L1 Adaptive Control — Race Drone Testbed

Built a custom race drone from scratch as a hardware testbed for validating L1 adaptive control on a highly agile, lightweight platform with significant model uncertainty.

Components selected and staged for assembly

Platform assembled and ready for integration

Motivation

Race-class quadrotors are an ideal testbed for adaptive control research — they operate at high bandwidth, have poorly characterized aerodynamic interactions between rotors at high speed, and experience significant gyroscopic and inertial cross-coupling during aggressive maneuvers. These are exactly the conditions where L1 adaptive augmentation provides the most benefit over a fixed-gain baseline.

L1 Adaptive Architecture

The L1 controller augments a baseline LQR attitude controller. A state predictor runs in parallel at high rate:

\[\dot{\hat{x}} = A_m \hat{x} + B\left(\hat{\sigma}(t) + u\right), \quad \hat{\sigma}(t) = \hat{\theta}^\top \phi(x)\]

The adaptive law updates at the predictor rate:

\[\dot{\hat{\theta}} = -\Gamma \text{Proj}(\hat{\theta},\ \tilde{x}^\top P B \phi(x))\]

where \(\tilde{x} = \hat{x} - x\) is the prediction error and \(\Gamma > 0\) is the adaptation gain. A low-pass filter \(C(s)\) on the adaptive signal provides the bandwidth separation that guarantees robustness:

\[u_{\text{ad}}(s) = C(s)\hat{\sigma}(s), \quad \|C(s)\|_{\mathcal{L}_1} < \frac{1}{L}\]

The \(\mathcal{L}_1\) gain condition bounds the transient response and ensures the adaptive loop does not destabilize the plant.

Platform Specifications

Parameter	Value
Frame size	5” race class
Flight controller	Custom (STM32-based)
Motor KV	High-KV for agile response
Control loop rate	1 kHz inner loop
Adaptive predictor rate	1 kHz

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