Allocation for Omnidirectional Aerial Robots: Incorporating Power Dynamics

TL;DR

The paper addresses the control-allocation challenge for tilt-rotor omnidirectional aerial robots under actuator dynamics and overactuation. It develops three novel, dynamics-aware allocation methods—adiff (augmented differential allocation without acceleration feedback), asecond (actuator-normalized differential allocation), and apower (propeller-power-curve-based allocation)—to extend geometric allocation and reduce reliance on acceleration feedback. Compared to existing geometric and differential schemes, these methods improve numerical conditioning, enable in-flight propeller deactivation, and sustain higher dynamic tracking with preserved nullspace usefulness, demonstrated on real hardware with up to 70% faster trajectories. The work provides practical tools for aerial manipulation and interaction by balancing propulsion and tilt actuation under realistic power and saturation constraints, and suggests future work on disturbances and more complex actuator models.

Abstract

Tilt-rotor aerial robots are more dynamic and versatile than fixed-rotor platforms, since the thrust vector and body orientation are decoupled. However, the coordination of servos and propellers (the allocation problem) is not trivial, especially accounting for overactuation and actuator dynamics. We incrementally build and present three novel allocation methods for tilt-rotor aerial robots, comparing them to state-of-the-art methods on a real system performing dynamic maneuvers. We extend the state-of-the-art geometric allocation into a differential allocation, which uses the platform's redundancy and does not suffer from singularities. We expand it by incorporating actuator dynamics and propeller power dynamics. These allow us to model dynamic propeller acceleration limits, bringing two main advantages: balancing propeller speed without the need for nullspace goals and allowing the platform to selectively turn off propellers during flight, opening the door to new manipulation possibilities. We also use actuator dynamics and limits to normalize the allocation problem, making it easier to tune and allowing it to track 70% faster trajectories than a geometric allocation.

Figures (14)

• Figure 1: An omnidirectional tilt-rotor aerial robot screwing a bolt into a wall. The robot can smoothly transition its arms from flying mode (propellers on) to interaction (propellers off) with our novel allocation method.
• Figure 2: The allocation methods introduced in this paper. The ageom and adiffold are the state-of-the-art geometric and differential allocation methods, respectively. The adiff is a novel differential allocation method that does not require acceleration feedback. The asecond normalizes the allocation problem with the actuator dynamics and limits, while the apower introduces propeller power dynamics to minimize the use of nullspace commands and allow propeller deactivation in flight.
• Figure 3: A general control architecture for tilt-rotor aerial robots. The pose controller compares the current odometry to a reference trajectory and produces a wrench command. The wrench command is finally allocated to the actuators of the robot, namely servomotors and propellers, to generate the desired wrench which drives the platform. In this work we focus on the allocation block, highlighted in red.
• Figure 4: The proposed differential allocation scheme. We first augment the wrench command to generate a jerk command, then normalize it and allocate it into numerically stable normalized joint speeds. Finally, we invert the actuator dynamics to obtain the desired tilt angles and propeller speeds to command the Aerial Robot.
• Figure 5: Example acceleration limit curves (solid lines) from the propellers power balance in \ref{['eq:power_equilibrium']}. The dashed lines represent the saturated versions of the curves, where the maximum and minimum accelerations have been capped to represent the internal software ESC limits. For very low propeller speeds, the drag torque has a very low effect, leading to very high acceleration and deceleration limits. As speed increases, the quadratic drag force overtakes the electrical torque, leading to a reduction in the maximum acceleration and deceleration, until the acceleration becomes zero when the propeller reaches the maximum speed. The curves were obtained with $\eta=0.8$, $V = 23V$, $\overline{I} = -\underline{I} = 17A$, $J = 4.5e^{-4} Kg m^2$, $d = 3.5e^{-7} N m s^2$ and $\overline{\dot{\omega}}=-\underline{\dot{\omega}}=1.3e^4 RPM/s$.