Attitude determination and control (ADCS 16.684 Space Systems Product Development pring 2001 S Olivier l de weck Department of Aeronautics and Astronautics Massachusetts Institute of Technology
Attitude Determination and Control Attitude Determination and Control (ADCS) Olivier L. de Olivier L. de Weck Department of Aeronautics and Astronautics Department of Aeronautics and Astronautics Massachusetts Institute of Technology Massachusetts Institute of Technology 16.684 Space Systems Product Development 16.684 Space Systems Product Development Spring 2001 Spring 2001
ADCS Motivation Motivation Sensors GPS star trackers. limb In order to point and slew optical sensors rate gy ros. inertial systems, spacecraft attitude control measurement units provides coarse pointing while Control laws optics control provides fine o Spacecraft Slew Maneuvers pointing Spacecraft Control Euler angles Q laterior Spacecraft stabilization Spin stabilization Key Question: Gravity gradient What are the pointing Three -Axis Control requirements for satellite Formation Flight Actuators NEED expendable propellant: Reaction wheel assemblies On-board fuel often determines life (RWAS) Failing gyros are critical(e.g. HST) Control moment gyros (CMGS) Magnetic Torque Rods Thrusters
ADCS Motivation ADCS Motivation Motivation — In order to point and slew optical systems, spacecraft attitude control provides coarse pointing while optics control provides fine pointing Spacecraft Control — Spacecraft Stabilization — Spin Stabilization — Gravity Gradient — Three-Axis Control — Formation Flight — Actuators — Reaction Wheel Assemblies (RWAs) — Control Moment Gyros (CMGs) — Magnetic Torque Rods — Thrusters — Sensors: GPS, star trackers, limb sensors, rate gyros, inertial measurement units — Control Laws Spacecraft Slew Maneuvers — Euler Angles — Quaternions Key Question: What are the pointing requirements for satellite ? NEED expendable propellant: • On-board fuel often determines life • Failing gyros are critical (e.g. HST)
Outline o Definitions and terminology o Coordinate systems and mathematical Attitude representations o Rigid Body dynamics o Disturbance Torques in Space o Passive attitude control schemes o Actuators o sensors o Active Attitude Control Concepts o ADCS Performance and stability Measures o Estimation and Filtering in Attitude Determination o maneuvers o Other System Consideration, Control/Structure interaction o Technological Trends and Advanced concepts
Outline Outline Definitions and Terminology Coordinate Systems and Mathematical Attitude Representations Rigid Body Dynamics Disturbance Torques in Space Passive Attitude Control Schemes Actuators Sensors Active Attitude Control Concepts ADCS Performance and Stability Measures Estimation and Filtering in Attitude Determination Maneuvers Other System Consideration, Control/Structure interaction Technological Trends and Advanced Concepts
Opening remarks o Nearly all ADCs design and Performance can be viewed in terms of rigid body dynamics o typically a Major spacecraft system o For large, light-weight structures with low fundamental frequencies the flexibility needs to be taken into account o ADCS requirements often drive overall s/c design o Components are cumbersome, massive and power-consuming o Field-of-View requirements and specific orientation are key o Design, analysis and testing are typically the most challenging of all subsystems with the exception of payload lesign o Need a true systems orientation to be successful at designing and implementing an ADCs
Opening Remarks Opening Remarks Nearly all ADCS Design and Performance can be viewed in terms of RIGID BODY dynamics Typically a Major spacecraft system For large, light-weight structures with low fundamental frequencies the flexibility needs to be taken into account ADCS requirements often drive overall S/C design Components are cumbersome, massive and power-consuming Field-of-View requirements and specific orientation are key Design, analysis and testing are typically the most challenging of all subsystems with the exception of payload design Need a true “systems orientation” to be successful at designing and implementing an ADCS
erminology ATTITUDE: Orientation of a defined spacecraft body coordinate system with respect to a defined external frame(GCl,HCi) ATTITUDE DETERMINATION: Real-Time or Post-Facto knowledge within a given tolerance, of the spacecraft attitude ATTITUDE CONTROL: Maintenance of a desired specified attitude within a given tolerance ATTITUDE ERROR: Low Frequency spacecraft misalignment usually the intended topic of attitude control ATTITUDE JITTER: "High Frequency spacecraft misalignment; usually ignored by adcs reduced by good design or fine pointing/optical control
Terminology Terminology ATTITUDE ATTITUDE : Orientation of a defined spacecraft body coordinate system with respect to a defined external frame (GCI,HCI) ATTITUDE ATTITUDE DETERMINATION: DETERMINATION: Real-Time or Post-Facto knowledge, within a given tolerance, of the spacecraft attitude ATTITUDE CONTROL: ATTITUDE CONTROL: Maintenance of a desired, specified attitude within a given tolerance ATTITUDE ERROR: ATTITUDE ERROR: “Low Frequency” spacecraft misalignment; usually the intended topic of attitude control ATTITUDE JITTER: ATTITUDE JITTER: “High Frequency” spacecraft misalignment; usually ignored by ADCS; reduced by good design or fine pointing/optical control
Pointing Control Definitions target target desired pointing direction estimate true actual pointing direction(mean) estimate estimate of true(instantaneous pointing accuracy (long-term) stability(peak-peak motion) true knowledge error control error a= pointing accuracy =attitude error s=stability=attitude jitter ource G mosi NASA GSFC
Pointing Control Definitions Pointing Control Definitions target desired pointing direction true actual pointing direction (mean) estimate estimate of true (instantaneous) a pointing accuracy (long-term) s stability (peak-peak motion) k knowledge error c control error target estimate true c k a s Source: G. Mosier NASA GSFC a = pointing accuracy = attitude error a = pointing accuracy = attitude error s = stability = attitude jitter s = stability = attitude jitter
Attitude Coordinate systems North celestial Pole) GCI: Geocentric Inertial Coordinates Cross product AA Geometry: Celestial Sphere YEZXX dihedral A Y VERNAL X EQUINOX a: right ascension Inertial Coordinate δ: Declination ystem X andy are in the plane of the ecliptic
Attitude Coordinate Systems Attitude Coordinate Systems X Z Y ^ ^ ^ Y = Z x X Cross product Cross product ^ ^ ^ Geometry: Celestial Sphere Geometry: Celestial Sphere : Right Ascension : Right Ascension : Declination : Declination (North Celestial Pole) Arc length dihedral Inertial Coordinate Inertial Coordinate System GCI: Geocentric Inertial Coordinates GCI: Geocentric Inertial Coordinates VERNAL EQUINOX EQUINOX X and Y are in the plane of the ecliptic
Attitude description notations &=Coordinate system P=Ⅴ ector P P=Position vector w.r. t. A 100 Unit vectors of (A]=XA YA Z0 1 0 001 Describe the orientation of a body (1)Attach a coordinate system to the body 2)Describe a coordinate system relative to an inertial reference frame
Attitude Description Notations Attitude Description Notations Describe the orientation of a body: (1) Attach a coordinate system to the body (2) Describe a coordinate system relative to an inertial reference frame ZA ˆ X A ˆ YA ˆ Position vector w.r.t. { } Vector { } Coordinate system P A P A = = ⋅ = P A Py Px Pz = z y x A P P P P [ ] = = 0 0 1 0 1 0 1 0 0 Unit vectors of { A } X A YA Z A ˆ ˆ ˆ
Rotation matrix A (A=Reference coordinate system B B= Body coordinate system Rotation matrix from b to Aj B 后R=|xB^BA2p A Special properties of rotation matrices B (1)Orthogonal RR=R=R (2 ) Orthonormal R=1 R=0 cos0-sin0 (3)Not commutative 0 sin] cosb RPR≠RRR
Rotation Matrix Rotation Matrix Rotation matrix from {B} to {A} Jefferson Memorial ZA ˆ XA ˆ YA ˆ {A} = Referencecoordinatesystem XB ˆ YB ˆ ZBˆ {B} = Body coordinate system [ B B B ] A A B R = Xˆ AYˆ AZˆ Special properties of rotation matrices: 1 , − R R = I R = R T T R =1 (1) Orthogonal: R R R R B A C BC AB ≠ B Jefferson Memorial ZA ˆ XA ˆ YA ˆ XB ˆ YB ˆ ZBˆ θ θ R = AB 0 sin cos 0 cos -sin 1 0 0 (2) Orthonormal: (3) Not commutative
Euler angles(1) Euler angles describe a sequence of three rotations about different axes in order to align one coord system with a second coord system Rotate about za by a Rotate about yb by B Rotate about Xc by y ZG C B B B C coSa -sina cosb 0 sinB 100 R= sina cosa 0 R=010 D R=0 coSy -siny inB 0 cosB 0 siny cosy AR-BR ER SR
Euler Angles (1) Angles (1) Euler angles describe a sequence of three rotations about different axes in order to align one coord. system with a second coord. system. = 0 0 1 sin cos 0 cos -sin 0 α α α α RAB Rotate about Z ˆ A byα Rotate about Y ˆ B by β Rotate about XC by γ ˆ ZA ˆ XA ˆ YA ˆ XB ˆ YB ˆ ZB ˆ α α ZB ˆ XB ˆ YB ˆ XC ˆ YC ˆ ZC ˆ β β ZC ˆ XC ˆ YD ˆ X D ˆ YC ˆ ZD ˆ γ γ = β β β β -sin 0 cos 0 1 0 cos 0 sin RBC = γ γ γ γ 0 sin cos 0 cos -sin 1 0 0 RCD R R R RCD BC AB AD =
