Safe Navigation and Obstacle Avoidance Using Differentiable Optimization Based Control Barrier Functions

Bolun Dai, Rooholla Khorrambakht, Prashanth Krishnamurthy, Vinicius Goncalves, Anthony Tzes, Farshad Khorrami

Research output: Contribution to journalArticlepeer-review


Control barrier functions (CBFs) have been widely applied to safety-critical robotic applications. However, the construction of control barrier functions for robotic systems remains a challenging task. Recently, collision detection using differentiable optimization has provided a way to compute the minimum uniform scaling factor that results in an intersection between two convex shapes and to also compute the Jacobian of the scaling factor. In this letter, we propose a framework that uses this scaling factor, with an offset, to systematically define a CBF for obstacle avoidance tasks. We provide theoretical analyses of the continuity and continuous differentiability of the proposed CBF. We empirically evaluate the proposed CBF's behavior and show that the resulting optimal control problem is computationally efficient, which makes it applicable for real-time robotic control. We validate our approach, first using a 2D mobile robot example, then on the Franka-Emika Research 3 (FR3) robot manipulator both in simulation and experiment.

Original languageEnglish (US)
Pages (from-to)5376-5383
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number9
StatePublished - Sep 1 2023


  • Robot safety
  • collision avoidance

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Biomedical Engineering
  • Human-Computer Interaction
  • Mechanical Engineering
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Control and Optimization
  • Artificial Intelligence


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