Learning a Family of Optimal State Feedback Controllers

Solving optimal control problems is well known to be very computationally demanding. In this paper we show how a combination of Pontryagin's minimum principle and machine learning can be used to learn optimal feedback controllers for a parametric cost function. This enables an unmanned system with limited computational resources to run optimal feedback controllers, and furthermore change the objective being optimised on the fly in response to external events. Thus, a time optimal control policy can be changed to a fuel optimal one, in the event of e.g., fuel leakage. The proposed approach is illustrated on both a standard inverted pendulum swing-up problem and a more complex interplanetary spacecraft orbital transfer.

Learning the optimal state-feedback via supervised imitation learning

Imitation learning is a control design paradigm that seeks to learn a control policy reproducing demonstrations from experts. By substituting expert's demonstrations for optimal behaviours, the same paradigm leads to the design of control policies closely approximating the optimal state-feedback. This approach requires training a machine learning algorithm (in our case deep neural networks) directly on state-control pairs originating from optimal trajectories. We have shown in previous work that, when restricted to relatively low-dimensional state and control spaces, this approach is very successful in several deterministic, non-linear problems in continuous-time. In this work, we refine our previous studies using as test case a simple quadcopter model with quadratic and time-optimal objective functions. We describe in detail the best learning pipeline we have developed and that is able to approximate via deep neural networks the state-feedback map to a very high accuracy. We introduce the use of the softplus activation function in the hidden units showing how it results in a smoother control profile whilst retaining the benefits of ReLUs. We show how to evaluate the optimality of the trained state-feedback, and find that already with two layers the objective function reached and its optimal value differ by less than one percent. We later consider also an additional metric linked to the system asymptotic behaviour - time taken to converge to the policy's fixed point. With respect to these metrics, we show that improvements in the mean average error do not necessarily correspond to significant improvements.

A Survey on Artificial Intelligence Trends in Spacecraft Guidance Dynamics and Control

The rapid developments of Artificial Intelligence in the last decade are influencing Aerospace Engineering to a great extent and research in this context is proliferating. We share our observations on the recent developments in the area of Spacecraft Guidance Dynamics and Control, giving selected examples on success stories that have been motivated by mission designs. Our focus is on evolutionary optimisation, tree searches and machine learning, including deep learning and reinforcement learning as the key technologies and drivers for current and future research in the field. From a high-level perspective, we survey various scenarios for which these approaches have been successfully applied or are under strong scientific investigation. Whenever possible, we highlight the relations and synergies that can be obtained by combining different techniques and projects towards future domains for which newly emerging artificial intelligence techniques are expected to become game changers.

On the stability analysis of optimal state feedbacks as represented by deep neural models

Research has shown how the optimal feedback control of several non linear systems of interest in aerospace applications can be represented by deep neural architectures and trained using techniques including imitation learning, reinforcement learning and evolutionary algorithms. Such deep architectures are here also referred to as Guidance and Control Networks, or G&CNETs. It is difficult to provide theoretical proofs on the control stability of such neural control architectures in general, and G&CNETs in particular, to perturbations, time delays or model uncertainties or to compute stability margins and trace them back to the network training process or to its architecture. In most cases the analysis of the trained network is performed via Monte Carlo experiments and practitioners renounce to any formal guarantee. This lack of validation naturally leads to scepticism especially in cases where safety and validation are of paramount importance such as is the case, for example, in the automotive or space industry. In an attempt to narrow the gap between deep learning research and control theory, we propose a new methodology based on differential algebra and automated differentiation to obtain formal guarantees on the behaviour of neural based control systems.

Machine learning and evolutionary techniques in interplanetary trajectory design

After providing a brief historical overview on the synergies between artificial intelligence research, in the areas of evolutionary computations and machine learning, and the optimal design of interplanetary trajectories, we propose and study the use of deep artificial neural networks to represent, on-board, the optimal guidance profile of an interplanetary mission. The results, limited to the chosen test case of an Earth-Mars orbital transfer, extend the findings made previously for landing scenarios and quadcopter dynamics, opening a new research area in interplanetary trajectory planning.

Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO

The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.

Differentiable Genetic Programming

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic regression, dCGP offers a new approach to the long unsolved problem of constant representation in GP expressions. On several problems of increasing complexity we find that dCGP is able to find the exact form of the symbolic expression as well as the constants values. We also demonstrate the use of dCGP to solve a large class of differential equations and to find prime integrals of dynamical systems, presenting, in both cases, results that confirm the efficacy of our approach.

Persistent self-supervised learning principle: from stereo to monocular vision for obstacle avoidance

Self-Supervised Learning (SSL) is a reliable learning mechanism in which a robot uses an original, trusted sensor cue for training to recognize an additional, complementary sensor cue. We study for the first time in SSL how a robot's learning behavior should be organized, so that the robot can keep performing its task in the case that the original cue becomes unavailable. We study this persistent form of SSL in the context of a flying robot that has to avoid obstacles based on distance estimates from the visual cue of stereo vision. Over time it will learn to also estimate distances based on monocular appearance cues. A strategy is introduced that has the robot switch from stereo vision based flight to monocular flight, with stereo vision purely used as 'training wheels' to avoid imminent collisions. This strategy is shown to be an effective approach to the 'feedback-induced data bias' problem as also experienced in learning from demonstration. Both simulations and real-world experiments with a stereo vision equipped AR drone 2.0 show the feasibility of this approach, with the robot successfully using monocular vision to avoid obstacles in a 5 x 5 room. The experiments show the potential of persistent SSL as a robust learning approach to enhance the capabilities of robots. Moreover, the abundant training data coming from the own sensors allows to gather large data sets necessary for deep learning approaches.