C OORDINATED P ATH F OLLOWING of MULTIPLE UNDERACTUATED VEHICLES WITH COMMUNICATION CONSTRAINTS António M. Pascoal antonio@isr.ist.utl.pt Institute for Systems and Robotics (ISR) IST, Lisbon, Portugal Pre-CDC WORKSHOP San Diego, USA, Dec. 12, 2006
C OORDINATED P ATH F OLLOWING of MULTIPLE UNDERACTUATED VEHICLES WITH COMMUNICATION CONSTRAINTS Presentation based on the compilation of joint work with Aguiar, António IST/ISR, PT Ghabchelloo, Reza IST/ISR, PT Hespanha, João UCSB, USA Kaminer, Isaac NPS, USA Pascoal, António IST/ISR, PT Silvestre, Carlos IST/ISR, PT
Outline Outline � Motivating applications � Motivating applications � Coordinated path following (definition) � Coordinated path following (definition) � Coordinated path following (wheeled robots): � Coordinated path following (wheeled robots): fixed communication topologies fixed communication topologies � Coordinated path following � Coordinated path following � general set � general set- -up up for path following for path following � underactuated � underactuated autonomous vehicles autonomous vehicles � switching � switching communication topologies communication topologies
Coordinated Motion Control Coordinated Motion Control ASC AUV Surface and underwater vehicles required to operate in a master / slave configuration
Coordinated Motion Control Coordinated Motion Control Radio Link Radio Link Radio Link DifferentialGPS Radio Link DifferentialGPS - Mobile Station - Support Ship - Reference Station - Unit (SSHU) Autonomous Surface Craft (ASC) Shore Station Unit (SSTU) low baud rate acoustic communication link (emergency commands) GIB System (buoy 1 of 4) high baud rate acoustic communication link (data) low baud rate acoustic communication link (commands/data) Autonomous Underwater Vehicle (AUV) Scanning sonar Doppler log The ASIMOV concept (project ASIMOV, EC - 2000)
Coordinated Motion Control Coordinated Motion Control Two AUVS carrying out a joint survey operation
Coordinated Motion Control Coordinated Motion Control AUV Fleet – Methane gradient “descent” Methane plume Deep water hydrothermal vent The quest for mid- -water column hydrothermal vents, Azores, PT water column hydrothermal vents, Azores, PT The quest for mid
Scientific Applications Scientific Applications � Microsatellites � Microsatellites : imaging, remote sensing, : imaging, remote sensing, interferometry interferometry � Autonomous Underwater Vehicles (AUVs) � Autonomous Underwater Vehicles (AUVs) : : coordinated bathymetric mapping, seafloor imaging coordinated bathymetric mapping, seafloor imaging � Autonomous Surface Vessels (ASVs) � Autonomous Surface Vessels (ASVs) : : coordinated ocean surveying coordinated ocean surveying � AUVs and ASVs � AUVs and ASVs : coordinated control : coordinated control for fast for fast communications and reliable navigation communications and reliable navigation
Other applications Other applications � Unmanned Air Vehicles(UAVs): � Unmanned Air Vehicles(UAVs): � Formation control � Formation control for increased aerodynamic for increased aerodynamic efficiency efficiency � Coordinated search and rescue operations � Coordinated search and rescue operations � Low cost small autonomous robots: � Low cost small autonomous robots: Exploration, mine detection, and neutralization Exploration, mine detection, and neutralization � Cooperative manipulation � Cooperative manipulation
How it all started at IST (1998) - - ASIMOV ASIMOV How it all started at IST (1998) “Reality” (IST-NPS mission) Dream Theoretical problems: key issues Theoretical problems: key issues Coordinated Path Following while keeping inter while keeping inter- -vehicle vehicle Coordinated Path Following geometric constraints geometric constraints Motion control in the presence of severe acoustic Motion control in the presence of severe acoustic communication constraints (multipath, failures, latency, (multipath, failures, latency, communication constraints asynchronous comms, reduced bandwidth...) asynchronous comms, reduced bandwidth...)
Path Following Inspired by the work of Claude Samson et al Claude Samson et al. for wheeled robots . for wheeled robots Inspired by the work of A. Micaelli and C. Samson (1992). Path following and time-varying feedback stabilization of a wheeled robot. In Proc. International Conference ICARCV’92 , Singapore. � . Use forward motion to make the robot track a desired speed profile. � . Compute the closest point on the path. � . Compute the Serret-Frenet (SF) frame at that point. � . Use rotational motion to align the body-axis with the SF frame and reduce the distance to closest point to zero.
Path Following I mportant related work “ Rabbit ” moving along the path R. Skjetne, T. I. Fossen, P. V. Kokotovic. Robust output maneuvering for a class of nonlinear systems. Automatica, 40(3):373—383, 2004. Avoiding Singularities! Avoiding Singularities! “Nonlinear Path Following with Applications to the Control of Autonomous Underwater Vehicles,” L. Lapierre, D. Soetanto, and A. Pascoal, 42 th IEEE Conference on Decision and Control , Hawai, USA, Dec. 2003
Coordinated AUV / ASC behavior Exploring an elegant concept introduced in Exploring an elegant concept introduced in ( in R. Hindman and J. Hauser, Maneuver Modified Trajectory Tracking , Proceedings of MTNS’96, International Symposium on the Mathematical Theory of Networks and Systems, St. Louis, MO, USA, June 1992) Solution is too complex! Too much data exchanged “Combined Trajectory Tracking and Path Following: an Application to the Coordinated P. Encarnação and A. Pascoal, 40 th IEEE Control of Autonomous Marine Craft,” between Conference on Decision and Control , Orlando, Florida, USA, Dec. 2001 the vehicles
FORMATION at a (a fresh start) Reach (in-line) desired speed ! L v Coordinated Path Following Coordinated Path Following PATHS (HIGHWAYS TO BE FOLLOWED) Initial configuration
FORMATION at a (a fresh start) Reach (in-line) desired speed ! L v Coordinated Path Following Coordinated Path Following PATHS (HIGHWAYS TO BE FOLLOWED) Initial configuration
IN-LINE FORMATION Divide to Conquer Approach Divide to Conquer Approach Each vehicle runs its own Vehicles TALK and adjust their PATH FOLLOWING SPEEDS in order to COORDINATE controller to steer itself to the path themselves (reach formation) Coordination error
Coordination state / error Coordination state / error Coordination error s (in-line formation): 12 s 2 = − s s s 12 1 2 s 1 Path lengths and s s 1 2
Coordinated Path Following (using the “ “inter inter- - Coordinated Path Following (using the rabbit” ” distance) distance) rabbit L. Lapierre, D. Soetanto, and A. Pascoal (2003). Coordinated L. Lapierre, D. Soetanto, and A. Pascoal (2003). Coordinated Motion Control of Marine Robots. Proc. 6th IFAC Conference Motion Control of Marine Robots. Proc. 6th IFAC Conference on Manoeuvering and Control of Marine Craft (MCMC2003) , , on Manoeuvering and Control of Marine Craft (MCMC2003) Girona, Spain. Girona, Spain. R. Skjetne, I.- -A. F. Ihle, and T. I. Fossen A. F. Ihle, and T. I. Fossen (2003) Formation (2003) Formation R. Skjetne, I. Control by Synchronizing Multiple Maneuvering Systems. Control by Synchronizing Multiple Maneuvering Systems. Proc. 6th IFAC Conference on Manoeuvering and Control of Proc. 6th IFAC Conference on Manoeuvering and Control of Marine Craft (MCMC2003) , Girona, Spain. , Girona, Spain. Marine Craft (MCMC2003) M. Egerstedt and X. Hu (2001) Formation Constrained Multi (2001) Formation Constrained Multi- - M. Egerstedt and X. Hu Agent Control, IEEE Trans. on Robotics and auto., vol. 17, no. Agent Control, IEEE Trans. on Robotics and auto., vol. 17, no. 6, Dec. 2001 6, Dec. 2001 They do not address communication constraints do not address communication constraints They explicitly. explicitly.
vehicle Communication Constraints link What is the communications topology? ( GRAPH ) Bidirectional Links Non-bidirectional links � directed graphs � undirected graphs R. Murray [2002], B. Francis [2003], A. Jadbabaie [2003]
Communication Constraints Communication Delays Temporary Loss of Comms Switching Comms Topology Asynchronous Comms Links with Networked Control and Estimation Theory
I n depth analysis I n depth analysis
SINGLE VEHICLE, PATH FOLLOWING 1. Drive the distance from Q to the rabbit to zero; 2. Align the flow frame with the Serret-Frenet v (align total velocity with the tangent to the path). t This will make the vehicle follow the path “guide” (rabbit) moving along the path – “a mind of its own” (control variable)
COORDINATED PATH FOLLOWING More general formations and paths Triangle formation In-line formation
COORDINATED PATH FOLLOWING Coordination Error = error between the “rabbits” • • • • Generalizable to multiple vehicles and other formation patterns, and paths
COORDINATED PATH FOLLOWING KEY INGREDIENTS: PATH FOLLOWING for each vehicle + Inter-vehicle COORDENATION (driving the coordination errors to zero: speed adjustments based on VERY LITTLE INFO EXCHANGED) ( space-time decoupling … maths work out!)
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