Learning-based Control and Estimation for Attitude Regulation of a Reusable Launcher for Landing Scenario
Authors:   Lund University, Lund, Sweden, Cervin Anton , Renganathan Venkatraman , Rantzer Anders , Grönqvist Johan , Rosa P , Belfo J.P. , Somma N , Botelho A , Tofanelli G , Marcos A , Vasconcelos J , Navarro-Tapia D , Belhadj J , Casasco M , Bennani S 
Published: January 2024

We have presented the learning-based model predictive control technique for controlling and learning-based state estimation using the Gaussian process approach for estimation of the attitude dynamics of a reusable launcher during its landing phase. An high fidelity model of the reusable launcher called RETALT was used to study the learning-based techniques during its landing scenario. It is proposed to augment the representativity of the on-board model upon which prediction and action is taken over the needed control horizon by using a learning-based technique. This additional modelling step permit us to catch non-linear unmodelled dynamics, off-nominal dynamical behaviour and update this on-board knowledge in a continuous fashion.

Traditional MPC techniques that can handle both hard input and state constraints critically rely on the availability of the full knowledge of true state space models without any model uncertainty. Since the performance of the reusable launcher’s landing is directly affected by the extent of the system dynamics knowledge used by the controller, the presence of inevitable model uncertainties causes the traditional MPC techniques to fail. However, using the input-output data collected over time, it is possible to efficiently learn the model uncertainty and the obtained adaptive model can be used to enhance the performance while the nominal system dynamics knowledge is enough to guarantee the constraint satisfaction. With the objective of achieving a soft landing for the reusable launcher despite the presence of inevitable model uncertainties, we propose to use the learning based MPC formulation which combines the guaranteed constraint satisfaction of the robust MPC formulation along with the enhanced performance improvement due to the usage of adaptive model for cost formulation. While the methodology used in this paper is tailored for learning the linear unmodeled dynamics, it can very well be extended to learn complex nonlinear unmodeled dynamics using appropriate nonlinear oracle modules. We consider the linearized model at different points along the nominal reference trajectory to construct the nominal model for the design of control action. The linearized attitude dynamics parameterized by different time steps with ground truth values of parameters defining the model being estimated was obtained using a simplified single axis rotation dynamics. The unmodelled dynamics were learned using an oracle function employing a linear least-squares based estimation. As a result of learning, both optimised performance objective and the robustness guarantees are obtained simultaneously. This specific control ideology was applied to regulate the attitude error dynamics of the RETALT model developed as a part of the ESA-i4GNC framework developed by the DEIMOS consortium funded by the ESA with the simulations resulting in promising results.

Most aerospace applications assume that there already exists a high-performing navigation system that provides estimates of all the state variables needed for feedback and learning algorithms. It is nevertheless interesting to study how navigation (state estimation) can be improved by online learning of unmodeled and possible state-dependent random disturbance processes because the quality of the state estimates directly impact the achievable control performance at the lower loop level. While the Kalman filter and its various extensions that rely on accurate models of the plant is realistic for space vehicles, knowing in advance the type and intensity of disturbances can sometimes be impossible. Hence learning can be crucial for fine-tuning the navigation system during a mission. We propose to apply the Learning-based Kalman filter to the reusable launch vehicle model, where we estimated two components of the vehicle attitude vector (the yaw or the pitch) and their derivatives (the yaw rate or the pitch rate) based on noisy measurements and knowledge of the control inputs. Specifically, the Gaussian process-based approach is advocated to learn the unknown stochastic function which represents the state-dependent disturbance vector. A simulation sequence with a learning-based Kalman filter with the linear correlation model for the vehicle highlighted a significant improvement in estimator performance.