Organizations: Department of Mathematical and Computing Science, School of Computing, Institute of Science Tokyo, Tokyo 152-8550, Japan · Department of Electrical Engineering, Indian Institute of Technology Jodhpur, Jodhpur 342030, India · Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab, 38000 Grenoble, France
Circumnavigating a stationary target with a team of robots requires each robot to hold its own standoff distance, to stay evenly spaced from its neighbours, and to avoid collisions with the target and with each other at every instant. The task becomes arduous when the robots are assigned different orbital radii, as their sensors or roles may demand. This paper presents a safety-critical control framework for this problem. Each robot commands both its acceleration and its turn-rate, measures only its distance to the target, and exchanges information only with its two ring neighbours. The design has three features. First, a structural property of the model lets one control law serve every robot regardless of its assigned radius. Second, the acceleration drives each radius exactly to its target, while the turn-rate balances the formation with the neighbours. Third, a higher-order control-barrier-function quadratic program enforces target, geofence, and inter-robot safety on both inputs at once; it leaves the nominal controller untouched away from the constraints and stays valid while the unmeasured range rate is still being estimated. Simulations confirm these guarantees. In a comparison, the closest existing multi-orbit design, even with full state information, violates both the target standoff and the inter-robot margin, whereas the proposed controller does not.
Figures & tables
Fig. 1 : Problem setup for N=3 : robots on heterogeneous orbits d1<d2<d3 around a stationary target, confined to the annulus between the safety boundary rmin and the geofence rmax , coordinating over the ring graph with desired chord lengths ℓij⋆ (gray dashed).
Fig. 2 : Control architecture of robot i . Estimation blocks (blue) use only the measured range ri ; the nominal controller (orange) produces (ainom,ωinom) ; the HOCBF-QP filter (green) enforces the safety constraints ( OBS- i ), ( GEO- i ), ( SPD- i ), ( INT- i j ) on both inputs jointly.
Fig. 3 : Trajectories and time evolution of range and radial error under the proposed HOCBF-QP controller ( 48 ) for N=3 robots. All robots converge to their heterogeneous orbits while remaining outside the safety boundary, and ed,i(t) decays to zero for every robot.
Fig. 4 : Obstacle-safety margin and control inputs under the proposed HOCBF-QP controller ( 48 ) for N=3 robots. Each robot’s distance from the obstacle boundary stays strictly positive throughout, confirming obstacle avoidance, while the acceleration and turn-rate commands settle from an initial transient to the steady values sustaining the converged orbits.
Fig. 5 : Proposed controller with N=4 robots on the sparse ring graph, where each robot coordinates with only two of its three teammates.
Fig. 6 : Baseline of [ 18 ] on the N=3 . The trajectories in (a) crosses the safety disc (red dashed) and cross one another near the target, and the ranges in (b) lie below rmin for the first seconds of the run before settling on the assigned orbits.
Safe decentralized navigation in heterogeneous robot teams is challenging because robots with different dynamics and control limits cannot satisfy identical collision-avoidance obligations equally well. Existing methods often rely on model-specific safety formulations or allocate avoidance responsibility without considering whether the assigned control is physically realizable, possibly leading to safety-constrained QP infeasibility and safety violations. We propose Capability-Aware Heterogeneous Control Barrier Functions (CA-HCBF), a decentralized framework for consistent safety enforcement and capability-aware responsibility allocation. We derive a unified operational-space second-order control-affine formulation for holonomic and nonholonomic mobile robots through canonical transformation and backstepping, addressing the relative-degree mismatch while preserving forward invariance of the pairwise safe set. Second, we quantify each robot's achievable control authority along the safety-critical direction using a support-function-based capability metric and use it to distribute pairwise avoidance responsibility. A feasibility-aware clipping mechanism further mitigates physically unrealizable responsibility assignments. Simulations with up to 30 heterogeneous robots and hardware experiments demonstrate high task completion with low safety violations and reduction in local QP infeasibility.
Joonkyung Kim, Yanze Zhang, Wenhao Luo +1
Department of Computer Science and Engineering, Texas A&M University · Department of Computer Science, University of Illinois Chicago
Ergodic control drives robots to spend time in each region in proportion to a spatial distribution of interest, making it well suited for dense spatiotemporal environmental monitoring. Existing safe ergodic controllers rely on offline trajectory optimization or hierarchical architectures, which limit real-time applicability and decouple the ergodicity objective from the safety constraint. This paper presents a quadratic programming (QP)-based controller that treats ergodicity and safety jointly. We first introduce a Gaussian-kernel ergodic metric that, unlike the classical indicator-based metric, is time differentiable. This allows the exponential decay of the metric to be imposed as a time-varying control barrier function (CBF) constraint, relaxed by a slack variable, alongside hard CBF constraints for region containment and inter-robot collision avoidance. We establish that the resulting QP remains feasible from any safe initial configuration and that, up to the slack term, the ergodic metric decays exponentially. Simulations show improved performance over baseline methods, and experiments with three aerial vehicles validate the work on real hardware.
Yo Toyomoto, Mohamed Elobaid, Bryce L. Ferguson +2
Electrical and Computer Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia · Thayer School of Engineering at Dartmouth College, Hanover, NH, USA · Department of Computer Science, Dartmouth College, Hanover, NH, USA
Density-Driven Optimal Control (D2OC) provides a principled approach to distributing multi-robot teams over non-uniform spatial distributions. Applying D2OC to nonholonomic robots, however, creates a gap between safety constraints imposed on a reference motion and the physical inputs that determine the actual robot motion. We address this issue by enforcing the safety constraint directly on the robot's physical inputs while preserving the density-driven coverage objective. The proposed framework combines D2OC with a control barrier function safety filter through a feedback-linearizing look-ahead point, allowing safety and actuator limits to be considered together during control. We further derive a safety margin that accounts for the look-ahead geometry, robot footprint, and motion during each control interval. Simulation results show that the proposed method maintains the required physical separation while achieving coverage performance comparable to a conventional reference-tracking approach, which can satisfy safety on the reference motion yet violate the corresponding physical clearance. Experiments on multiple nonholonomic robots in the Robotarium further demonstrate safe execution while driving the robots toward the desired spatial distribution. These results show that enforcing safety directly on the physical inputs can eliminate the mismatch between safety certification and physical robot motion in density-driven multi-robot coverage.
Julian Martinez, Kooktae Lee
Department of Mechanical and Aerospace Engineering, Texas Tech University, Lubbock, TX 79409, USA