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Safe Navigation of Vertical Take-off and Landing Unmanned Aerial Vehicles using Model Predictive Control with Control Barrier Functions

Core Concepts
The proposed cascaded scheme of Model Predictive Control with Control Barrier Functions and Dynamic Feedback Linearization enables safe and efficient navigation of underactuated VTOL-UAVs by converting the nonlinear system into a linear equivalent model.
The paper proposes a cascaded control scheme for safe navigation of Vertical Take-off and Landing Unmanned Aerial Vehicles (VTOL-UAVs). The key components of the scheme are: Dynamic Feedback Linearization (DFL): The nonlinear underactuated dynamics of the VTOL-UAV are converted into a linear equivalent model by introducing a cascaded scheme with DFL. This allows the use of linear Model Predictive Control (MPC) while considering the full nonlinear dynamics. MPC with Control Barrier Functions (CBF): The linear equivalent model is used in an MPC formulation with CBF constraints. The CBF represents a safety metric and enforces the forward invariance of a safe set, ensuring obstacle avoidance even when obstacles are far away. Stability and Feasibility: The closed-loop stability and recursive feasibility of the proposed MPC-CBF-DFL scheme are proved. The terminal cost function is designed to ensure asymptotic convergence of the VTOL-UAV states to the origin. The key advantages of the proposed approach are: Unlocking the benefits of linear MPC, such as computational efficiency and stability guarantees, while considering the full nonlinear VTOL-UAV dynamics. Incorporating CBF constraints to activate the safety requirements globally, leading to smoother trajectories and shorter prediction horizons compared to using Euclidean distance constraints. Providing a comprehensive solution for safe navigation of underactuated VTOL-UAVs by combining DFL, MPC, and CBF in a cascaded scheme.
The VTOL-UAV model has a total mass of m and inertia matrix J. The distance from the center of mass to the rotors is d. The gravity constant is g.
"The proposed solution bridges the above-identified literature gaps by formulating MPC using CBF to control the VTOL-UAV such that the safety constraint gets activated everywhere providing smooth trajectory with the constraints are likely to be satisfied compared to usage of Euclidean norms as a constraint." "The CBF provides the notion of the global forward invariance of the safe set. The VTOL-UAV avoids the obstacle even if it is far from it leading to a shorter prediction horizon, unlike the Euclidean distance case where the constraint is activated once it near the obstacle."

Deeper Inquiries

How can the proposed MPC-CBF-DFL scheme be extended to handle uncertainties and disturbances in the VTOL-UAV dynamics

To extend the proposed MPC-CBF-DFL scheme to handle uncertainties and disturbances in the VTOL-UAV dynamics, one can incorporate robust control techniques. One approach is to implement robust MPC, where uncertainty models are included in the optimization problem to account for variations in the system dynamics. Robust MPC formulations can utilize set-based methods to ensure feasibility and stability in the presence of uncertainties. By defining robust constraints based on the uncertainty sets, the MPC controller can adapt to varying conditions and disturbances while maintaining safety and performance requirements. Additionally, one can integrate adaptive control strategies to continuously update the controller parameters based on real-time feedback, allowing the system to adjust to changing dynamics and disturbances.

What are the potential limitations of the CBF-based safety constraints, and how can they be addressed to handle more complex obstacle configurations

The CBF-based safety constraints, while effective in ensuring forward invariance of the safe set, may have limitations when dealing with complex obstacle configurations. One potential limitation is the conservative nature of CBFs, which can lead to overly cautious behavior and suboptimal trajectories, especially in environments with densely packed obstacles. To address this limitation, one approach is to incorporate learning-based methods to adapt the safety constraints dynamically. By leveraging reinforcement learning or adaptive techniques, the system can learn from interactions with the environment and adjust the safety margins based on the perceived risk. Another strategy is to combine CBFs with probabilistic methods, such as chance constraints, to account for uncertainties in obstacle positions and enable more flexible and adaptive obstacle avoidance strategies.

What are the implications of the proposed approach for the broader field of safe control of underactuated robotic systems beyond VTOL-UAVs

The implications of the proposed approach for the broader field of safe control of underactuated robotic systems extend beyond VTOL-UAVs to various robotic platforms with limited control inputs. By integrating MPC with CBFs and DFL, the framework offers a systematic and efficient way to address safety-critical constraints while optimizing control performance. This methodology can be applied to diverse underactuated systems, including mobile robots, manipulators, and autonomous vehicles, to ensure safe and reliable operation in complex environments. The use of linear MPC-CBF with DFL provides a computationally tractable solution that guarantees stability and safety, making it applicable to a wide range of robotic applications. Furthermore, the integration of advanced control techniques, such as reinforcement learning and adaptive control, can enhance the adaptability and robustness of the system, paving the way for safer and more efficient control strategies in the field of robotics.