Linear vs Nonlinear MPC for Trajectory Tracking Applied to Rotary Wing Micro Aerial Vehicles (1611.09240v2)

Abstract: Precise trajectory tracking is a crucial property for \acp{MAV} to operate in cluttered environment or under disturbances. In this paper we present a detailed comparison between two state-of-the-art model-based control techniques for \ac{MAV} trajectory tracking. A classical \ac{LMPC} is presented and compared against a more advanced \ac{NMPC} that considers the full system model. In a careful analysis we show the advantages and disadvantages of the two implementations in terms of speed and tracking performance. This is achieved by evaluating hovering performance, step response, and aggressive trajectory tracking under nominal conditions and under external wind disturbances.

Linear vs Nonlinear Model Predictive Control for Trajectory Tracking in Rotary Wing MAVs

This paper presents a technical comparison of Linear Model Predictive Control (LMPC) and Nonlinear Model Predictive Control (NMPC) approaches for trajectory tracking in rotary wing Micro Aerial Vehicles (MAVs). The primary focus is on evaluating these control techniques' performance in terms of speed, precision, and disturbance handling.

Model Predictive Control (MPC), with its ability to handle multi-variable control problems and constraints, is particularly suitable for guiding MAVs that must operate in complex environments. The authors investigate LMPC and NMPC, both of which are state-of-the-art techniques in predictive control, applied to MAV trajectory tracking.

MAV Dynamics and Control Approaches

The dynamics of MAVs are inherently nonlinear, characterized by aerodynamic effects and disturbances such as wind. LMPC utilizes a linearized version of these dynamics, simplifying computation and enabling real-time control. NMPC, by contrast, accounts for the full nonlinear system dynamics, offering a potentially more accurate model of the MAV's behavior but requiring more computational resources.

The authors employ a cascade control structure, where a low-level attitude controller manages the MAV's orientation, and the trajectory tracking controller acts as an outer loop adjusting the overall path. This separation helps in ensuring system stability, especially relevant when executing on-board calculations in real-time.

Experimental Comparison

To provide a rigorous comparison, the paper details experiments under various conditions, including hovering, step response, and aggressive trajectory tracking. These experiments are performed on an Asctec NEO hexacopter, showcasing real-world applicability.

1. Hovering Performance: In nominal conditions, both LMPC and NMPC exhibit similar hovering performance. When subjected to wind disturbances, NMPC shows a marginal improvement in disturbance rejection. The root mean squared error (RMSE) in positioning is lower with NMPC, indicating better handling of unpredictable forces.
2. Step Response: NMPC demonstrates superior performance in step response scenarios, achieving faster response times and better utilization of thrust capabilities compared to LMPC. The NMPC's exploitation of the full system dynamics allows for more aggressive motion control without overshoot.
3. Aggressive Trajectory Tracking: During aggressive maneuvers with wind disturbances, NMPC outperforms LMPC significantly. The ability to model full dynamics allows NMPC to handle the non-intuitive flight characteristics better, maintaining lower RMSE compared to its linear counterpart. Additionally, NMPC exhibits enhanced computational efficiency when using real-time iteration schemes, reducing solver time drastically.

Implications and Future Directions

The evidence supports that NMPC, while computationally demanding, offers several advantages over LMPC in environments where dynamic system changes and external disturbances must be managed effectively. This aligns with the growing computational power available on UAV platforms, which increasingly makes NMPC a viable option for real-world applications.

For future developments, enhancing NMPC's computational efficiency remains a priority. This could involve integrating machine learning techniques to predict and accommodate dynamic environmental changes swiftly or employing more sophisticated real-time optimization algorithms. Additionally, hybrid approaches that adaptively switch between LMPC and NMPC based on current computational load and environmental conditions could leverage the strengths of both control strategies.

In conclusion, this paper provides a comprehensive analysis of linear versus nonlinear MPC for MAV trajectory tracking, substantiating the prevailing advantage of NMPC in complex operational scenarios. The practical insights drawn from this research advance the capability of autonomous MAVs, crucial for applications ranging from infrastructure inspection to emergency response operations.