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Transcript of 1 Cooperative and Noncooperative Operations of Swarms Hoam Chung, David Shim, Mike Eklund, Shankar...
1
Cooperative and Noncooperative Operations
of Swarms
Hoam Chung, David Shim, Mike Eklund, Shankar Sastry
University of California, Berkeley
www.swarms.org
SWARMS
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Cooperative Operations of Swarms
Heterogeneous formation flight of MD500s and UH-60s
Various helicopter formations are now being used in many applications
Some level of automation during formation flight can reduce pilot stress and fatigue
Few research results on autonomous helicopter formation exist due to helicopter’s complicated dynamic properties, and technical difficulties
SWARMS
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Mesh Controller Mesh Controller tasks:
Obtain the leader and 2 neighboring helicopters’ current positions
Compute mesh stable trajectories based on the acquired position information and send commands to the navigation computer
FlightComputer
MeshController
RS-232Wireless
Token Ring
Neighbor 1
Neighbor 2
Leader
On UAV
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2001 Experiment
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2001 Experiment
Animation by A. Pant and X. Xiao
Withoutleader
info
Withleader
info
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Mesh Stable Controllers are OK, but…
The use of leader information improves the performance of the autonomous formation flight
For a heterogeneous mesh, an extension of mesh stability theory should be considered
“Mesh Stability” does not mean the “Safety”
It’s a starting point for autonomous formation flight
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Model Predictive Control
Computes control inputs using real-time optimization
Shows better performance than non-predictive controls
Can consider various safety constraints in on-line manner Easily accommodates adaptive
disturbance rejection algorithms
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Model Predictive Control
Compute control inputsminimizing gap errors
considering helicopterdynamics
at every sampling time
optimization can dealwith various constraints
Positions of neighboring
vehicles
Informationof formation
velocitiesdesired
gaps
Structure of MPC
Controlinputs
Weather conditions/Mission characteristics
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Simulation Scenario 1
• 3DOF Point mass model• Homogeneous formation• Echelon right (45 deg. off lead)• Forward flight at 67.5 mi/h• Disturbance on 2nd helicopter• No safety constraints, no explicit disturbance rejection
t
n
Heli0
Heli1
Heli2
Heli3
* Formation from FM 1-112 Attack Helicopter Operations, Headquarters, Dept. of the Army
SWARMS
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Animation
Animation generated by MATLAB
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Simulation
Mesh stability is achieved without any explicit disturbance rejection algorithm
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Bi-directional Information Flow
For safer autonomous formation, the communication between neighbors should be bi-directional
In case of mesh stability concept, it’s difficult to deal with bi-directional information
What will happen if directions of disturbancesare reversed?
Information flow
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Bi-directional Information Flow
j
In case of MPC, simple redefinition of error signal can deal with bi-directional information flow
For example, we can redefine the error vector of jth helicopter so that - Keep the center between j-1 and j+1 in tangential direction - Keep the desired gap in normal direction
j-1
j+1
t
n
This flexibility of MPC allows various formations in 3D space with enhanced safety
SWARMS
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Forming a Formation Adding vehicles one by one
1. Establish communication with vehicle A2. Acquire variables about existing formation
from vehicle A3. Compute a merging trajectory and track it4. Finish merging procedure if the gap error
is within a certain bound5. Engage formation controller
Merging procedures on the vehicle B:
A
B
SWARMS
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Forming a Formation Adding vehicles group by group
1. Vehicle b establishes communication with vehicle a in A
2. Vehicle b acquires variables about leading formation from vehicle a
3. Compute merging trajectory
4. Propagate acquired variables and computed trajectory through B
5. Track the merging trajectory
6. Finish merging procedure
Merging procedures on the group B:
A B
+
a
b
a b
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Terminating a Formation Terminating a formation one by one
1. Compute a trajectory to get more gap from the existing formation
2. Notify termination schedule to vehicle A3. Track the computed trajectory4. Send “Separation Completed” to vehicle A
and close the communication channel5. Disengage formation controller and give
control back to pilots
Termination procedures on the vehicle B:
A
B
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Terminating a Formation Terminating a formation group by group
1. Compute a trajectory to get more gap from the leading formation
2. Propagate the computed plan to followers
3. Notify termination schedule to vehicle a
4. Track the computed trajectory
5. Send “Separation Completed” to vehicle a and close the communication channel between a and b
Termination procedures on b:
A B
a
ba b
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Modifying a Formation in the Air
Modification of a formation MPC is basically a tracking controller By manipulating local formation variables(gap info), reconfiguration
of a formation without reorganization can be easily achieved
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Simulation Scenario 3
• 3DOF Point mass model• Heterogeneous formation• 3D Vee formation (45 deg. off lead, 5m gaps in n, t, and z)• Forward flight at 67.5 mi/h, 5m(about 1.7 rotor radius) spacing• Disturbances on the leader and the last follower in right wing• No safety constraints, no explicit disturbance rejection
t
n
Mass Ratio
Heli0 100%
Heli1 200%
Heli2 300%
Heli3 100%
Heli4 300%
Heli5 100%
Heli6 200%
Heli0
Heli1
Heli2
Heli3
Heli6
Heli5
Heli4
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Simulation of formation split and rejoin
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Formation Rejoining
Consider a situation that a vehicle is approaching to the existing 3D Vee formation for joining
1
2
Safe region
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Formation Rejoining
Objectives for a perfect formation rejoining A joining vehicle is positioned at predefined location in the formation When it finishes the procedure, its velocities and heading should be
close enough with those of the entire formation During the procedure, the joining vehicle should remain in a safe region
The motion of the future neighbor acts like a disturbance during the joining procedure For the vehicle in the formation, the first priority is maintaining the
formation Disturbances deteriorate ideal navigation conditions always exist
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Formation Rejoining
The formation joining problem can be regarded as a differential gaming under input/state constraints
Following question should be answered: Does RHC scheme guarantee reachability under
disturbances? If so, how close is the reachable set rendered by RHC to
that by infinite-horizon problem?
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Finite-horizon Differential Game
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Finite-horizon Differential Game
The reachable set by the solution of FHODG problem is identical with that of a modified infinite-horizon problem
As becomes small, the reachable set of RHC approaches to that of infinite-horizon solution with
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Finite-horizon Differential Game
This lemma plays important role in designing a receding horizon controller satisfying the condition
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Finite-horizon Differential Game
The reachable set can be enlarged by introducing longer prediction horizon
These theorems and lemma tell us that, if the FHODG is feasible with some prediction length L, then it guarantees a successful formation rejoining
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Works in Progress
A RHC scheme will be designed for 3D nonlinear kinematics plus linear dynamics model
Various numerical methods are now being investigated Continuation method – Ravio et al. Piecewise linear approximation and SQP – Fabien Lagrange multipliers method – Sutton and Bitmead
For reducing computational burdens, the performance of open-loop and Stackelberg solutions under RHC scheme will be evaluated
The algorithm will be implemented and tested on BEAR hardware-in-the-loop systems
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20
40
60
80
-20
0
20
40
25303540
Collision pt:(50,0,33)ft
Collision Avoidance using MPC
20
40
60
80
-20
0
20
40
25303540
•Five helicopters are given destination points.•The shortest (optimal) trajectory will lead to a collision.
•Each vehicle can detect other vehicles position only within the sensing/communication region.
•Can each vehicle fly safely and optimally?
Unsafe Desired Trajectory Resolved by NMPTC with Collision Avoidance
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Collision Avoidance using MPC
•Two UAVs are intentionally set on a head-on crash course
• Model-predictive control-based trajectory planner computes safe trajectories with sufficient clearance in real time
• Each vehicle’s current coordinate is used for MPC at each computation
May 2003
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Collision Avoidance using MPC
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Obstacle Avoidance System
• Dynamic path planning: real-time path generation using model predictive control
• Sensing: onboard 3D laser scanner or preprogrammed obstacle maps
• Experiment system: Berkeley UAV architecture implemented on Yamaha industrial helicopter platform with 3D laser scanner
min/O BX
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Urban Flight Experiment10’ X 10’ Easy-up Canopy
• 6 canopies to simulate urban environment• Secured by stakes at four corners• Resistant to wind gust of rotor downwash• Sufficient distances each other for helicopters to fly through
Original path
Adjusted path by MPC
Vehicle Launching Pt.
Ground Station
Obstacles
Richmond Field Station, UC Berkeley, Richmond, California
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Urban Navigation Experiment
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Non Cooperative Actions of Swarms:
David Shim, Jongho Lee, Mike Eklund, Jonathan Sprinkle, Shankar Sastry
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Aerial Pursuit-Evasion in MPC framework
Pursuer wants to position itself in a good position to “shoot down” the evader, e.g., follow the target’s tail and align its heading with the relative position vector, XE-XP
Evader wants to shake off the pursuer, e.g., get out of the hotspot
Pursuer and evader avoid colliding into each other within a closed 3-D space
State variables such as roll and pitch angles are constrained
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Pursuer and Evader in a closed 3-D space with the additional cost
Aerial Pursuit-Evasion in MPC framework
Cost function also includes collision avoidance between aircraft and other obstacles including terrain
Illustration by Mike Eklund and Jonathan Sprinkle
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ANIMATION 2004
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Multiplayer PEGs: Proposed Solution
A close analogy is football: Multi player Initial (global) strategies well
defined Limited (local) coordination
after the snap
What can we learn? How can we apply this? How far does the
analogy go?
Back
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Multiplayer PEGs Preseason (Off-line precomputed strategy)
Play book: Evaluate strategies and configurations that will maximize chance of success
based on best estimate of other team’s tactics Practice and preseason games:
Test playbook and find problems Game time (On-line adaptive strategy)
Choose play based on best knowledge and experience Line up (in best detection configuration, not necessarily static)
Execute the play Active and reactive actions (respond to detected evader) Local communication Adapt to evolving behavior
Learn from experience, repeat as necessary (Learning by Doing)
Back