Launcher Attitude Control based on Incremental Nonlinear Dynamic Inversion: a Feasibility Study towards Fast and Robust Design Approaches
Authors:   Aurora Technology for the European Space Agency, Noordwijk, Netherlands, Simplicio Pedro , Acquatella Paul , Bennani Samir 
Published: January 2024

The so-called “New Space era” has been marked by a disruptive change in the business models, manufacturing technologies and agile practices of launch vehicle companies, aimed at minimising their production and operating costs in an ever more competitive market. Yet, only limited consideration has been given to the benefits that innovation in the field of control theory can bring, not only in terms of increasing the limits of performance, but also reducing mission preparation (“missionisation”) efforts. Also on government-led developments, recent launchers such as Ares I and VEGA [R1] still use the same design approach of the Saturn V rocket, i.e. linear controllers. This approach relies on single channel-at-a-time tuning and ad hoc gain-scheduling followed by extensive V&V, which are very time and cost consuming processes.

In contrast to the approach presented above, the past few years have seen a growing interest in the application of artificial intelligence and machine learning methods for launcher GNC, but the industrial use of such data-driven/model-free methods remains limited by well-known issues related to training and certification of the algorithms on the full flight envelope of intended operation. In that sense, there is a clear gap between these strategies and the current state-of-practice, in which other techniques could bring relevant improvements; this is the case for nonlinear control algorithms, especially those based on Nonlinear Dynamic Inversion (NDI). On one hand, agile practices of New Space companies provide the ideal opportunity to explore the benefits of this type of design approach. On the other hand, a successful adoption of nonlinear launcher control will likely facilitate the augmentation with and transition to data-driven methods in the future.

The NDI technique consists in cancelling the nonlinearities of a nonlinear system by means of state feedback so that the system is transformed into a linear form (for this reason, NDI is often known as “feedback linearisation”). For the resulting linear system, a single linear control law can be applied without the need for gain-scheduling to tailor the controller to different conditions. Being a multivariable technique, NDI allows to decouple and handle all the control channels in a systematic manner. The main drawback of this technique is that the linearisation fully relies on the accurate knowledge of the system, thus model mismatches may lead to substantial performance and stability losses. To tackle this drawback, an approach called Incremental NDI (INDI) was proposed in the early 2000s. By generating incremental commands (instead of total inputs) and employing acceleration feedback, the model dependency of the INDI technique is greatly reduced (for this reason, INDI is also known as a “sensor-based” approach). Being less model-dependent, INDI-based controllers become easier to design and significantly more robust. The resulting nonlinear control law still relies on an approximate model of the system’s control effectiveness, which in turn can be integrated with data-driven methods.

Incremental NDI has been elaborated theoretically and applied successfully to high-performance systems including advanced aircraft flight control and a few studies for spacecraft attitude control. More recently, it has been applied to fault-tolerant control of aircraft subjected to sensor and actuator faults, as well as in real flight tests of small unmanned aircraft and of a business passenger jet [R2], demonstrating INDI’s performance and robustness against aerodynamic model uncertainties and disturbance rejection. However, to the best of the authors’ knowledge, its applicability to launch vehicles has never been adequately investigated. The potential benefits of INDI become even more relevant for the case of reusable launchers, which are characterised by much tighter dynamical couplings between (online-generated) trajectory and attitude during descent flight.

It is therefore the objective of this study to present and raise awareness of the INDI technique among the launcher GNC community, to showcase its implementation on a representative application scenario, and to highlight its strengths and challenges in the face of the industrial state-of-practice. To achieve this, the paper provides a concise description of the NDI and INDI approach, followed by the detailed design and comparison of different control laws: linear, linear with angular acceleration feedback and INDI-based. The application scenario is that of a launcher model in ascent flight featuring attitude and drift degrees-of-freedom, actuator dynamics and moving-mass effects. All the controllers and filters are implemented at a sampling frequency that is compatible with current onboard capabilities (25 Hz).

There are mainly two well-known challenges associated with the practical implementation of INDI-based control. The first one is that, by relying on angular acceleration and control input measurements/estimates, INDI controllers are generally more sensitive to sensor noise and actuator delay than classical controllers. The second challenge of INDI is that, due to its nonlinear nature, attaining an analytical proof of stability is not trivial [R3]. To assess the severity of the first challenge, the paper shows a comprehensive nonlinear simulation campaign with wind disturbances, uncertainties, as well as different levels of sensor noise and actuator delay. For the second challenge, the paper proposes a simple yet insightful linearisation-based approach to evaluate stability degradation related to an inexact feedback linearisation and to deviations from the control tuning conditions.

From the results obtained in this feasibility study, the two limitations above seem to be outweighed by the potential benefits of INDI-based launcher control. Further analysis on this topic will address the impact of flexible modes and non-collocated sensing.

[R1] A. Marcos, D. Navarro-Tapia, P. Simplício, S. Bennani, “Robust Control for Launchers: VEGA Study Case,” Journal of the Society of Instrument and Control Engineers, vol. 59, March 2020;

[R2] F. Grondman, G. Looye, R. Kuchar, Q.P. Chu, E. van Kampen, “Design and Flight Testing of Incremental Nonlinear Dynamic Inversion-based Control Laws for a Passenger Aircraft,” AIAA SciTech Forum 2018;

[R3] X. Wang, E. van Kampen, Q.P. Chu, P. Lu, “Stability Analysis for Incremental Nonlinear Dynamic Inversion Control”, Journal of Guidance, Control, and Dynamics, vol. 42, May 2019.