Geometry-Aware Safety-Critical Local Reactive Controller for Robot Navigation in Unknown and Cluttered Environments

Yulin Li, Xindong Tang, Kai Chen, Chunxin Zheng, Haichao Liu, Jun Ma*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review


This work proposes a safety-critical local reactive controller that enables the robot to navigate in unknown and cluttered environments. In particular, the trajectory tracking task is formulated as a constrained polynomial optimization problem. Then, safety constraints are imposed on the control variables invoking the notion of polynomial positivity certificates in conjunction with their Sum-of-Squares (SOS) approximation, thereby confining the robot motion inside the locally extracted convex free region. It is noteworthy that, in the process of devising the proposed safety constraints, the geometry of the robot can be approximated using any shape that can be characterized with a set of polynomial functions. The optimization problem is further convexified into a semidefinite program (SDP) leveraging truncated multi-sequences (TMS) and moment relaxation, which favorably facilitates the effective use of off-the-shelf conic programming solvers, such that real-time performance is attainable. Various robot navigation tasks are investigated to demonstrate the effectiveness of the proposed approach in terms of safety and tracking performance.
Original languageEnglish
Pages (from-to)3419-3426
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number4
Early online date31 Jan 2024
Publication statusPublished - Apr 2024

Scopus Subject Areas

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

User-Defined Keywords

  • Collision avoidance
  • motion control
  • optimization and optimal control


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