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Autonomous Vehicles




Physics-Informed Neural Networks




Robot learning (navigation/localization) through dynamical systems

(supervised, unsupervised and reinforcement learning/PhD at Ghent University)


Proxy models and Recurrent neural learning for control in Oil and Gas

(cooperation with Petrobras and DAS/UFSC, Brazil)

Deviation detection through dynamical reservoir models 

(cooperation with Halmstad University)

Time Series-based Fraud detection

(University of Luxembourg/Choice technologies)






They are also listed below:

On Learning Navigation Behaviors for Small Mobile Robots with Reservoir Computing Architectures

on Wed, 12/16/2015 - 14:56

This work proposes a general Reservoir Computing (RC) learning framework which can be used to learn navigation behaviors for mobile robots in simple and complex unknown, partially observable environments. RC provides an efficient way to train recurrent neural networks by letting the recurrent part of the network (called reservoir) fixed while only a linear readout output layer is trained.
The proposed RC framework builds upon the notion of navigation attractor or behavior which can be embedded in the high-dimensional space of the reservoir after learning. 
The learning of multiple behaviors is possible because the dynamic robot behavior, consisting of a sensory-motor sequence, can be linearly discriminated in the high-dimensional nonlinear space of the dynamic reservoir. 
Three learning approaches for navigation behaviors are shown in this paper. The first approach learns multiple behaviors based on examples of navigation behaviors generated by a supervisor, while the second approach learns goal-directed navigation behaviors based only on rewards. The third approach learns complex goal-directed behaviors, in a supervised way, using an hierarchical architecture whose internal predictions of contextual switches guide the sequence of basic navigation behaviors towards the goal.






Robot learning through dynamical systems (PhD thesis)

on Wed, 12/09/2015 - 14:12

During my PhD, I've worked mainly on Reservoir Computing (RC) architectures with application to modeling cognitive capabilities for mobile robots from sensor data and sometimes through interaction with the environment.

Reservoir Computing (RC) is an efficient method for trainning recurrent neural networks, which can handle spatio-temporal processing tasks, such as speech recognition. These networks are also biological plausible, as recently argued in the literature.

In my case, I used these RC networks for modeling a wide range of capabilities for mobile robots, such as:

These tasks were modeled basically using regression for learning behaviors or classification for discrete localization.

My PhD thesis can be download here. It is entitled: "Reservoir Computing Architectures for Modeling Robot Navigation Systems".

My publications are listed and can be downloaded in Google Scholar or here.

Some simulated and real robots employed in the experiments:


Environment used for localization experiments using the real e-puck robot:


After using unsupervised learning methods for self-localization, the plots below show the mean activation of place cells as a function of the robot position in the environment.
Red denotes a high response whereas blue denotes a low response.

It is possible to perform map generation through sensory prediction given the robot position as input. Black points represent the sensory readings whereas gray points are the robot trajectory.


Hierarchical Generative Adversarial Imitation Learning with Mid-level Input Generation for Autonomous Driving on Urban Environments

on Thu, 02/09/2023 - 20:43

Deriving robust control policies for realistic urban navigation scenarios is not a trivial task. In an end-to-end approach, these policies must map high-dimensional images from the vehicle's cameras to low-level actions such as steering and throttle. While pure Reinforcement Learning (RL) approaches are based exclusively on rewards, Generative Adversarial Imitation Learning (GAIL) agents learn from expert demonstrations while interacting with the environment, which favors GAIL on tasks for which a reward signal is difficult to derive.

In this work, the hGAIL architecture was proposed to solve the autonomous navigation of a vehicle in an end-to-end approach, mapping sensory perceptions directly to low-level actions, while simultaneously learning mid-level input representations of the agent's environment. The proposed hGAIL consists of an hierarchical Adversarial Imitation Learning architecture composed of two main modules: the GAN (Generative Adversarial Nets) which generates the Bird's-Eye View (BEV) representation mainly from the images of three frontal cameras of the vehicle, and the GAIL which learns to control the vehicle based mainly on the BEV predictions from the GAN as input.

Our experiments have shown that GAIL exclusively from cameras (without BEV) fails to even learn the task, while hGAIL, after training, was able to autonomously navigate successfully in all intersections of the city.

Fig. 1 - Hierarchical Generative Adversarial Imitation Learning (hGAIL) for policy learning with mid-level input representation. It basically consists of chained GAN and GAIL networks, where the first one (GAN) generates BEV representation from the vehicle's three frontal cameras, sparse trajectory and high-level command, while the latter (GAIL) outputs the acceleration and steering based on the predicted BEV input (generated by GAN), the current speed and the last applied actions. Both GAN and GAIL learn simultaneously while the agent interacts to the CARLA environment. The discriminator parts of both networks are not shown for the sake of simplicity.

This research has been summarized in a paper that is under review. More details at:

Some of the results can be seen on Youtube as series of videos, showing the learning through interaction with the urban environment:

Both the intermediate mid-level input BEV representation and the control policy are learned as the agent navigates in an urban town.
After training, we can see the autonomous vehicle navigation in the video below:

We can also observe the learning of the Bird's-Eye view representation of the Conditional GAN embedded in the hGAIL architecture, which learns concomitantly with the GAIL policy:

Generative Adversarial Imitation Learning for End-to-End Autonomous Driving on Urban Environments

on Fri, 11/04/2022 - 20:35

Autonomous driving is a complex task, which has been tackled since the first self-driving car ALVINN in 1989, with a supervised learning approach, or behavioral cloning (BC). In BC, a neural network is trained with state-action pairs that constitute the training set made by an expert, i.e., a human driver. However, this type of imitation learning does not take into account the temporal dependencies that might exist between actions taken in different moments of a navigation trajectory. These type of tasks are better handled by reinforcement learning (RL) algorithms, which need to define a reward function. On the other hand, more recent approaches to imitation learning, such as Generative Adversarial Imitation Learning (GAIL), can train policies without explicitly requiring to define a reward function, allowing an agent to learn by trial and error directly on a training set of expert trajectories. % In this work, we propose two variations of GAIL for autonomous navigation of a vehicle in the realistic CARLA simulation environment for urban scenarios. Both of them use the same network architecture, which process high-dimensional image input from three frontal cameras, and other nine continuous inputs representing the velocity, the next point from the sparse trajectory and a high-level driving command. We show that both of them are capable of imitating the expert trajectory from start to end after training ends, but the GAIL loss function that is augmented with BC outperforms the former in terms of convergence time and training stability.

Images from the three frontal cameras located at the left, central, and right part of the vehicle, respectively. They were taken after the first few interactions of the agent in the CARLA simulation environment considering our defined trajectory. Each camera produces a RGB image with 144 pixels of height and 256 pixels of width. These images are fed to the networks as they are.


Architecture of the actor-critic network and discriminator - each of them has its own separate network, with the latter having an additional input for the action, in orange color, and a sigmoidal output $D(s,a)$ instead of the output layer of the actor-critic network which consists of the steering direction, throttle as actions for the actor (policy) and value of the current state $V(s)$ for the critic. The common, though not shared architecture (in blue) is composed of a convolutional block that process the images of the three frontal cameras, whose output features are concatenated with other nine continuous inputs for speed, next target point in the sparse GPS trajectory, and a high-level driving command. The resulting feature vector is input to a block of two fully-connected (FC) layers.

Average rewards vs environment interactions during training in the long route (setup 2). For each method (GAIL and GAIL with BC), the average performance of two runs (i.e, two agents trained from scratch) is shown with a stochastic policy (left plot) and a deterministic policy (right plot). The shaded area represents the standard deviation. The behavior cloning (BC) attains an average reward of 173.6 for ten episodes, while the maximum is at 760, achieved by both GAIL and GAIL augmented with BC.




Proximal Policy Optimization with Continuous Bounded Action Space via the Beta Distribution

on Fri, 11/04/2022 - 21:38

Reinforcement learning methods for continuous control tasks have evolved in recent years generating a family of policy gradient methods that rely primarily on a Gaussian distribution for modeling a stochastic policy. However, the Gaussian distribution has an infinite support, whereas real world applications usually have a bounded action space. This dissonance causes an estimation bias that can be eliminated if the Beta distribution is used for the policy instead, as it presents a finite support. In this work, we investigate how this Beta policy performs when it is trained by the Proximal Policy Optimization (PPO) algorithm on two continuous control tasks from OpenAI gym. For both tasks, the Beta policy is superior to the Gaussian policy in terms of agent's final expected reward, also showing more stability and faster convergence of the training process. For the CarRacing environment with high-dimensional image input, the agent's success rate was improved by 63% over the Gaussian policy.

The CarRacing-v0 environment simulates an autonomous driving environment in 2D.

The observation space consists of top down images of 96x96 pixels and three (RGB) color channels. The latest four image frames were stacked and given as input to the agent's network after rescaling and preprocessing them to gray scale (totalling 84x84x4 input dimensions).
The action space has three dimensions: one encodes the steering angle and is bounded in the interval [-1, +1]. The other two dimensions encode throttle and brake, both bounded to [0, 1]. 

In the plot below, we can see the average rewards for 5 agents with different seeds for the CarRacing environment.
The final performance is shown on the bottom plots at a bigger scale, for agents with Gaussian policy (bottom left) and Beta policy (bottom right). 

Next, we see an illustration of the Gaussian and Beta stochastic policy distributions in relation to the action space of the CarRacing environment. 
For a fixed observation s (preprocessed image in left plot), we sampled the Gaussian and Beta policies for 5000 actions. 
For the Gaussian distribution, a significant portion of the actions fall out of the valid direction and brake/throttle range (both [-1, 1]), whereas for the Beta distributions, all actions fall within boundaries.


OpenAI CarRacing-v0 Leaderboard hosts a series of self-reported scores. We compare our results only to those found in peer-reviewed articles since they provide a basis for comparison and discussion.
Our proposal currently (as of 2021) surpass state-of-the-art models, beating all work reported previously in the literature.





Physics-Informed Neural Nets for Control of Dynamical Systems

on Tue, 09/28/2021 - 16:00

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by Ordinary Differential Equations (ODEs), the conventional PINN has a continuous time input variable and outputs the solution of the corresponding ODE. In their original form, PINNs do not allow control inputs neither can they simulate for long-range intervals without serious degradation in their predictions. In this context, this work presents a new framework called Physics-Informed Neural Nets for Control (PINC), which proposes a novel PINN-based architecture that is amenable to control problems and able to simulate for longer-range time horizons that are not fixed beforehand. The framework has new inputs to account for the initial state of the system and the control action. In PINC, the response over the complete time horizon is split such that each smaller interval constitutes a solution of the ODE conditioned on the fixed values of initial state and control action for that interval. The whole response is formed by feeding back the predictions of the terminal state as the initial state for the next interval. This proposal enables the optimal control of dynamic systems, integrating a priori knowledge from experts and data collected from plants into control applications. We showcase our proposal in the control of two nonlinear dynamic systems: the Van der Pol oscillator and the four-tank system.

MPC: Representation of the output prediction in a time instant, where the proposed actions generate a predicted behavior that reduces the distance between the value predicted by the model and a reference trajectory:


The PINC network has initial state y(0) of the dynamic system and control input u as inputs, in addition to continuous time scalar t. Both y(0) and u can be multidimensional. The output y(t) corresponds to the state of the dynamic system as a function of t 2 [0; T], and initial conditions given by y(0) and u. The deep network is fully connected even though not all connections are shown:


Below, modes of operation of the PINC network. (a) PINC net operates in self-loop mode, using its own output prediction as next initial state, after T seconds. This operation mode is used within one iteration of MPC, for trajectory generation until the prediction horizon of MPC completes (predicted output from the first Figure). (b) Block diagram for PINC connected to the plant. One pass through the diagram arrows corresponds to one MPC iteration applying a control input u for Ts timesteps for both plant and PINC network. Note that the initial state of the PINC net is set to the real output of the plant. In practice, in MPC, these two operation modes are executed in an alternated way (optimization in the prediction horizon, and application of control action).

a). pinc_feedback.png           

b) pinc_plant.png

Below, the representation of a trained PINC network evolving through time in self-loop mode (previous Figure a)) for trajectory generation in prediction horizon. The top dashed black curve corresponds to a predicted trajectory y of a hypothetical dynamic system in continuous time. The states y[k] are snapshots of the system in discrete time k positioned at the equidistant vertical lines. Between two vertical lines (during the inner continuous interval between steps k and k + 1), the PINC net learns the solution of an ODE with t \in [0; T], conditioned on a fixed control input u[k] (blue solid line) and initial state y(0) (green thick dashed line). Control action u[k] is changed at the vertical lines and kept fixed for T seconds, and the initial state y(0) in the interval between steps k and k + 1 is updated to the last state of the previous interval k  1 (indicated by the red curved arrow). The PINC net can directly predict the states at the vertical lines without the need to infer intermediate states t < T as numerical simulation does. Here, we assume that T = Ts and, thus, the number of discrete timesteps M is equal to the length of the prediction horizon in MPC.


ESN-PNMPC: Efficient data-driven model predictive control of unknown nonlinear processes

on Tue, 03/17/2020 - 19:12

The control of nonlinear industrial processes is a challenging task since the model of the plant may not be completely known a priori. In addition, the application of nonlinear model predictive control may be affected by modeling errors and subject to high computational complexity.

In this work, a new efficient data-driven scheme is proposed that alleviates some known issues in the so called Practical Nonlinear Model Predictive Controller (PNMPC). In PNMPC, the model is only linearized partially: while the free response of the system is kept fully nonlinear, only the forced response is linearized.  The general model for PNMPC proposed in this work consists of an Echo State Network (ESN), a recurrent neural network with very efficient training for system identification. 

The benefit of the proposed ESN-PNMPC scheme is that it allows:

  • fast system identification for nonlinear dynamic systems with arbitrary accuracy; 
  • analytical computation of derivatives from the ESN model for the forced response.  

This last feature assures significantly lower computational complexity for derivative computation when compared to the original finite difference method of PNMPC.

The proposed scheme is also enhanced with a correction filter that provides robustness to unforeseen disturbances during execution time, and compared to an LSTM (Long-Short Term Memory) implementation for the model as well as to a PI controller. The universality of the approach is shown by application to the control of different nonlinear plants.



Figure from J. Jordanou 2020, et al (submitted).

Online recurrent neural network learning for control of nonlinear plants in oil and gas production platforms

on Wed, 10/17/2018 - 12:54

This research line aims at designing adaptive controllers by using Echo State Networks (ESN) as a efficient data-driven method for training recurrent neural networks capable of controlling complex nonlinear plants, with a focus on oil and gas production platforms from Petrobras.

The resulting ESN-based controllers should learn inverse models of the controlled plant in an online fashion by interacting with the industrial plant and observing its dynamical behaviors.

In collaboration with supervised Master Student Jean P. Jordanou.

Well model. Figure by Jahanshahi et al. (2012).          


Manifold connecting two oil wells and a riser. Figure by Jordanou.

Scheme of Adaptive ESN-based controller and nonlinear plant. Figure by Jordanou

UTEMA (Unbiased Temporal Machine for General-purpose Times series-based Fraud detection)

on Thu, 05/03/2018 - 11:10

In the context of energy distribution networks, frauds are non-technical losses (NTL) that may account for up to 40% of the total distributed energy in some developing countries. The fraudster alters the eletricity meter in order to pay less than the right amount. In this context, the discovery or detection of frauds is necessary in order to decrease the non-technical losses of the energy distribution networks, consequently enhancing the stability and reliability of the network.

This project proposes the use of Recurrent Neural Networks (RNNs) for projecting a times series into a spatial dimension such that it can be used as a universal temporal feature for fraud detection predictive models. The particular problem tackled here jointly with the partner company is to predict whether a given time series of monthly energy consumption data is likely to indicate a fraud (NTL) or not.

Two main approaches are planned to be used with RNNs: supervised learning with bias correction techniques, and self-organized models for unsupervised learning of new fraud (anomaly) patterns.Finally, a last step is to integrate both of the previously developed models into an unified architecture that learns the responsibilities of each model in an online way by feedback from the environment using the results of the inspections of the fraudsters - the ground truth for some of the predictions.

This project has potential not only for generating significant technological and commercial value for the industrial partner, but also outstanding scientific output, being applicable in the long-term to other fields such as monitoring, prognosis/diagnostics in robotics, medical systems and security applications.

Funding: AFR-PPP / FNR, Luxembourg.


Proxy dynamical models of offshore oil production platforms via recurrent neural networks

on Wed, 12/09/2015 - 14:52

Process measurements are of vital importance for monitoring and control of industrial plants. When we consider offshore oil production platforms, wells that require gas-lift technology to yield oil production from low pressure oil reservoirs can become unstable under some conditions. This undesirable phenomenon is usually called slugging flow, and can be identified by an oscillatory behavior of the downhole pressure measurement.

Given the importance of this measurement and the unreliability of the related sensor, this work aims at designing data-driven soft-sensors for downhole pressure estimation in two contexts: one for speeding up first-principled model simulation of a vertical riser model; and another for estimating the downhole pressure using real-world data from an oil well from Petrobras based only on topside platform measurements. Both tasks are tackled by employing Echo State Networks (ESNs) as an efficient technique for training Recurrent Neural Networks.

We show that a single ESN is capable of robustly modeling both the slugging flow behavior and a steady state based only on a square wave input signal representing the production choke opening in the vertical riser. Besides, we compare the performance of a standard network to the performance of a multiple timescale hierarchical architecture in the second task and show that for some periods the latter architecture performs better.