Joint-Feasibility Margin Feedback for Bounded-Input Second-Order Control Barrier Functions

Key points

• Multiple second-order control barrier function constraints can exhaust their common control authority under bounded acceleration, even when the current state remains feasible.1
• We predict the margin one sample ahead for nine task-directed candidates, selecting either the least-deviating candidate that attains a desired margin or the candidate with the largest predicted margin before solving the same hard HOCBF quadratic program.1
• A controlled one-step case shows that, at the state predicted under the hard-QP command, two constraints remain individually feasible but become jointly infeasible, whereas the margin-feedback controller retains a positive next margin.1
• Separately, across 20 paired initial conditions, the margin-feedback controller retains the hard-QP command in a low-pressure task and acts at positive margin in a critical task before the hard-QP problem becomes infeasible; its trajectories remain feasible at that time and complete the task.1

Sources (1)

• [1]Joint-Feasibility Margin Feedback for Bounded-Input Second-Order Control Barrier Functions
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 12, 03:38 PM

  We define a signed local joint-feasibility margin whose sign exactly identifies whether the current barrier half-spaces intersect the admissible input set.

  Multiple second-order control barrier function constraints can exhaust their common control authority under bounded acceleration, even when the current state remains feasible.

Extractive summary: sentences quoted from the sources.