Trajectory Tracking with Convergence Guarantees

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Overview

Trajectory tracking requires a vehicle to follow a time-parameterized reference trajectory, which is a stricter requirement than path following. My research develops controllers that guarantee finite-time or exact-time convergence to the desired trajectory even in the presence of model uncertainties, external disturbances, and state constraints such as bounded velocities and attitude angles.

Key tools employed include sliding mode control, Barrier Lyapunov functions for handling state constraints, and exact-time stability theory. These methods have been applied to quadrotor UAVs and autonomous surface vessels, with rigorous formal proofs of convergence.

Key Contributions

  • Exact-time convergent trajectory tracking for quadrotor UAVs under uncertainties.

  • Finite-time convergent robust control with almost global stability guarantees.

  • Barrier Lyapunov function-based trajectory following with bounded state constraints.

  • Robust exact-time trajectory tracking for autonomous surface vessels.

  • 3D trajectory tracking for UAVs under motion constraints.

Relevant Publications

Journal Papers

  1. Saurabh Kumar, Shashi Ranjan Kumar, and Abhinav Sinha, Three-dimensional Trajectory Tracking for Unmanned Aerial Vehicles Under Motion Constraints, AIAA Journal of Guidance, Control, and Dynamics, Vol. 49, No. 1, 2026, pp. 78–96.

  2. Susan Basnet, Saurabh Kumar, and Shashi Ranjan Kumar, Robust Exact-time Trajectory Tracking Control for Autonomous Surface Vessels, IEEE Journal of Oceanic Engineering, Vol. 50, No. 2, 2025, pp. 1184–1195.

  3. Saurabh Kumar and Shashi Ranjan Kumar, Robust Trajectory Tracking of an Uncertain Quadrotor with Almost Global Finite-time Convergence, Proceedings of the IMechE Part G: Journal of Aerospace Engineering, Vol. 239, No. 8, 2025, pp. 792–817.

Conference Papers

  1. Saurabh Kumar, Shashi Ranjan Kumar, and Abhinav Sinha, Robust Nonlinear Control for Exact-time Stability of a Quadrotor UAV under Uncertainties, AIAA GNC Conference, Orlando, USA, 2024.

  2. Susan Basnet, Saurabh Kumar, and Shashi Ranjan Kumar, Nonlinear Cooperative Strategy for Active Aircraft Defence with Exact-time Convergence, Indian Control Conference, Vishakhapatnam, 2023, pp. 239–244.

  3. Saurabh Kumar and Shashi Ranjan Kumar, Barrier Lyapunov-based Nonlinear Trajectory Following for UAVs with Constrained Motion, ICUAS, Dubrovnik, Croatia, 2022, pp. 1146–1155.

  4. Saurabh Kumar and Shashi Ranjan Kumar, Finite-Time Convergent Robust Trajectory Tracking for Unmanned Aerial Vehicles, ICUAS, Dubrovnik, Croatia, 2022, pp. 1166–1175.

  5. Saurabh Kumar and Shashi Ranjan Kumar, Exponential Reaching Law based Robust Trajectory Tracking for UAVs, Indian Control Conference, Chennai, 2022, pp. 302–307.