OMEGA-1: Bare-Metal Model Predictive Control

OMEGA-1 is a deterministic, constrained Model Predictive Control (MPC) engine designed for safety-critical embedded systems. Running on an STM32H743 (ARM Cortex-M7) at 400 MHz, the solver guarantees a strictly bounded Worst-Case Execution Time (WCET) by replacing unpredictable interior-point methods with a fixed-iteration Fast Gradient Method (FGM).

Phase 1: Simulation & Constraint Verification

Before touching hardware, the continuous-time physics were derived via Lagrangian mechanics and discretized exactly at 100 Hz. The FGM solver was verified in C++ to guarantee it actively utilizes physical constraints to arrest a catastrophic 45-degree fall.

Physical proof of constrained MPC: The solver hits and rides the hard torque limits ($\pm$0.5 Nm) to recover the pendulum, successfully dropping the peak angle below 0.05 radians during the settling phase.

Hardware Architecture (STM32H743VIT6)

To achieve zero-wait-state determinism and eliminate bus contention with the DMA2D display pipeline, memory placement is strictly enforced via the linker script:

Component	Memory Region	Address Space	Bus Segment
FGM Solver Hot-Loop	ITCM	0x00000000	64-bit ITCM Bus
State Matrices & Data	DTCM	0x20000000	2x 32-bit D0/D1 Buses
Display Framebuffers	AXI SRAM	0x24000000	AXI Matrix (Isolated)

WCET Profiling (Phase 2)

Statistics drawn directly from 10,000 on-device perturbations spanning $\pm$ 30 degrees, measured via DWT cycle counter.

Metric	Cycles	Time (ms)
Worst-Case	[TBD]	[TBD]
Mean	[TBD]	[TBD]
Std Dev ($\sigma$)	[TBD]	[TBD]

Full System Demo (Phase 3)

[Link to Video / GIF placeholder]