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Robust Trajectory Generation and Control for Quadrotor Motion Planning with Field-of-View Control Barrier Certification

Lishuo Pan, Mattia Catellani, Lorenzo Sabattini, Nora Ayanian

TL;DR

This work tackles distributed multi-robot coordination under communication-denied conditions with perception uncertainty by proposing a real-time trajectory and control framework certified by High-Order Control Barrier Functions. It unifies continuous-time HO-CBF safety with a discrete MPC-CBF optimization, using a linear surrogate and SQP to generate spline-based trajectories and controls that respect safety and field-of-view constraints at sampled times. The key contributions are a real-time distributed controller that preserves visual contact despite temporary tracking loss, a continuous-time trajectory/controller synthesis certified by CBFs, and an efficient MPC-CBF algorithm that approximates the certified solution for practical deployment. Demonstrated in simulations with up to 10 robots and in physical two-robot UAV experiments, the approach shows robustness to sensing noise, delays, and missed detections, improving task success rates over baseline reactive methods. This enables reliable, sensing-based coordination in environments with limited communications, with significant implications for search-and-rescue, formation control, and autonomous collaboration.

Abstract

Many approaches to multi-robot coordination are susceptible to failure due to communication loss and uncertainty in estimation. We present a real-time communication-free distributed navigation algorithm certified by control barrier functions, that models and controls the onboard sensing behavior to keep neighbors in the limited field of view for position estimation. The approach is robust to temporary tracking loss and directly synthesizes control to stabilize visual contact through control Lyapunov-barrier functions. The main contributions of this paper are a continuous-time robust trajectory generation and control method certified by control barrier functions for distributed multi-robot systems and a discrete optimization procedure, namely, MPC-CBF, to approximate the certified controller. In addition, we propose a linear surrogate of high-order control barrier function constraints and use sequential quadratic programming to solve MPC-CBF efficiently.

Robust Trajectory Generation and Control for Quadrotor Motion Planning with Field-of-View Control Barrier Certification

TL;DR

This work tackles distributed multi-robot coordination under communication-denied conditions with perception uncertainty by proposing a real-time trajectory and control framework certified by High-Order Control Barrier Functions. It unifies continuous-time HO-CBF safety with a discrete MPC-CBF optimization, using a linear surrogate and SQP to generate spline-based trajectories and controls that respect safety and field-of-view constraints at sampled times. The key contributions are a real-time distributed controller that preserves visual contact despite temporary tracking loss, a continuous-time trajectory/controller synthesis certified by CBFs, and an efficient MPC-CBF algorithm that approximates the certified solution for practical deployment. Demonstrated in simulations with up to 10 robots and in physical two-robot UAV experiments, the approach shows robustness to sensing noise, delays, and missed detections, improving task success rates over baseline reactive methods. This enables reliable, sensing-based coordination in environments with limited communications, with significant implications for search-and-rescue, formation control, and autonomous collaboration.

Abstract

Many approaches to multi-robot coordination are susceptible to failure due to communication loss and uncertainty in estimation. We present a real-time communication-free distributed navigation algorithm certified by control barrier functions, that models and controls the onboard sensing behavior to keep neighbors in the limited field of view for position estimation. The approach is robust to temporary tracking loss and directly synthesizes control to stabilize visual contact through control Lyapunov-barrier functions. The main contributions of this paper are a continuous-time robust trajectory generation and control method certified by control barrier functions for distributed multi-robot systems and a discrete optimization procedure, namely, MPC-CBF, to approximate the certified controller. In addition, we propose a linear surrogate of high-order control barrier function constraints and use sequential quadratic programming to solve MPC-CBF efficiently.

Paper Structure

This paper contains 27 sections, 1 theorem, 20 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Bézier Curve
  5. High-Order Control Barrier Functions
  6. Neighbors State Estimation
  7. Problem Formulation
  8. Robot model
  9. Sensing model
  10. HOCBFs Design
  11. Trajectory and Control Generation with Safety Certification
  12. Trajectory and Control Prediction Model
  13. HOCBF Constraints and Relaxation
  14. Collision Avoidance Constraints
  15. Output and Derivatives Continuity
  16. ...and 12 more sections

Key Result

Theorem 1

Consider the HOCBF in eq:hocbf_formulation and the set $\mathcal{C}:=\mathcal{C}_1 \cap \mathcal{C}_2$. Let $\alpha_{1}$, $\alpha_{2}$ be differentiable extended class $\mathcal{K}$ functions. If $\mathbf{x}(t_0)\in \mathcal{C}$, the controller $\mathbf{u}(t)$ from eq:12gen, $\forall t\in [t_{0},t_{

Figures (8)

  • Figure 1: Long exposure top view of $2$ quadrotors navigating with distributed controller respecting field-of-view constraints. The red and blue triangles are the fields of view of UAV1 and UAV2. The sensing ranges extend beyond triangles and are omitted in the figure. Curves represent the robot routes.
  • Figure 2: The sensing region $\mathcal{F}$ of a robot is modeled as truncated spherical sector. $\beta_{H}$, $\beta_{V}$ are the horizontal and vertical field of view angles. $R_{s}$ is the sensing range and $D_{s}$ is the safety distance. The blue volume (or red plane in 2D) is the region where the neighbor can be safely detected.
  • Figure 3: Robot navigates to its goal (red dot) with predicted field of views (blue triangles). MPC-CBF imposes constraints at sampled steps.
  • Figure 4: Snapshots for 5 robots in the circle instance. The ovals are 95% confidence ellipsoids of estimation (the source of estimations is indicated by colors). The predicted output is depicted as blue curves and purple field of views. The path is shown as a solid line.
  • Figure 5: Performance of our algorithm across $\beta_H$, $\gamma_s$, and different robot counts in "circle" instances. Bars show means, error bars show 95% confidence intervals over 15 trials.
  • ...and 3 more figures

Theorems & Definitions (4)

  • Definition 3.1: CBF ames2014controlames2019control
  • Definition 3.2: HOCBF xiao2021high
  • Theorem 1
  • proof