# Thruster Control Allocation --- ## About Me --- ## Biggest Lesson **Solving the interesting problem, not the actual problem** _Autonomous tractor safety system — Python GIL bottleneck_ | Built | Should Have Built | | -------------------------------- | ---------------------- | | Distributed architecture | Simple multiprocessing | | Rust processes + gRPC + protobuf | A few subprocesses | | "Cloud-native" on embedded | Boring and appropriate | **Worked on dev hardware. Collapsed on production ARM.** → _"What are the constraints here?"_ before _"What's the cleanest design?"_ --- ## Problem Statement > Thruster control algorithm which commands a set of 5 pulsed thrusters - > What (additional) assumptions about the system did you make? <!-- .element: class="fragment" --> - Thrusters used for RW desat + maneuver pointing and *not* three-axis fine-pointing - Limitation is the minimum thruster on-time + 5-second lockout - Need canted thrusters to have roll control - > What are the inputs, outputs, and parameters? <!-- .element: class="fragment" --> - Body torque and axial thrust is the input - Thruster on-times is the output - 10N thrust per thruster, one on each corner and one in the center - > What are the key performance metrics? <!-- .element: class="fragment" --> - Torque/Force accuracy - Time-delays and minimum errors (driven by dead-time on the thrusters) - Redundancy/Failover --- ## Possible Algorithms for Thruster Allocation * <!-- .element: class="fragment fade-in" data-fragment-index="1"--> <strong>Pseudo-inverse</strong> + clipped output <!-- .element: class="fragment fade-in" data-fragment-index="1"--> - Simplest to implement * <!-- .element: class="fragment" data-fragment-index="2" --> <strong>Bounded least-squares</strong> (`scipy.optimize.lsq_linear`) <!-- .element: class="fragment fade-in" data-fragment-index="2"--> - Gives results that already bounded to constraints ($x_l \leq x \leq x_u$) - More complicated compared to pseudo-inverse * <!-- .element: class="fragment" data-fragment-index="3" --><strong>Simplex Optimizer</strong> (fuel-optimal allocation) - Needs initial guess - Allocation could fail - More computationally complex - <!-- .element: class="fragment" data-fragment-index="4" --> Likely overkill in this case --- ## Implementation The system is formulated as a linear allocation problem: $ \min\limits_{x(t)} ||A \cdot x - b ||_2$ - <!-- .element: class="fragment fade-in" data-fragment-index="1" --> $A \in \mathbb{R}^{4×5}$ : Control authority matrix (maps on-times to impulses) - Each column corresponds to one thruster - First three rows give the torque generated by the thruster - Last row is force generated by thruster in Z direction - <!-- .element: class="fragment fade-in" data-fragment-index="2" --> $b \in \mathbb{R}^4$ : Desired impulse. $\begin{bmatrix} M_x \Delta t & M_y \Delta t & M_z \Delta t & F_z \Delta t \end{bmatrix}$ - <!-- .element: class="fragment fade-in" data-fragment-index="3" --> $x \in \mathbb{R}^5$ : Thruster on-times [seconds] <mark class="fragment fade-in" data-fragment-index="4">$\leftarrow$ Solve for this</mark> - <!-- .element: class="fragment fade-in" data-fragment-index="5" --> Remove the last row when in torque-only mode --- ## Thruster Failure Analysis <style> .two-col { display: grid; grid-template-columns: 1fr 1fr; gap: 1.5em; font-size: 0.55em; } .two-col table { margin: 0; width: 100%; } .two-col th, .two-col td { padding: 0.2em 0.4em; } .two-col h4 { margin: 0 0 0.3em 0; font-size: 1.3em; } .slide-note { font-size: 0.6em; text-align: center; margin-top: 0.8em; font-style: italic; } </style> <div class="two-col"> <div> #### Single Thruster Failures | Config | Rank | σ | Effect | |--------|------|---|--------| | Nominal | 2/3 | 10, 10, 0 | No roll | | Corner | 2/3 | 10, 7, 0 | −30% | | Center | 2/3 | 10, 10, 0 | None | </div> <div> #### Two-Thruster Failures | Failed | Rank | Result | |--------|------|--------| | T1+T5 | 1/3 | 1-axis | | T2+T4 | 1/3 | 1-axis | | Other | 2/3 | OK | </div> </div> <p class="slide-note">Diagonal pairs (T1+T5, T2+T4) are critical. Center thruster = zero torque at CoM.</p> --- ## Controllability Demo <style> main { max-width: none !important; } .container-container { height: calc(100vh - 120px); width: 100%; } </style> <embed class="container-container" type="text/html" src="./controllability-demo/index.html"> --- ## Live Demo <style> main { max-width: none !important; } .container-container { height: 100vh; width: 100%; } </style> <embed class="container-container" type="text/html" src="./allocator-live-demo/index.html"> --- ## Simulator architecture <figure> <?xml version="1.0" encoding="UTF-8" standalone="no"?> <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd"> <!-- Generated by graphviz version 14.0.5 (20251129.0259) --> <!-- Title: SimTiming Pages: 1 --> <svg width="479pt" height="93pt" viewBox="0.00 0.00 479.00 93.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 89)"> <title>SimTiming</title> <polygon fill="white" stroke="none" points="-4,4 -4,-89 474.75,-89 474.75,4 -4,4"/> <g id="clust1" class="cluster"> <title>cluster_ctrl</title> <polygon fill="none" stroke="#4a90d9" stroke-dasharray="5,2" points="8,-8 8,-77 230.25,-77 230.25,-8 8,-8"/> <text xml:space="preserve" text-anchor="middle" x="119.12" y="-15.2" font-family="Times,serif" font-size="14.00">25 Hz</text> </g> <g id="clust2" class="cluster"> <title>cluster_dyn</title> <polygon fill="none" stroke="#66bb6a" stroke-dasharray="5,2" points="238.25,-8 238.25,-77 462.75,-77 462.75,-8 238.25,-8"/> <text xml:space="preserve" text-anchor="middle" x="350.5" y="-15.2" font-family="Times,serif" font-size="14.00">100 Hz</text> </g> <!-- pid --> <g id="node1" class="node"> <title>pid</title> <polygon fill="none" stroke="black" points="70,-69.4 16,-69.4 16,-40.6 70,-40.6 70,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="43" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">PID</text> </g> <!-- alloc --> <g id="node2" class="node"> <title>alloc</title> <polygon fill="none" stroke="black" points="146.25,-69.4 92,-69.4 92,-40.6 146.25,-40.6 146.25,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="119.12" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">Allocator</text> </g> <!-- pid->alloc --> <g id="edge1" class="edge"> <title>pid->alloc</title> <path fill="none" stroke="black" d="M70.34,-55C73.62,-55 77.02,-55 80.43,-55"/> <polygon fill="black" stroke="black" points="80.35,-58.5 90.35,-55 80.35,-51.5 80.35,-58.5"/> </g> <!-- tif --> <g id="node3" class="node"> <title>tif</title> <polygon fill="none" stroke="black" points="222.25,-69.4 168.25,-69.4 168.25,-40.6 222.25,-40.6 222.25,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="195.25" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">Thr Mgr</text> </g> <!-- alloc->tif --> <g id="edge2" class="edge"> <title>alloc->tif</title> <path fill="none" stroke="black" d="M146.47,-55C149.74,-55 153.14,-55 156.55,-55"/> <polygon fill="black" stroke="black" points="156.48,-58.5 166.48,-55 156.48,-51.5 156.48,-58.5"/> </g> <!-- tstate --> <g id="node4" class="node"> <title>tstate</title> <polygon fill="none" stroke="black" points="302.75,-69.4 246.25,-69.4 246.25,-40.6 302.75,-40.6 302.75,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="274.5" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">Thr State</text> </g> <!-- tif->tstate --> <g id="edge5" class="edge"> <title>tif->tstate</title> <path fill="none" stroke="black" d="M222.4,-55C226.29,-55 230.36,-55 234.43,-55"/> <polygon fill="black" stroke="black" points="234.27,-58.5 244.27,-55 234.27,-51.5 234.27,-58.5"/> </g> <!-- ftau --> <g id="node5" class="node"> <title>ftau</title> <polygon fill="none" stroke="black" points="378.75,-69.4 324.75,-69.4 324.75,-40.6 378.75,-40.6 378.75,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="351.75" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">F, τ</text> </g> <!-- tstate->ftau --> <g id="edge3" class="edge"> <title>tstate->ftau</title> <path fill="none" stroke="black" d="M303.09,-55C306.4,-55 309.81,-55 313.22,-55"/> <polygon fill="black" stroke="black" points="313.15,-58.5 323.15,-55 313.15,-51.5 313.15,-58.5"/> </g> <!-- integ --> <g id="node6" class="node"> <title>integ</title> <polygon fill="none" stroke="black" points="454.75,-69.4 400.75,-69.4 400.75,-40.6 454.75,-40.6 454.75,-69.4"/> <text xml:space="preserve" text-anchor="middle" x="427.75" y="-51.12" font-family="Helvetica,sans-Serif" font-size="10.00">6-DOF</text> </g> <!-- ftau->integ --> <g id="edge4" class="edge"> <title>ftau->integ</title> <path fill="none" stroke="black" d="M379.05,-55C382.32,-55 385.71,-55 389.11,-55"/> <polygon fill="black" stroke="black" points="389.02,-58.5 399.02,-55 389.02,-51.5 389.02,-58.5"/> </g> <!-- integ->pid --> <g id="edge6" class="edge"> <title>integ->pid</title> <path fill="none" stroke="black" stroke-dasharray="1,5" d="M400.31,-41.92C393.42,-38.94 385.92,-36.05 378.75,-34 334.16,-21.26 321.87,-19 275.5,-19 194.25,-19 194.25,-19 194.25,-19 148.32,-19 136.15,-21.35 92,-34 88.41,-35.03 84.75,-36.26 81.11,-37.62"/> <polygon fill="black" stroke="black" points="79.81,-34.37 71.85,-41.36 82.43,-40.86 79.81,-34.37"/> </g> </g> </svg> </figure> - <!-- .element: class="fragment" --> <strong>PID Controller</strong>: Quaternion error → body torque command - <!-- .element: class="fragment" --> <strong>Thruster Manager</strong>: Converts on-times to binary on/off states - <!-- .element: class="fragment" --> <strong>6-DOF Dynamics</strong>: Euler + quaternion kinematics integration --- ## Live Demo <style> main { /*Override the main CSS so that the Editors can be wide*/ max-width: none !important; } .container-container { height: 100vh; width: 100%; } </style> <embed class="container-container" type="text/html" src="./slew-sim-demo/index.html"> --- ## HITL/Sim testing? - Split out the sim into a separate machine with I/O card - Run the Valve/Engine control lines to the I/O card from the flight computer - Add interface in sim to read I/O pin state to determine thruster state --- ## What's missing? - Inputs from Thermal, Prop (for thrust profile), Avionics (electrical limitations) - Controls analysis for stability --- ## Conclusion