Decentralized Control of a Quadrotor Aircraft Fleet to seek Information

Transcription

1 Decentralized Control of a Quadrotor Aircraft Fleet to seek Information Claire J. Tomlin, Gabe Hoffmann, Maryam Kamgarpour, Robin Raffard, and Steven Waslander Electrical Engineering and Computer Sciences UC Berkeley Aeronautics and Astronautics Stanford University 14 February 2007 CHESS Winter Meeting

2 Planning operations for teams of aircraft Local objectives: Safety and efficiency with respect to vehicle s dynamics and actuation Global objectives: Region coverage, collision avoidance Constraints: Communication private information Computation performed on each vehicle (Source: Prof. Robin Murphy, Univ. South Florida, Katrina Search and Rescue)

3 Collision Avoidance

4 Region Surveillance (Source: Prof. Robin Murphy, Univ. South Florida, Katrina Search and Rescue) Problems: Information gathering, fast decomposition of team commands into actions for each vehicle

5 Testbed Quadrotor Design: Autonomous Control Wireless Full Onboard Sensing IMU, GPS, SODAR Stereo vision Laser range finder

6 Objectives: Safe and efficient control Automatic information gathering Constraints: Communication bandwidth Computational resources Collision avoidance A Mobile Sensor Network

7 Outline Decentralized optimization using dual decomposition Cooperative control to seek information Initial results with the testbed

8 Decentralized optimization based on dual decomposition Consider the following simple example: aircraft, each with dynamics Private (local) cost function: Global cost function:

9 Centralized Optimization

10 Dual Decomposition: Overview One primal problem leads to many dual problems The dual decomposition method solves one instance of these many dual problems breaks the primal problem into a set of small problems provides a lower bound on the global optimal solution If the problem is convex, dual decomposition returns the global optimal solution

11 Primal Problem Dual Decomposition: Overview Decoupled Primal Problem Dual Problem

12 Decentralized Optimization

13 Decentralized Algorithm Each vehicle picks a starting value for Repeat 1. Each vehicle communicates its values to the aircraft with which it shares constraints, 2. Each vehicle computes its optimal trajectory. 3. Each vehicle computes and updates Terminate when are small

14 after 5 iterations Decentralized results

15 Complexity Results Centralized Decentralized Algorithm Solve primal Apply dual decomposition Solution Memory Optimal solution if convex Optimal if convex Suboptimal, with duality gap given, otherwise Flop count Practice Communication with all agents, once Communication with a few agents, iteratively

16 Outline Decentralized optimization using dual decomposition Cooperative control to seek information Initial results with the testbed

17 Objectives: Safe and efficient control Automatic information gathering Constraints: Communication bandwidth Computational resources Collision avoidance A Mobile Sensor Network

18 Modeling Uncertainty to Increase Knowledge Target State: Observations: Target State Model: Vehicle States: Control Inputs: Motion Model: Sensor model: Use Bayes Rule to update the target state model, Minimize the expected future uncertainty,

19 Maximizing Information Ask a broad question Expected Observation Probability with a distinct answer Sensor Model

20 Bayes Rule using Particle Filters Uses available prior knowledge Allows multimodal posterior Permits nonlinear & non-gaussian models Particle Set Correction (weighting) Resampling Prediction Particle Set

21 Mutual Information from Particle Filters

22 Expanding the Mutual Information Single Node Decomposition for Distributed Optimization Pairwise Node Decomposition for Distributed Optimization

23 Distributed Optimization Program

24 Bearings Only Example Measure the direction to the target

25 Range Only Example Measure the distance to the target

26 Beacon Field Example Measure the field line orientation

27 4 Vehicles, Bearings-Only Results Mean and Quartile Error Bars for 1000 Trials Pairwise Approximation Solo Approximation Probability of Target being < 1 unit from Estimate Time Elapsed

28 Comparison of Pairwise Approx. Results Mean and Quartile Error Bars for 1000 Trials Probability of Target being < 1 meter from Estimate Time Time Elapsed

29 Development of the Testbed

30 Research Directions Communication models Decentralized optimization computation load distributed among resources allows for flexibility in shared information Implementation Generalizing to Other Applications Beacon tracking scenarios, RFID tracking Survey of disaster areas Highway accident discovery and monitoring Biological studies, animal monitoring Geological studies etc Embedded humans Fit into POMDP framework

31 Dynamics Two pairs of counterrotating blades One motor for each blade Dynamics decouple into sets of double integrators Controlling Altitude Controlling Roll/Pitch Controlling Yaw

32 Actuation Propellors Designed for Electric, Low Speed RC Planes Brushless DC Outrunner Motors Characteristics Brushless = No Commutator brush Outrunner = Coils connected to casing, not rotor Advantages over brushed DC motors Dissipates power through casing More coils = more torque = no gear box needed No wear Speed control inherent to use Less EMF noise

33 Sensing Videre Design Stereo-on-Chip (STOC) Camera SRI Small Vision System on FPGA 8 bit disparity 640x480 resolution 30 fps 140 grams Hokuyo URG-04LX LIDAR 4 m range 1 cm standard deviation 240 laser points / sweep 10 Hz sweeps 240 range 150 grams Avalanche Beacon Transceiver

34 LIDAR System