Where to Place a Heavy Payload on a Multirotor UAV for Best Control Performance

TL;DR

This work investigates how rigidly attached heavy payload placement affects the stability and control performance of a multirotor UAV. By linearizing the complete nonlinear model around hover and analyzing the zero dynamics through the parameter $\alpha = z_{POI}-\frac{m_{PL}}{m_{tot}}z_{PL}$, the authors show that negative $\alpha$ yields unstable zero dynamics (RHP zeros) while positive $\alpha$ yields marginal or better stability. They derive an $\mathcal{H}_2$-norm expression via an ARE-based LQR framework to quantify disturbance rejection and identify the optimal vertical output position $z_{POI}^* = \sqrt{\frac{2g}{\hat{q}_i}}$ with $z_{PL}^*=0$, and show that smaller control authority increases the optimal $\alpha$. Simulation results validate both nonlinear and linearized models, confirming that placing the payload above the CoG improves performance under white-noise disturbances and providing practical guidelines for payload placement in heavy-lift UAVs.

Abstract

This paper studies the impact of rigidly attached heavy payload placement - where the payload mass significantly influences the UAV's dynamics - on the stability and control performance of a multirotor unmanned aerial vehicle (UAV). In particular, we focus on how the position of such a payload relative to the vehicle's Center of Gravity (CoG) affects the stability and control performance at an arbitrary point of interest on the UAV, such as the payload position, and on how this position can be optimized. Our conclusions are based on two key contributions. First, we analyze the stability of the zero-dynamics of a complete nonlinear model of the UAV with payload. We demonstrate that the stability of the zero dynamics depends on the vertical signed distance in the body-fixed frame between the controlled output position and the combined CoG of the UAV with payload. Specifically, positioning the output below the CoG yields unstable zero dynamics, while the linearized zero dynamics are marginally stable when placing it above, indicating reduced sensitivity to input disturbances. Second, we analyze the performance of the linearized UAV model with payload by providing an analytical expression for the H2-norm, from which we can quantify the system's attenuation to white noise input disturbances. We conclude that less control authority leads to a higher optimal position of the controlled output with respect to the CoG for closed-loop white-noise disturbance rejection capabilities, also when the heavy payload is the controlled output. The results are illustrated through numerical examples.

Figures (6)

• Figure 6: Configuration of the $POI$ and payload as in Assumption \ref{['asu:exactlyabove']}
• Figure 7: $\mathcal{H}_2$-norm for varying $z_{PL}$ and $z_{POI}$, verifying the optimal values $z_{PL}^* = 0$ and $z_{POI}^* = \sqrt{\frac{2g}{q_i}} + z_{PL}$
• Figure 8: UAV trajectory for the linearized and complete nonlinear system in (\ref{['eq:simplified_linear']}) and (\ref{['eq:full_nonlinear']}) respectively, for the above- and below-configuration, using the ode45 solver in MATLAB, with $\bm{p}_0 = [-0.5\,\,\,0\,\,\,0.5]$ and $q_i=10$
• Figure 9: Norm of the state error between the nonlinear and linearized system, showing that larger angles result in a larger difference between the two systems, using the ode45 solver in MATLAB, for $q_i=10$
• Figure 10: Analytical and numerical values for the $\mathcal{H}_2$-norm for varying $\alpha$, showing that for both the simulated complete nonlinear and linearized system, the calculated $\mathcal{H}_2$-norm matches the analytical results, using an RK4 fixed-step simulation suli_introduction_2003, for $q_i=5$ and input disturbances with $\sigma_w=0.1$.

Theorems & Definitions (7)

• Remark 7
• Proposition 8
• Proposition 9
• Theorem 10
• Remark 11
• Remark 12
• Theorem 13