Multi Robot Physical Interaction Dongun Lee@RSS MultirobotSystems WS - PDF document

Control of the Physical Interaction in/with Multi ‐ Robot Systems Dongjun Lee Interactive & Networked Robotics Laboratory (INRoL) Department of Mechanical & Aerospace Engineering Seoul National University * research supported in part by Korea NRF ‐ MEST 2012 ‐ R1A2A2 ‐ A01015797 Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Multi ‐ Robot Physical Interaction Dongun Lee@RSS MultirobotSystems WS 7/16/2015 1

Categorization Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Issues of Their Own Dongun Lee@RSS MultirobotSystems WS 7/16/2015 2

Content Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Decentralized Physical Interaction Control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 3

Decentralized Physical Interaction Control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Multi ‐ UAV Teleoperation ‐ issues/challenges: uav4 u t ‐ single user can manage only small ‐ DOF vp4 ‐ information ‐ flow among UAVs should uav1 uav3 u t be distributed, yet, no collision/separation vp3 under arbitrary human tele ‐ command vp1 connectivity uav2 graph G vp2 * semi ‐ autonomous teleoperation obstacle = teleoperation + local autonomous control internet 1. UAV control layer (bakcstepping): ‐ under ‐ actuated UAV tracks its own kinematic virtual point (VP) 2. VP control layer: ‐ N VPs as a deformable flying object on G ‐ deforms to obstacles w/o VP ‐ VP separation or VP ‐ obstacle/VP ‐ VP collisions 3. teleoperation layer: ‐ PSPM for flexible/stable teleoperation Dongun Lee@RSS MultirobotSystems WS 7/16/2015 4

Distributed VP Control Layer ‐ render N kinematic VPs as a N ‐ nodes uav4 deformable flying object with artificial potentials distributed over vp4 uav1 connectivity graph G uav3 vp3 vp1 ‐ same architecture can be used for connectivity uav2 interaction with real objects graph G vp2 internet obstacle kinematic VP VP ‐ obstacle teleoperation VP ‐ VP VP velocity potential command potential VP ‐ VP/VP ‐ obstacle VP ‐ VP collision avoidance separation neighbors on connectivity graph G preservation distance ‐ based artificial potential  rotational symmetry obstacle set Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Swarming Property [TMech13] collision/separation impending � Prop. 1: Suppose � � � � � ∀� � 0 , and, if ���� � � ,  at least one VP, s.t., � �� � 1 if �  �� ; � �� � 0 if �  �� Then, all VPs are stable (i.e., bounded �� � ); no VP ‐ VP/VP ‐ obstacle collisions; and no VP ‐ VP separations. � �  ���� � � detect can’t detect collision collision � � ‐ only one VP needs to detect ���� � � , w/ potential not exactly aligned �  guaranteed by PSPM ‐ stable for any bounded teleoperation command � � Dongun Lee@RSS MultirobotSystems WS 7/16/2015 5

Experiments distributed multi ‐ UAV teleoperation: flying ‐ over obstacle distributed multi ‐ UAV teleoperation: adapt to narrow passage * joint work with Max Planck Institute for Biological Cybernetics, Tübingen, Germany haptic teleoperation of UAV multi ‐ modal semi ‐ autonomous teleoperation of UAV/UGV Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Multiuser Haptic Interaction haptic device local copy (heterogen.) of virtual object local hybrid coupling p2p architecture deformable synchronization virtual object over Internet Dongun Lee@RSS MultirobotSystems WS 7/16/2015 6

Discrete ‐ Time Passivity Suppose VO synchronization gains B i ,K i are set to be: ∀ users i=1,…,N Then, total p2p architecture is N ‐ port discrete ‐ time passive : ∀ M  0, total energy VO damping (B) = VO kinetic (M) + VO potential (K) + synchronization potential (K ij ) (f i ,v i ) ‐ non ‐ iterative passive integrator [DSCC08] VO + passive synchronization [ACC10] (u i ,v i ) ‐ extend [Lee&SpongTRO06] to discrete domain ‐ robust stability for any devices & passive users ‐ not require specific kind/number of device/user  portability/scalability for heterogeneous devices/users Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Local Copy Synchronization If user forces f i (k)=0 and VO damping B is positive ‐ definite, v i (k)  0 and VO local copies will be configuration ‐ synchronized s.t. Kronecker product effect of synchronization K ij effect of VO spring K ‐ all the VO local copies’ configurations x(k) = [x 1 (k);x 2 (k);…x N (k)]  R 3nN converge to stable equilibria K int /N x 2 x 3 x(k)  null(P)  null(I N  K) K ij j j x 2 x 3 ‐ VO synchronization guaranteed i i with null(P) = {x i =x j =d, d  R 3n } K int /N x 3 x 2 d if G is connected [Huang&LeeACC10] d x 4 x 1 j j ‐ K int : VO internal shape x 4 x 1 i i – K ext : symmetry breaking K ext /N K ext /N e.g. if K ext = 0, x i  x j  I N  c, c  R 3 x 1 x 4 d d Dongun Lee@RSS MultirobotSystems WS 7/16/2015 7

Network Topology Optimization VO VO Which (connected) network topology should we choose?  fastest mixing graph G op from the set of all candidates graphs G i information mixing model communication K ij : information user i’s information delay normalization mixing strength state Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Experiments Dongun Lee@RSS MultirobotSystems WS 7/16/2015 8

Centralized Physical Interaction Control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Centralized Physical Interaction Control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 9

Multirobot Fixture ‐ Less Grasping maneuver ‐ total ‐ DOF = 15 (locked) ‐ three behaviors: 1) grasping 2) grasped object maneuver 3) internal motion (e.g., avoidance, reconfiguration) formation  decomposition into these three behaviors even with (shape) nonholonomic constraints? internal motion (shape) orthogonal decomposition w.r.t. M(q) ‐ metric permissible permissible permissible quotient: perturb motion maneuver+internal grasping maneuver & formation Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Behavior Decomposition and Control * hierarchical control = simultaneous/separate control of each behavioral mode autonomously or teleoperatedly grasping simple grasping autonomous autonomous, internal motion yet, rich (avoidance, reconfiguration) (or teleoperation?) object maneuvering cognitive required level of intelligence Dongun Lee@RSS MultirobotSystems WS 7/16/2015 10

NPD Expression grasp regulation � � � �� � ��� no ‐ excitation ��� ( � � ∩ Δ � � grasping �� � � : object maneuvering: internal motion: grasping: simple simple autonomous teleoperation autonomous (rich) autonomous � �� � , � � � � � � � � Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Simulation ‐ autonomous obstacle avoidance using combination of maneuver mode and internal dynamics mode ‐ rigid grasping enforced with no grip ‐ holding fixture ‐ autonomous grasping control ‐ object maneuver haptic teleoperation completely decoupled from grasping behaviors ‐ object teleoperation with interaction force feedback ‐ rigid grasping maintained regardless of object interaction Dongun Lee@RSS MultirobotSystems WS 7/16/2015 11

Quadrotor ‐ Manipulator System quadrotor ‐ arm dynamic coupling quadrotor ‐ arm dynamic coupling center ‐ of ‐ mass dynamics in E(3) (coarse operation) platform rotation + internal motion (precise operation) quadrotor ‐ arm coarse ‐ fine control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Configuration ‐ Space Decomposition tangent space decomposition tangential distribution: integrable orthogonal w.r.t. M(r) ‐ metric normal distribution: also integrable! passive decomposition [ICRA14] center ‐ of ‐ mass dynamics in E(3) platform rotation + internal motion Dongun Lee@RSS MultirobotSystems WS 7/16/2015 12

Coarse ‐ Fine QM ‐ System Control control redundancy: cooperative control freely ‐ assignable w/o affecting control objective possible with kinematically decoupled manipulator Dongun Lee@RSS MultirobotSystems WS 7/16/2015 QM System Control Examples end ‐ effector trajectory tracking coarse ‐ fine control tracking+obstacle avoidance admittance force control Dongun Lee@RSS MultirobotSystems WS 7/16/2015 13

Hierarchical Cooperative Control Framework trajectory tracking physical interaction peg ‐ in ‐ hole Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Object Behavior Design Layer translation dynamics rotation dynamics external moment trajectory tracking physical interaction peg ‐ in ‐ hole Dongun Lee@RSS MultirobotSystems WS 7/16/2015 14

� Optimal Cooperative Force Distribution Layer force of all N QM systems desired object wrench minimize internal force normal/tangential decomposition friction cone constraint Dongun Lee@RSS MultirobotSystems WS 7/16/2015 Admittance Force Control Layer unknown stiffness � ‐ tracking error in � error in � � � ‐ tracking �,� integral error � �� ≔ �� � �� � � � Dongun Lee@RSS MultirobotSystems WS 7/16/2015 15

Multiple Cooperative QM ‐ System compliant object pushing trajectory tracking with unknown added mass Dongun Lee@RSS MultirobotSystems WS 7/16/2015 SmQT System: Modeling decoupled from : joint center axis and motion range tool dynamics : inertia matrix : quadrotor thrust in fixed frame : angular velocity : tool and quadrotor attitude : control torque control input : inertia matrix : gravity : external force : centrifugal/Coriolis term : tool angular velocity quadrotor thrusts as control actions Dongun Lee@RSS MultirobotSystems WS 7/16/2015 16