Receding-Horizon Nullspace Optimization for Actuation-Aware Control Allocation in Omnidirectional UAVs

Abstract

Fully actuated omnidirectional UAVs enable independent control of forces and torques along all six degrees of freedom, broadening the operational envelope for agile flight and aerial interaction tasks. However, conventional control allocation methods neglect the asymmetric dynamics of the onboard actuators, which can induce oscillatory motor commands and degrade trajectory tracking during dynamic maneuvers. This work proposes a receding-horizon, actuation-aware allocation strategy that explicitly incorporates asymmetric motor dynamics and exploits the redundancy of over-actuated platforms through nullspace optimization. By forward-simulating the closed-loop system over a prediction horizon, the method anticipates actuator-induced oscillations and suppresses them through smooth redistribution of motor commands, while preserving the desired body wrench exactly. The approach is formulated as a constrained optimal control problem solved online via Constrained iterative LQR. Simulation results on the OmniOcta platform demonstrate that the proposed method significantly reduces motor command oscillations compared to a conventional single-step quadratic programming allocator, yielding improved trajectory tracking in both position and orientation.

Figures (8)

• Figure 1: Conceptual overview of the proposed approach. The baseline allocator (MBNO) solves a single-step QP that is agnostic to actuator dynamics, resulting in chattering motor commands. The proposed method embeds the asymmetric motor dynamics into a receding-horizon iLQR framework, producing smooth, predictive actuator commands that anticipate and suppress oscillatory behavior.
• Figure 2: Closed-loop control architecture of the OmniOcta. The trajectory generator provides reference states and their derivatives to the controller, which computes a desired six-dimensional wrench $\boldsymbol{\xi}^{*}$. The allocator maps this wrench to individual motor commands $\mathbf{u}_{\mathrm{cmd}} \in \mathbb{R}^8$. Onboard sensors close the loop by providing state estimates back to the controller.
• Figure 3: Architecture of the proposed receding-horizon nullspace optimization. The lower loop represents the real-time control pipeline, where the optimal allocation policy maps the desired wrench to motor commands $\mathbf{u}_{\mathrm{cmd}} \in \mathbb{R}^8$. The upper block depicts the CiLQR solver, which internally forward-simulates the controller, the rigid-body dynamics, and the asymmetric first-order motor model over a short prediction horizon. By optimizing the nullspace allocation variables $\mathbf{X}^{*}$ subject to motor limits $[\mathbf{u}_{\min},\, \mathbf{u}_{\max}]$, the solver produces smooth actuator commands that are fed back to the allocation policy at each receding-horizon cycle.
• Figure 4: Reference trajectory: the OmniOcta translates from $(0,0,3)\,\mathrm{m}$ to $(1,1,2)\,\mathrm{m}$ over 60 s while executing a full rotation about the y-axis.
• Figure 5: Actual motor commands $\mathbf{u}_{\mathrm{act}}$ under the baseline MBNO allocator. Oscillatory behavior is clearly visible between $t = 30\,\mathrm{s}$ and $t = 37\,\mathrm{s}$.