SPHERES Reconfigurable Control Allocation for Autonomous Assembly

Swati Mohan, David W. MillerMIT Space Systems Laboratory

AIAA Guidance, Navigation, and Controls Conference 200808-21-2008

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Outline

• Motivation• Reconfigurable control overview• SPHERES Overview• Control allocation methods• Testing Results• Conclusions

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Motivation: Autonomous Assembly

• On-orbit assembly is an enabling technology • Challenges: Sequencing, Accurate Sensors & Actuators, etc• Current methods high in risk, cost, and time

– Human EVAs, Tele-operated robotic arms– Limited to Low Earth Orbit

• Desire to fully automate assembly process using robotics

• Additional Challenges for Autonomous Robotic On-Orbit Assembly:– Design challenges

• Autonomy• Autonomous Control and Reconfiguration

– Systems challenges• No unified design principles or guidelines• Requirements may vary drastically with application

International Space Station

Space Solar Power Station

Space Telescope (ex. JWST)

Address reconfigurable control system design for autonomous robotic on-orbit assembly.

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Motivation: Control Allocation

Suppose we want to …

assemble N segments from an initial to final configuration, using a propellant tug with docking capability

Issue: How to maintain performance at each docking/undocking to complete assembly, in spite of large mass and stiffness property variations?

Initial Config Final Config Assembler

Tug Only Tug + Seg Tug + Seg + Base Tug Only, Base Tug + Seg, Base Tug Only, Base

Assembly Sequence

• Configuration: static configuration for a given time period, (eg. Tug Only, Tug + Segment)

• Transition: change from one configuration to another (eg. Docking: Tug Tug + Segment)

• Single Control System Tug• Need to design control system to handle all configurations• Want to maintain performance (ie stability, efficiency,

accuracy) and versatility (ex. minimal hardcoded transitions and properties)

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Reconfigurable control

• Reconfigurable control – on-line model calculation:– Identify a vector of properties p upon which the model

depends– Develop the analytic expressions to calculate the model (N)

based on the vector p– At each transition, update the vector p– At each update of the vector p, re-calculate the model N

based on the analytic expressions– Use the model N to calculate the control input (u)

• Goal: Implement and Demonstrate on hardware

Currently implemented p

DirThrusterLocThrusterCMInertiaMassp __

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SPHERES Overview

+ Z

- Y

- XUltrasonic Receivers

CO2 Tank

Adjustable Regulator

Pressure Gauge

Thruster

Satellite body axes

Diameter 0.22 m

Dry Mass 3.5 kg

Wet Mass 4.3 kg

Thrust(single thruster)

0.11 N

CO2 Capacity 170g

Control Panel

Lexan Shell

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Control Allocation Methods

• Assumptions of SPHERES baseline control allocation algorithm– Symmetric thruster placement– Center of mass fixed in center of thruster envelope– Fixed thruster configuration

• Intermediate reconfigurable control allocation algorithms– Mixer A: Reconfigurable to thruster configuration

• Assumes symmetric thrusters• Application – Docking to an active payload

– Mixer B: Reconfigurable to center of mass location• Assumes fixed thruster configuration• Application – Docking to a passive payload

• Mixer C: Reconfigurable to thruster configuration AND center of mass location– Generalized mixer– Removes all assumptions of baseline SPHERES control allocation

algorithm

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Mixer C Implementation

Control Vector

(Hardcoded) Mixing Matrix

Calculate thruster forces & durations

Thruster on / off times

Original

ReconfigurableInputs Outputs

Thruster Config (rgc, F)

Calc location of thruster (rcm) from rgc

and CM

Calculate thruster forces & durations

Thruster on / off times

Torque = rcm x F

Mapping Matrix

Invert to get full Mixing Matrix

Control Vector

Control Allocation Algorithm on SPHERES

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Testing

• Objectives:– Stability: actuation of control input stabilizes the system– Accuracy: can achieve ± 2cm position control required for docking– Fuel Performance: fuel usage is improved by updating the model

• Four test configurations– C1: SPHERE only– C2: SPHERE + Battery Proof Mass– C3: SPHERE + SPHERE Proof Mass– C4: 2 SPHERE attached (joint firing)

• Test Cases– Attitude Control only– Position and Attitude Control

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Results: Attitude Control C4

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Results: Attitude Control C4• Two SPHERES attached by Velcro.

Both can fire thrusters.• Two 90˚ Z axis rotations

– 1st rotation OLD gains, Ts = 40s, O=30˚

– 2nd rotation NEW gains, Ts = 20s, O=20˚

• Two SPHERES attached by Velcro. Only one can fire thrusters.

• Two 90˚ Z axis rotations– 1st rotation OLD gains, O=47˚– 2nd rotation NEW gains, O=41˚

Fuel usage given in percent usage of tank (170g CO2 in one tank)

1.77% 2.77% 1.22% 1.18%

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Results: Position & Attitude Control

• C4: 2 SPHERES attached, joint thruster firing• Targets: [0.4, 0, 0], [0.4, 0.4, 0], [-0.4, -0.4, -0.4],

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Results: Position & Attitude Control

C4: Two Satellite Joint FiringC1: Satellite Only

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Results: Position & Attitude Control

• C3: SPHERES plus SPHERE Proof Mass• Targets: [0.4, 0, 0], [-0.4, -0.4, -0.4], [0.4, 0.4, 0]

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Results: Position & Attitude Control

C3: Satellite with Sat Proof MassC1: Satellite Only

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Conclusions / Future Work

• Motivation:– Update model on-line during a test to account for

configuration changes– Want to maintain control performance in terms of stability,

efficiency, and accuracy• Conclusions

– Demonstrated reconfiguration for attitude and position– In process of increasing accuracy in 2 SPHERE case to be

sufficient for docking and assembly• Future Work

– Demonstrate reconfiguration in full assembly test– Introduce flexible dynamics– Augment to include sensor reconfiguration

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Questions?

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Back-up

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Control Reconfiguration MethodsA

-Prio

ri In

form

atio

n

Complete

No Information

Method of Model Determination Segment Properties

Operational States

Transitions

Gain Scheduling (Parlos & Sunkel) Known Known Known

Multiple Model (Maybeck & Stevens) Known Known Unknown

On-line Model Calculation Known Unknown Unknown

System Identification (Wilson et al) Unknown Unknown Unknown

• Multiple model reconfiguration (Maybeck and Stevens)

– Multiple Kalman filters for each operational states

– Transition between models is seamless, based on analysis of measurement residuals

• On-line model calculation– Takes in a properties vector (eg. p = [Mass, Inertia, Center of Mass, …] )– Generates the model from the list of properties– Uses the model to generate the appropriate control input

• ISS Attitude Gain Scheduling (Parlos & Sunkel)

– Implemented for docking, series of equilibrium states

– Assumes look-up table for mass properties at each equilibrium state

• System Identification (Wilson et al)

– Maneuvers to determine model (mass and inertia) using recursive least squares

– Assumes thruster maneuvers

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Approach

• Center of Mass (CM),• Thruster locations w.r.t CM• Thruster Number &

Directions• Thrusters available

• Mass, Inertia,

BuxAx ˆ̂

Cxy xKu ˆ

vHxz

State Space Model General

• Controller Gains

• Sensor locations w.r.t CM• Sensors available• Estimation statistics

wBuAxx ))(( pNfu

Np

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On-line Model Calculation (2/3)

• Example of analytic expressions (similar for position gains)• Assumes small cross products for inertias• Attitude Gains: K = f(p)

PD control PID control

432

2

zz

yy

xx

nd

zz

yy

xx

np

II

IwK

II

IwK

4312

;2

2

2

zz

yy

xx

nd

zz

yy

xxn

i

n

zz

yy

xx

np

II

I

TwK

II

I

TwK

Tw

II

IwK

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On-line Model Calculation (3/3)

• Analytic expressions for thruster configuration update• Mixing matrix (M): 6 (forces and torques) by num thrusters

– Inverse of Mixing matrix converts control vector to thruster forces

z

y

x

z

y

x

thruster

TTTFFF

Mu 1 Control vector input

dirThrusterrlocThrusterdirThrusterM CM _)_(_

Inverse of Mixing Matrix

Thruster forces

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Results: Position & Attitude (1)

C1: Satellite Only C2: Satellite Plus Batt Proof Mass