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ICRA 2015 Workshop onNext Generation of Space Robotic Servicing Technologies
May 26, 2012
Space Robotics Lab.Dept of Aerospace EngineeringTohoku University, Japan
Kazuya Yoshida
Recent results on contact dynamics controlfor capturing and handling a tumbling object
The Space Robotics Lab.Dept. of Aerospace Engineering
Tohoku University, JAPANDirected by Prof. Kazuya Yoshida
[email protected]://www.astro.mech.tohoku.ac.jp/home-e.html
Free-Flying Space Robot
Planetary Exploration Rovers Asteroid Sampling
Robotic Systems on ISS
The SPACE ROBOTICS
Lab.
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
Telerobotic Servicerin ARAMIS report, 1983
Satellite Servicing : Concept in early 80’s
SPACE APPLICATIONS OF AUTOMATION, ROBOTICS AND MACHINE INTELLIGENCE SYSTEMS (ARAMIS)-Phase II, By D. L. Akin, M. L. Minsky, E. D. Thiel, and C. R. Kurtzman, NASA-CR-3734, 1983
Satellite Servicing : Concept in early 80’s
Telerobotic Servicerin ARAMIS report, 1983
SPACE APPLICATIONS OF AUTOMATION, ROBOTICS AND MACHINE INTELLIGENCE SYSTEMS (ARAMIS)-Phase II, By D. L. Akin, M. L. Minsky, E. D. Thiel, and C. R. Kurtzman, NASA-CR-3734, 1983
Challenge to Satellite Servicing in Early Days of Space Shuttle Mission
STS-14(51A), 1984 Retrieval of malfunctioning Wester-6 satellite ©NASA
ETS-VII: Engineering Test Satellite forthe demonstration of RVD and
Space Robotic technologies1997-1999
Mission by National Space Development Agency, NASDA, Japan Purpose:
Study and demonstrate robotics capability for orbital missions and autonomous RVD technology
Feature:A 2m-long, 6 DOF manipulator arm is mounted on an unmanned base satellite. A sub-satellite is separated for the RVD experiments.
Mission:Launched on Nov. 28, 1997, the mission successfully completed bythe end of 1999.
► Orbital Express (2007, DARPA)was also successful in demonstrating RVD and robotics technology in space, including fuel transfer and target capture operation.
Dynamics and Control of Free-Flying Multibody Systems
Ground-based manipulator Free-flying manipulator
Control of Free-Floating Arms using Generalized Jacobian Matrix
(Umetani & Yoshida 1987, 1989) Expand conventional manipulator kinematics
by combining with the momentum equation.
xh = J*φ
φ = (J*)-1 xh
Technologies for Robotic Satellite Servicing
Rendezvous and Fly-around Orbital mechanics and control Proximity sensors, Visual inspection
Capture and Berthing Manipulator control Teleoperation, Latency, Bandwidth Reaction dynamics, Impact/contact dynamics
In-Orbit Servicing Tasks Refuel, Assemble, Exchange, Repair… De-orbit, Re-orbit
Robotic Satellite Servicing
ETS-VII / Orbital Express– A Milestone for Future Satellite Servicing– Success in capture & berthing of a
Cooperative target.– With a dedicated handle/gripper system,
and attitude stabilization of the target satellite.
Capture of a Non-Cooperative target is a key issue to the next step.
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
Impact/Contact:is a complex phenomenon that occurs when two or more bodies undergo a collision.
Impact/Contact/Collision
Object A Object B
Impact/Contact: occurs during a very short time. generates a large impulsive force. accompanies rapid energy loss and large
accelerations. sometimes changes mechanical properties
of the system
Two Modeling Approaches
discrete model continuous model
Real profile of the contact force
Example of measured contact normal force
High-Freq. Force
Low-Freq. Force
SPACE ROBOTICS, Jan. 14, 2015
Discrete model = impulse-momentum model
impact process is instantaneous. impact forces are impulsive. kinetic variables discontinuously change. other finite forces are negligible. collisions between rigid (very hard) bodies. single point contact occurs.
Assumption
Coefficient of RestitutionPoisson’s Model (momentum)
where,
compression part
total normal impulse
restitution part
Before Contact Contact After Contact
compression restitution
perfectlyelastic collision
perfectlyinelastic collision
Continuous model = force based model
impact process is a finite period of time. impact forces continuously change. bodies are deformable. impact forces depend on penetration depth. friction forces are also explicitly modeled.
Assumption
Contact Force Model
Before Contact Contact
Typical Normal Force during Contact:
coefficient
Contact Force Model
w/ damping w/o damping
linear damping nonlinear dampingHertz Model
Spring-DashpotModel
Impact-PairModel
Lee-WangModel
Hunt-CrossleyModel
Contact Dynamics in SpaceDyn
Hφ + c = τ + JTF
-F
F
Modeling of Contact Dynamics Dynamics of the system
Free-Flying Multibody Dynamics
+
Modeling of Contact Force
ContactDynamics =
Contact force
Fn = kn(δn)s + dn(δn)t
Impact Dynamics: modeling
V1
V2
Rigid wall Mass point
Infinitesimal Contact
Impact Dynamics: modeling
V1
V2
Articulated rigid bodies Mass point
Impedance of articulated body system
Finite-time Contact
Stiffness + damping
Lumped mass system
Impact Dynamics: modeling
Dominant eigen-frequency is determined by lowest stiffness element
Insert soft element for longer contact duration and easy contact force control
Introduction of a low-stiffness element in the system
contact duration is prolonged. system’s eigen-frequency < force-control frequency contact-force control becomes possible. peak impulsive force becomes smaller. the continuous model is needed. the discrete model may be useful for approximation
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
Satellite Capture Model
絵
Impedance Control of a Space Robot
eiii FxKxDxM =∆+∆+∆
The equation of motion of a space robot
Ideal impedance characteristics
The joint torque to realize the ideal impedance characteristics
( ){ }{ } cFJMJH
xKxDMJJH
eT
i
iii
+−+
∆+∆+−=−−
−−
*11**
1*1** φτ
:::::::
*
*
xc
FJφ
Hτ
e
Joint torqueGeneralized inertia matrixJoint angleGeneralized Jacobean matrixExternal forceNonlinear velocity termHand position in the inertial frame
cFJH eT
+−= **φτ
The impedance characteristics Zas an evaluation index of impact
2sk
sdm ii
i ++≡Z
Uniaxial Satellite Capture Model
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
Impedance Matchingin contact-force control scenario
Kinetic energy of the target before the contact is fully absorbed by the chaser’s manipulator arm (under the impedance control)
Hard ImpactManipulator impedance is HighCoefficient of Restitution=1.0
Soft ImpactManipulator impedance is Low
“Impedance matching”Coefficient of Restitution=0.0
Contact Force Target Velocity
(Dr. Uyama’s thesis work)
Collaboration with Space Robotics Group, Tsukuba Space Center, NASDA
Nozzle of the Target:The motion of the target satellite is emulated based on the F/T sensor.
Capture Probe:Impedance Control
F/T Sensor
7DOF Robot Arm
F/T Sensor
A Case Study: Experiment
A Case Study: Target Model
DRTS Geostational SatelliteMass:1300 [kg] (EOL)Size of body:2.2 ×2.4 ×2.2 [m]Size of solar paddle:2.4 ×7.3 [m] (1 wing)
Size of nozzle coneφ296 [mm]×450 [mm]
X
Z
Impedance Matching
][
][
N/m50[N/(m/s)]500kg10
=
=
=
i
i
i
kdm
20 25 30 35 40 45-2
0
2
4
time [s]
forc
e [
N]
20 25 30 35 40 45-1.5
-1
-0.5
0
0.5
time [s]
forc
e [
N]
X方向
Z方向
*tim mZZ =≈
(Dr. Nakanisi’s thesis work)
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
Collision of two rigid bodies
Translational motion and rotational motion are coupled in general.
Case 1 Case 2
With a Sweet Spot contact, the rotational motion before the contact can be fully transferred to the translational motion.
•48
Model based simulation
Experimental result
𝑥𝑥
𝑦𝑦
Collision of two rigid bodies (Mr. Kobayashi’s thesis work)
With a flexible element in the system
Experimental result Model based simulation
(Mr. Kobayashi’s thesis work)
Technologies for Robotic Satellite Servicing
Rendezvous and Fly-around Orbital mechanics and control Proximity sensors, Visual inspection
Capture and Berthing Manipulator control Teleoperation, Latency, Bandwidth Reaction dynamics, Impact/contact dynamics
In-Orbit Servicing Tasks Refuel, Assemble, Exchange, Repair… De-orbit, Re-orbit
Agenda
Quick overview on motivation and previous developments
Contact modeling Contact control Impedance matching Contact with rotation
The Space Robotics Lab.Dept. of Aerospace Engineering
Tohoku University, JAPANDirected by Prof. Kazuya Yoshida
[email protected]://www.astro.mech.tohoku.ac.jp/home-e.html
Free-Flying Space Robot
Planetary Exploration Rovers Asteroid Sampling
Robotic Systems on ISS
The SPACE ROBOTICS
Lab.