Feasible Force Set Shaping for a Payload-Carrying Platform Consisting of Tiltable Multiple UAVs Connected Via Passive Hinge Joints

TL;DR

This work tackles payload transport with a multi-UAV platform connected through passive hinge joints. It develops a modeling framework that maps rotor thrusts to payload wrenches and joint torques, and introduces a concept of a hoverable force set (HFS) whose shape is controllable via tilting the UAVs. By offline optimization using PSO, tilt angles are chosen so the HFS completely includes a user-defined required force set (RFS), enabling force redundancy and mitigating tilt-delay in control. A two-loop controller exploits this redundancy to track payload motion and allocate rotor thrusts via a linear program, demonstrated through simulations that show accurate tracking and disturbance rejection even under wind perturbations.

Abstract

This paper presents a method for shaping the feasible force set of a payload-carrying platform composed of multiple Unmanned Aerial Vehicles (UAVs) and proposes a control law that leverages the advantages of this shaped force set. The UAVs are connected to the payload through passively rotatable hinge joints. The joint angles are controlled by the differential thrust produced by the rotors, while the total force generated by all the rotors is responsible for controlling the payload. The shape of the set of the total force depends on the tilt angles of the UAVs, which allows us to shape the feasible force set by adjusting these tilt angles. This paper aims to ensure that the feasible force set encompasses the required shape, enabling the platform to generate force redundantly -meaning in various directions. We then propose a control law that takes advantage of this redundancy.

Figures (12)

• Figure 1: Illustration of force sets feasible during hovering. Blue polytope, blue arrow, and red line are force set, tilt motion, and UAVs' direction, respectively. The force set is deformable by changing the tilt angles.
• Figure 2: An example of the payload-carrying platform with four UAVs.
• Figure 3: Enlarged view of the UAV. One UAV has four rotors: two rotate clockwise, and the other two rotate counter-clockwise, arranged alternately at positions $[\pm r, \pm r, 0]^\top$ in $\Sigma_{q_i}$.
• Figure 4: Examples of HFS and RFS. HFS and RFS are drawn as light blue and deep blue polytopes, respectively. $x$ and $y$ axes of force are enlarged five times of the $z$ axis. (a) $\gamma_i=-\pi/24$, (b) $\gamma_i=-\pi/6,~\forall i\in\{1,\cdots,N\}$.
• Figure 5: The optimized tilt angles.

Theorems & Definitions (13)

• Remark 1
• Lemma 1: Hoverability conditions
• Definition 1: Hoverability force set (HFS)
• Theorem 1: Hoverability condition of the platform
• proof
• Remark 2
• Theorem 2: Inclusion and optimality
• proof
• Proposition 1
• proof