Collision-free Source Seeking and Flocking Control of Multi-agents with Connectivity Preservation

TL;DR

This work addresses safe source-seeking and flocking for networks of nonholonomic unicycle agents with limited sensing and dynamic connectivity. It combines a leader-driven gradient-ascent source search with two distributed flocking controllers (orientation-free and orientation-based) that rely on local source-gradient measurements, paired with a distributed control barrier function (CBF) framework and quadratic programs to guarantee inter-agent safety and connectivity. The key contributions include (i) a gradient-based flocking pattern tied to the local Hessian of the source field, (ii) two scalable, distributed flocking controllers that respect nonholonomic constraints, and (iii) a CBF-QP architecture with a zeroing CBF that ensures feasibility under dynamic topology while preserving connectivity. Simulation results demonstrate safe, connected, collision-free source-seeking and flocking under dynamic graphs, highlighting practical applicability in cluttered environments where on-board sensing is local and global information is unavailable.

Abstract

In this article, we present a distributed source-seeking and flocking control method for networked multi-agent systems with non-holonomic constraints. Based solely on identical on-board sensor systems, which measure the source local field, the group objective is attained by appointing a leader agent to seek the source while the remaining follower agents safely form a cohesive flocking with their neighbors using a distributed flocking control law in a connectivity-preserved undirected network. To guarantee safe separation and group motion for all agents and to solve the conflicts with the "cohesion" flocking rule of Reynolds, the distributed control algorithm is solved individually through feasible CBF-based optimization problem with complex constraints, which guarantees the inter-agent collision avoidance and connectivity preservation. Stability analysis of the closed-loop system is presented and the efficacy of the methods is shown in simulation results.

Figures (9)

• Figure 1: Unicycle model in 2D plane.
• Figure 2: Illustration of orientation-free flocking alignment in a quadratic signal field. Agent $i$ (solid red dot) is controlled to flock with its two neighbors $j$ and $k$ (solid black dots). The dark dashed arrow points to the centroid of the neighbor's gradient vectors (dark hollow circle). Flocking error (scalar, denoted as a green line) is defined to coordinate the gradient difference (red arrow line) between the agent $i$ and this neighbor centroid in a desired distance $d^*_{\nabla \bm{J}}$ (solid blue line).
• Figure 3: Illustration of an orientation-based flocking alignment in a quadratic signal field. The red arrow line denotes the difference vector between the agent $i$ and its neighbors' averaging signal gradient. The flocking error vector (green arrow line) is defined to align the agent $i$'s orientation (blue arrow line) with this averaging gradient difference vector (red arrow line) in a desired distance $d^*_{\nabla \bm{J}}$ (c.f. the scalar flocking error in the orientation-free flocking setup in Figure \ref{['fig:2D_free']}).
• Figure 4: Orientation-free flocking cohesion with the distributed controller in \ref{['eq:ori_free_error_v']}-\ref{['eq:ori_free_error_w']}, where the control gain is set to be $K_f = 5$. (a) Flocking cohesion trajectory; (b) Orientation-free flocking error between offset point $P_{io}$ of agent $i$ and its neighbors: $e_{io} = \mu_{io} - d^*_{\nabla \bm{J}}$ with $\mu_{io} = \left \| \left( \frac{1}{{N}_i}\sum_{j\in \mathcal{N}_i} \nabla \bm{J}_{j}\right) - \nabla \bm{J}_{io} \right \|$; (c) Flocking measurement error between offset $P_{io}$ and the agent's center $P_i$: $e_{\mu_i} = \mu_i - \mu_{io}$ with $\mu_i =\left \| \left( \frac{1}{{N}_i}\sum_{j\in \mathcal{N}_i} \nabla \bm{J}_{j}\right) - \nabla \bm{J}_{i} \right \|$; (d) Sum of the offset error norm: $\sum_{i\in\mathcal{V}} \left\| \mu_i - \mu_{io}\right\|$.
• Figure 5: Orientation-based flocking cohesion with the distributed controller in \ref{['eq:ori_con_error_v']}-\ref{['eq:ori_con_error_w']}, where the control gain is set to be $k_{fv} = 1, k_{f\omega} = 20$. (a) Flocking trajectory; (b) Orientation-based flocking error norm of agent $i$: $\left\|\widetilde{\bm{e}}_{i} \right\| = \left\|\widetilde{\bm{u}}_i - d^*_{\nabla \bm{J}} [\cos(\theta_i),\,\sin(\theta_i) ]\right\|$.

Theorems & Definitions (15)

• Definition 2.1
• Remark 3.1
• Remark 3.2
• Theorem 3.3: Orientation-free Flocking Cohesion
• Theorem 3.4: Orientation-based Flocking Cohesion
• Remark 4.1: Inter-agent Connectivity
• Remark 4.2: Safety
• Remark 4.3
• Proposition 4.4: Uniform Relative Degree
• Remark 4.5: CBF-QP Feasibility Condition