains = 0.5– Gains = 0.5 with velocity commands sent in the order:

Robot 3 → Robot 2 → Robot 1– Gains = 0.25 with reversed order

LV+Ref(gains = 0.25)



Ref Tracking(gains = 0.25)



Error "Energy" (mm-s)

Robot 1 942.59 588.69 1722.70 596.31 646.89Robot 2 670.56 388.75 unstable 242.88 390.29 253.44Robot 3 704.67 445.58 274.96 565.68 233.35

Maximum Error (mm)


Error at end (mm)


Project Results

• Video demonstration: piece-wise trajectory

Project Results• Circular trajectory: Lead-vehicle and reference-trajectory

tracking (kp=kv=cp=cv = 0.5).

0 500 1000 1500 2000 2500 30000

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x (mm)

y (m

m)


0 5 10 15 20 25 300

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time (sec)

err

ors

(m

m)

Robot 1Robot 2Robot 3

Project Results

• Test resultsRef Tracking(gains = 1)

LV + Ref(gains = 0.5)

LV + Ref(gains = 0.5)

(Bad IC's)

Lead Veh(gains = 0.5)

Order 123


Order 312


Order 321

Error "Energy"

Robot 1 402.78 296.00 616.57 612.02 447.71 550.36Robot 2 258.91 409.17 1005.50 946.90 655.99 940.13Robot 3 143.25 392.34 946.83 7.28E+07 797.78 1654.60

Maximum Error


Error at end


Project Results

0 500 1000 1500 2000 2500 30000

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1500

2000

2500

x (mm)

y (m

m)


Lead-Vehicle Tracking (gains = 0.5). Velocity commands sent in order Robot 3 → Robot 2 → Robot 1.

0 500 1000 1500 2000 2500 30000

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1500

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2500

x (mm)

y (m

m)


Lead-Vehicle and Reference-Trajectory Tracking (gains = 0.5).

Project Results

• Video Demonstration: circular trajectory with poor initial conditions.

Conclusions• The full-state measurement cooperative formation control

laws were demonstrated in hardware.

• The control-law implementation on the central PC yields good results despite the computational and communication delays and the discrete implementation.

• The aggressive velocity changes in the piece-wise trajectory caused some instabilities for the lead-vehicle-only tracking schemes.

• Delay effects can be seen in the results of the third vehicle.

• All vehicles using reference-trajectory information greatly improves convergence and mitigates delay effects.

Acknowledgments

• Thank you to NASA-JSC for sponsoring the project.

• Thanks to Dr. Hurtado (Faculty Advisor) and Ms. Lagoudas (SEI Director).

autonomous robotics team autonomous robotics lab: cooperative control of a three-robot formation...

Documents

autonomous slide

control inputs

cooperative controllers

controllaw code

robot formation texas

robot controls

formation stability

robot equations of motion