A Constrained Attitude Control Module for Small Satellites

Transcription

1 A Constrained Attitude Control Module for Small Satellites Henri Kjellberg and E. Glenn Lightsey The University of Texas at Austin Small Satellite Conference Logan, Utah August 14, 2012

2 Motivation for Attitude Constraints Common constraints for a small satellite Goal: A practical algorithm that can be used on CubeSats

3 Example: 3U CubeSat ARMADILLO

4 GN&C Module Design Overview Magnetometer Reaction Wheels Gyroscopes Sun Sensors Thruster Module Torque Rods LPC3250 GN&C Computer (200 MHz) 4

5 Pictures of the Hardware Right Now Top: GN&C Module being assembled Right: Front and back of the flight coldgas thruster module

6 Traditional Constrained Control Methods McInnes, C. R. - Large Angle Slew Maneuvers with Autonomous Sun Vector Avoidance Artificial potential functions Hablani, H., B. - Attitude Commands Avoiding Bright Objects and Maintaining Communications with Ground Station Tangential path around exclusion cones Frazzoli, E., - A Randomized Attitude Slew Planning Algorithm for Autonomous Spacecraft Randomized motion planning algorithms Kim, Y. - On the Convex Parameterization of Constrained Spacecraft Reorientation Semi-definite programming

7 A New Approach to Maneuver Planning Represent all possible directions as pixels on a discretized unit sphere Determine the directions of pointing constraints as regions on the discretized unit sphere Use a pre-existing path finding algorithm to plan a maneuver from the current direction to the desired direction while meeting constraints Provide solved maneuver to attitude control system for execution 7

8 Overview Constrained Control Scheme Note: Step 0 only has to be executed once

9 Step 0: Discretize Sphere Icosahedron shell discretization algorithm developed by Tegmark (1996) Converts unit vector to pixel number and vice versa Step 0 Algorithm: 1. Find icosahedron vertices 2. Create rotation matrices for each triangular face 3. Discretize a hexagonal grid onto each triangle 4. Project hexagonal grid onto unit sphere 5. Identify and store each pixel s set of neighbors

10 Step 1: Find keep-out regions Constraint imposed by sun sensor field-of-view Moon Constraint Sun Constraint Earth Constraint No maximum number of constraints (as long as a feasible path exists) Constraints can take on any shape

11 A* Pathfinding Algorithm Overview

12 A* Pathfinding Cost Model The distance plus path cost for the pixel k is f p k = g p k + h p k The path cost for the pixel k g p k = θ e k, e k 1 + d + g p k 1 The heuristic estimate of distance to goal from the current pixel is h p k, p m = arccos v p k v p m

13 Step 2: X-axis admissible path Turning points (red dots) Goal Final trajectory (blue line) Start Pixels checked by A* (cyan) Note: Earth constraint hidden for clarity

14 Step 2: Find rotation quaternion Find vector to next turning point in body frame n B x k + 1 = qi 0 B k n x I k + 1 q I B k 0 Find angle of rotation from current pixel to next turning point pixel φ = arccos n B x k + 1 n B x k Compute quaternion rotation from current pixel of next turning point pixel n B x k + 1 n B x k q B B k + 1 = n B x k + 1 n B x k sin φ 2 cos φ 2 Form inertial quaternion rotation that satisfies the x-axis constraint I q B = q B I B q B

15 Step 2: Rotate about x-axis Rotate the Sun vector from the inertial frame to the body frame B n s k I = q B k n s I k I q B 0 0 k Keep only y and z components B n B s k = 0 n B sy k n sz k Taking the dot product of the sun sensor and y and z components of the sun vector in the body frame yields the angle of rotation about the x-axis that minimizes the sun sensor to Sun angle ψ = arccos n y B k n s B k Form the rotation quaternion and stack with the previous results to form quaternion that satisfies all constraints n y B k n s B k B q B k + 1 = n y B k n s B k sin ψ 2 cos ψ 2 I q B B = q B q B B q B I

16 Step 3: Command rotation sequence From the previous computations we have a set of rotation quaternions to each turning point pixel Using B. Wie s (2008) body rate and torque constrained quaternion error controller u = sat Ksat Pq e + Cw K i = q I i B k 1 I q B k 1 θ max, i = 1,2,3 KP = cjθ max When spacecraft gets close to the next turning point, it moves on to the next one in the set

17 Step 3: Final trajectory End X-axis trajectory (blue) avoiding bright objects Start Y-axis trajectory (red) maintaining sun within sensor field-of-view

18 QUESTIONS? Contact Information Henri Kjellberg NASA Space Technology Research Fellow E. Glenn Lightsey +1(512)