Invariant Set Distributed Explicit Reference Governors for Provably Safe On-Board Control of Nano-Quadrotor Swarms

Abstract

This article provides a theory for provably safe and computationally efficient distributed constrained control, and describes an application to a swarm of nano-quadrotors with limited on-board hardware and subject to multiple state and input constraints. We provide a formal extension of the explicit reference governor framework to address the case of distributed systems. The efficacy, robustness, and scalability of the proposed theory is demonstrated by an extensive experimental validation campaign and a comparative simulation study on single and multiple nano-quadrotors. The control strategy is implemented in real-time on-board palm-sized unmanned erial vehicles, and achieves safe swarm coordination without relying on any offline trajectory computations.

Safe, Fast, and Efficient Distributed Receding Horizon Constrained Control of Aerial Robot Swarms

“…The ERG, initially introduced in [21], [22], is a general framework for the closed-form (i.e., explicit) control of nonlinear pre-stabilized systems f (x, v) with state x, applied reference v, equilibrium xv and constraints c(x, v) ≥ 0. An Invariant-Set Distributed ERG (IS-D-ERG) has been presented in [18] to handle multi-agent collision avoidance with very low computational power and limited communication received from the agents with IDs N i = N i i in a one-hop neighbourhood of agent i 1 . The main drawbacks are that law [18, (21)] uses a Lyapunov-based Dynamic Safety Margin (DSM) [18, (64)] which is a conservative approximation of the actual trajectory and requires a sufficiently large constant collision radius S a in its Navigation Field (NF) [18, (37)] and DSM [18, (38)] for good individual performance.…”

“…To over come these issues, we will formulate the general theory of the TT-D-ERG and highlight the differences with [18]. The specific formulation of the tubes, NF and DSM are treated subsequently.…”

“…As opposed to the majority of the related works, our method is optimization-free and still well suited for fast real-time dynamic collision-avoidance scenarios. This research extends the predictive control of [17] to distributed systems and complements the Invariant-Set Distributed Explicit Reference Governor (IS-D-ERG) of [18]:…”

“…The idea is based on the computation and communication of safety tubes in which the predicted UAV dynamics are embedded. To handle potential overlaps between tubes, the theoretical guarantees are obtained using a combination of safety and strong returnability instead of the invariance-based proof found in [18]. • Validations in real-world outdoor conditions with single and multiple quadrotors and numerical Gazebo simulation benchmarks with multiple UAVs in dynamic collision avoidance scenarios show the benefits of the proposed method over our prior work [18] and D-MPC [10], [11].…”

“…• A novel Trajectory-Tube D-ERG formulation is proposed offering major improved dynamic performance and scalabilty compared to [18] with still low computational and communication cost. The idea is based on the computation and communication of safety tubes in which the predicted UAV dynamics are embedded.…”