Tube-Certified Trajectory Tracking for Nonlinear Systems with Robust Control Contraction Metrics

Pan Zhao, Arun Lakshmanan, Kasey Ackerman, Aditya Gahlawat, Marco Pavone, Naira Hovakimyan

Research output: Contribution to journalArticlepeer-review


This letter presents an approach to guaranteed trajectory tracking for nonlinear control-affine systems subject to external disturbances based on robust control contraction metrics (CCM) that aims to minimize the L∞ gain from the disturbances to nominal-actual trajectory deviations. The guarantee is in the form of invariant tubes, computed offline and valid for any nominal trajectories, in which the actual states and inputs of the system are guaranteed to stay despite disturbances. Under mild assumptions, we prove that the proposed robust CCM (RCCM) approach yields tighter tubes than an existing approach based on CCM and input-to-state stability analysis. We show how the RCCM-based tracking controller together with tubes can be incorporated into a feedback motion planning framework to plan safe trajectories for robotic systems. Simulation results illustrate the effectiveness of the proposed method and empirically demonstrate reduced conservatism compared to the CCM-based approach.

Original languageEnglish (US)
Pages (from-to)5528-5535
Number of pages8
JournalIEEE Robotics and Automation Letters
Issue number2
StatePublished - Apr 1 2022


  • Planning under uncertainty
  • integrated planning and control
  • nonlinear systems
  • robot safety
  • robust control
  • Integrated planning and control
  • planning under uncertainty

ASJC 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


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