Efficient Optimization-based Cable Force Allocation for Geometric Control of a Multirotor Team Transporting a Payload

TL;DR

This work proposes an efficient optimization-based cable force allocation for a geometric payload transport controller to effectively avoid inter-robot collision, while retaining the stability properties of the geometric controller.

Abstract

We consider transporting a heavy payload that is attached to multiple multirotors. The current state-of-the-art controllers either do not avoid inter-robot collision at all, leading to crashes when tasked with carrying payloads that are small in size compared to the cable lengths, or use computational demanding nonlinear optimization. We propose an efficient optimization-based cable force allocation for a geometric payload transport controller to effectively avoid such collisions, while retaining the stability properties of the geometric controller. Our approach introduces a cascade of carefully designed quadratic programs that can be solved efficiently on highly constrained embedded flight controllers. We show that our approach exceeds the state-of-the-art controllers in terms of scalability by at least an order of magnitude for up to 10 robots. We demonstrate our method on challenging scenarios with up to three small multirotors with various payloads and cable lengths, where our controller runs in realtime directly on a microcontroller on the robots.

Figures (5)

• Figure 1: We contribute an efficient payload-type-agnostic approach to compute desired cable forces that avoids collisions. Left: Three multirotors carrying a rigid body payload with the baseline controller lee2017geometric . The desired cable forces are allocated with \ref{['eq:baseline']}, causing inter-robot collisions. Right: Our approach with computed hyperplanes that define a safe convex set for the cable forces, while considering the desired motion of the payload.
• Figure 2: Controller architecture of the state-of-the-art geometric controller for payload transport. We contribute an optimization-based cable force allocation (shown in red). Green states are only needed when transporting a rigid body rather than a point mass.
• Figure 3: A cascade of three QPs allocate the desired cable forces $\boldsymbol \mu_{i_d}$ for $n\geq2$ robots. The final QP, $\text{QP}_{\boldsymbol\mu}$, computes $\boldsymbol \mu_{i_d}$ by constraining the cable forces to fulfill the allocation constraints \ref{['eq:Reducedlinearmap']} (point mass) or \ref{['eq:linearmap']} (rigid body) and limiting them to be inside a polyhedra. This volume is defined by a set of hyperspaces, which are constructed by two other QPs that are solved for each robot pair, $\text{QP}_{svm}$ and $\text{QP}_{\mathbf{F}_d}$. Black represents both payload types and green is exclusively used for the rigid payload.
• Figure 4: 2D projection of the hyperplane manipulation, where $\text{QP}_{svm}$ computed $\mathbf{n}_{ij}$. Left: Point mass case, where $\mathbf{n}_{ij}$ is rotated around $\mathbf{p}_0$ such that the distance to $\mathbf{n}_{ij}$ is $r_i$ or $r_j$. Right: Rigid body case, where new intermediate hyperplanes $n_i'$ and $n_j'$ are constructed followed by the same rotation as in the point mass case.
• Figure 5: Four frames (manually highlighted for better visibility) of three multirotors carrying a point mass payload in a teleoperation use-case while avoiding inter-robot collisions. There are two obstacles forming a narrow passage. The operator controls the payload position as well as the desired formation. Here, a line configuration as shown in $t = 10 s$ and $t = 15 s$ is used. After passing the obstacles, the operator disables the manual formation control and our approach computes to a more energy-efficient triangle formation ($t = 25 s$).