Heuristic Predictive Control for Multi-Robot Flocking in Congested Environments

TL;DR

The paper tackles distributed optimal flocking for multiple robots operating in congested environments by framing the problem as MAP inference on a Gibbs Random Field (GRF). It defines bio-inspired potential energies for inter-robot interactions, obstacle avoidance, and goal tracking, and uses a mean-field approximation to enable fully distributed inference, with a gradient-based heuristic to bias the control search around a locally informed input u_g for real-time feasibility. Key contributions include the GRF-based predictive control framework, a multi-level collision avoidance mechanism, a convergence analysis of the mean-field approximation, and extensive simulations plus real UAV experiments demonstrating improved computation efficiency and safety. The work advances practical, scalable flocking in cluttered spaces, enabling reliable multi-robot coordination for applications like search and rescue and delivery in complex environments.

Abstract

Multi-robot flocking possesses extraordinary advantages over a single-robot system in diverse domains, but it is challenging to ensure safe and optimal performance in congested environments. Hence, this paper is focused on the investigation of distributed optimal flocking control for multiple robots in crowded environments. A heuristic predictive control solution is proposed based on a Gibbs Random Field (GRF), in which bio-inspired potential functions are used to characterize robot-robot and robot-environment interactions. The optimal solution is obtained by maximizing a posteriori joint distribution of the GRF in a certain future time instant. A gradient-based heuristic solution is developed, which could significantly speed up the computation of the optimal control. Mathematical analysis is also conducted to show the validity of the heuristic solution. Multiple collision risk levels are designed to improve the collision avoidance performance of robots in dynamic environments. The proposed heuristic predictive control is evaluated comprehensively from multiple perspectives based on different metrics in a challenging simulation environment. The competence of the proposed algorithm is validated via the comparison with the non-heuristic predictive control and two existing popular flocking control methods. Real-life experiments are also performed using four quadrotor UAVs to further demonstrate the efficiency of the proposed design.

Figures (9)

• Figure 1: Two UAV groups flying seperately through openings. UAVs 1 and 2 belong to one group, while UAVs 3 and 4 belong to the other group.
• Figure 2: Inter-robot potential energy (a), repulsion energy (b), and transition function (c). In (a), $r_f = 0.421, k_a = 0.2, k_t = 1.95$; in (b), $r_f = 0.421, k_{or} = 0.2$; in (c), $k_{\rho} = 1.5$.
• Figure 3: The collision avoidance strategy for robot $i$. The risk level varies across different sectors around the robot, which is represented using sectors with different colors. Sector I represents the highest-risk region, bounded by an angle $\theta_{\mathrm{I}} = \arcsin \left({r_{\beta} + r_c}/{\|\mathbf{p}_{i\beta}\|}\right)$. Sectors II and III have lower-level risks, which are determined by the function $\rho(\lambda, \delta, z)$. Sector IV is the safe region where $\rho (\lambda,\delta,z) = 0$. The safe boundary is given by $\theta_{\mathrm{III}} = \arcsin \left({(1 + k_{\delta})(r_{\beta} + r_c)}/{\|\mathbf{p}_{i\beta}\|}\right)$.
• Figure 4: (a) Control discretization (green arrow). (b) Uniform discretization. (c) Biased local discretization (solid green arrow) based on $\mathbf{u}_g$ which has a cone-like shape in space.
• Figure 5: Simulation trajectories. (a)(e):The non-heuristic method;(b)(f): Our method; (c)(g): Olfati-saber's method; and (d)(h): Vásárhelyi's method. The first row shows the trajectories from a view angle of $az = -135^{\circ}$ and $el = 42^{\circ}$, while the second row shows the trajectories from a view angle of $az = 121^{\circ}$ and $el = 38^{\circ}$. In the colorbar, the light blue lines leading from different positions indicate the distance between the robot and its nearest neighbor when the four methods form a stable motion (i.e., the robot has the same velocity as the reference state $\mathbf{v}_r$). Obviously, the distance between the UAVs is closer to the expected value $r_f = 0.421 \ \mathrm{m}$ in the absence of obstacles when using the first two methods(non-heuristic $0.417 \ \mathrm{m}$, our method $0.412 \ \mathrm{m}$, Olfati-saber $0.3912 \ \mathrm{m}$, Vásárhelyi $0.3978 \ \mathrm{m}$). The UAV trajectories by our method are smoother in comparison with the other methods.

Theorems & Definitions (7)

• Theorem 1
• proof
• Theorem 2
• proof
• Remark 1
• Proposition 1
• proof