Real-time optimal control of high-dimensional parametrized systems by deep learning-based reduced order models

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical system to be controlled. Moreover, the control action needs to be updated whenever the underlying scenario undergoes variations. Full-order models based on, e.g., the Finite Element Method, do not meet these requirements due to the computational burden they usually entail. On the other hand, conventional reduced order modeling techniques such as the Reduced Basis method, are intrusive, rely on a linear superimposition of modes, and lack of efficiency when addressing nonlinear time-dependent dynamics. In this work, we propose a non-intrusive Deep Learning-based Reduced Order Modeling (DL-ROM) technique for the rapid control of systems described in terms of parametrized PDEs in multiple scenarios. In particular, optimal full-order snapshots are generated and properly reduced by either Proper Orthogonal Decomposition or deep autoencoders (or a combination thereof) while feedforward neural networks are exploited to learn the map from scenario parameters to reduced optimal solutions. Nonlinear dimensionality reduction therefore allows us to consider state variables and control actions that are both low-dimensional and distributed. After (i) data generation, (ii) dimensionality reduction, and (iii) neural networks training in the offline phase, optimal control strategies can be rapidly retrieved in an online phase for any scenario of interest. The computational speedup and the high accuracy obtained with the proposed approach are assessed on different PDE-constrained optimization problems, ranging from the minimization of energy dissipation in incompressible flows modelled through Navier-Stokes equations to the thermal active cooling in heat transfer.

Tactical Game-theoretic Decision-making with Homotopy Class Constraints

We propose a tactical homotopy-aware decision-making framework for game-theoretic motion planning in urban environments. We model urban driving as a generalized Nash equilibrium problem and employ a mixed-integer approach to tame the combinatorial aspect of motion planning. More specifically, by utilizing homotopy classes, we partition the high-dimensional solution space into finite, well-defined subregions. Each subregion (homotopy) corresponds to a high-level tactical decision, such as the passing order between pairs of players. The proposed formulation allows to find global optimal Nash equilibria in a computationally tractable manner by solving a mixed-integer quadratic program. Each homotopy decision is represented by a binary variable that activates different sets of linear collision avoidance constraints. This extra homotopic constraint allows to find solutions in a more efficient way (on a roundabout scenario on average 5-times faster). We experimentally validate the proposed approach on scenarios taken from the rounD dataset. Simulation-based testing in receding horizon fashion demonstrates the capability of the framework in achieving globally optimal solutions while yielding a 78% average decrease in the computational time with respect to an implementation without the homotopic constraints.

ZAPP! Zonotope Agreement of Prediction and Planning for Continuous-Time Collision Avoidance with Discrete-Time Dynamics

The past few years have seen immense progress on two fronts that are critical to safe, widespread mobile robot deployment: predicting uncertain motion of multiple agents, and planning robot motion under uncertainty. However, the numerical methods required on each front have resulted in a mismatch of representation for prediction and planning. In prediction, numerical tractability is usually achieved by coarsely discretizing time, and by representing multimodal multi-agent interactions as distributions with infinite support. On the other hand, safe planning typically requires very fine time discretization, paired with distributions with compact support, to reduce conservativeness and ensure numerical tractability. The result is, when existing predictors are coupled with planning and control, one may often find unsafe motion plans. This paper proposes ZAPP (Zonotope Agreement of Prediction and Planning) to resolve the representation mismatch. ZAPP unites a prediction-friendly coarse time discretization and a planning-friendly zonotope uncertainty representation; the method also enables differentiating through a zonotope collision check, allowing one to integrate prediction and planning within a gradient-based optimization framework. Numerical examples show how ZAPP can produce safer trajectories compared to baselines in interactive scenes.

Nonlinear In-situ Calibration of Strain-Gauge Force/Torque Sensors for Humanoid Robots

High force/torque (F/T) sensor calibration accuracy is crucial to achieving successful force estimation/control tasks with humanoid robots. State-of-the-art affine calibration models do not always approximate correctly the physical phenomenon of the sensor/transducer, resulting in inaccurate F/T measurements for specific applications such as thrust estimation of a jet-powered humanoid robot. This paper proposes and validates nonlinear polynomial models for F/T calibration, increasing the number of model coefficients to minimize the estimation residuals. The analysis of several models, based on the data collected from experiments with the iCub3 robot, shows a significant improvement in minimizing the force/torque estimation error when using higher-degree polynomials. In particular, when using a 4th-degree polynomial model, the Root Mean Square error (RMSE) decreased to 2.28N from the 4.58N obtained with an affine model, and the absolute error in the forces remained under 6N while it was reaching up to 16N with the affine model.

Vehicle State Estimation through Modular Factor Graph-based Fusion of Multiple Sensors

This study focuses on the critical aspect of robust state estimation for the safe navigation of an Autonomous Vehicle (AV). Existing literature primarily employs two prevalent techniques for state estimation, namely filtering-based and graph-based approaches. Factor Graph (FG) is a graph-based approach, constructed using Values and Factors for Maximum Aposteriori (MAP) estimation, that offers a modular architecture that facilitates the integration of inputs from diverse sensors. However, most FG-based architectures in current use require explicit knowledge of sensor parameters and are designed for single setups. To address these limitations, this research introduces a novel plug-and-play FG-based state estimator capable of operating without predefined sensor parameters. This estimator is suitable for deployment in multiple sensor setups, offering convenience and providing comprehensive state estimation at a high frequency, including mean and covariances. The proposed algorithm undergoes rigorous validation using various sensor setups on two different vehicles: a quadricycle and a shuttle bus. The algorithm provides accurate and robust state estimation across diverse scenarios, even when faced with degraded Global Navigation Satellite System (GNSS) measurements or complete outages. These findings highlight the efficacy and reliability of the algorithm in real-world AV applications.

Predicting human motion intention for pHRI assistive control

This work addresses human intention identification during physical Human-Robot Interaction (pHRI) tasks to include this information in an assistive controller. To this purpose, human intention is defined as the desired trajectory that the human wants to follow over a finite rolling prediction horizon so that the robot can assist in pursuing it. This work investigates a Recurrent Neural Network (RNN), specifically, Long-Short Term Memory (LSTM) cascaded with a Fully Connected layer. In particular, we propose an iterative training procedure to adapt the model. Such an iterative procedure is powerful in reducing the prediction error. Still, it has the drawback that it is time-consuming and does not generalize to different users or different co-manipulated objects. To overcome this issue, Transfer Learning (TL) adapts the pre-trained model to new trajectories, users, and co-manipulated objects by freezing the LSTM layer and fine-tuning the last FC layer, which makes the procedure faster. Experiments show that the iterative procedure adapts the model and reduces prediction error. Experiments also show that TL adapts to different users and to the co-manipulation of a large object. Finally, to check the utility of adopting the proposed method, we compare the proposed controller enhanced by the intention prediction with the other two standard controllers of pHRI.

Nonlinear Model Identification and Observer Design for Thrust Estimation of Small-scale Turbojet Engines

Jet-powered vertical takeoff and landing (VTOL) drones require precise thrust estimation to ensure adequate stability margins and robust maneuvering. Small-scale turbojets have become good candidates for powering heavy aerial drones. However, due to limited instrumentation available in these turbojets, estimating the precise thrust using classical techniques is not straightforward. In this paper, we present a methodology to accurately estimate the online thrust for the small-scale turbojets used on the iRonCub - an aerial humanoid robot. We use a grey-box method to capture the turbojet system dynamics with a nonlinear state-space model based on the data acquired from a custom engine test bench. This model is then used to design an extended Kalman filter that estimates the turbojet thrust only from the angular speed measurements. We exploited the parameter estimation algorithm to ensure that the EKF gives smooth and accurate estimates even at engine failures. The designed EKF was validated on the test bench where the mean absolute error in estimated thrust was found to be within 2% of rated peak thrust.

Centroidal Aerodynamic Modeling and Control of Flying Multibody Robots

This paper presents a modeling and control framework for multibody flying robots subject to non-negligible aerodynamic forces acting on the centroidal dynamics. First, aerodynamic forces are calculated during robot flight in different operating conditions by means of Computational Fluid Dynamics (CFD) analysis. Then, analytical models of the aerodynamics coefficients are generated from the dataset collected with CFD analysis. The obtained simplified aerodynamic model is also used to improve the flying robot control design. We present two control strategies: compensating for the aerodynamic effects via feedback linearization and enforcing the controller robustness with gain-scheduling. Simulation results on the jet-powered humanoid robot iRonCub validate the proposed approach.

Competitors-Aware Stochastic Lap Strategy Optimisation for Race Hybrid Vehicles

World Endurance Championship (WEC) racing events are characterised by a relevant performance gap among competitors. The fastest vehicles category, consisting in hybrid vehicles, has to respect energy usage constraints set by the technical regulation. Considering absence of competitors, i.e. traffic conditions, the optimal energy usage strategy for lap time minimisation is typically computed through a constrained optimisation problem. To the best of our knowledge, the majority of state-of-the-art works neglects competitors. This leads to a mismatch with the real world, where traffic generates considerable time losses. To bridge this gap, we propose a new framework to offline compute optimal strategies for the powertrain energy management considering competitors. Through analysis of the available data from previous events, statistics on the sector times and overtaking probabilities are extracted to encode the competitors' behaviour. Adopting a multi-agent model, the statistics are then used to generate realistic Monte Carlo (MC) simulation of their position along the track. The simulator is then adopted to identify the optimal strategy as follows. We develop a longitudinal vehicle model for the ego-vehicle and implement an optimisation problem for lap time minimisation in absence of traffic, based on Genetic Algorithms. Solving the optimisation problem for a variety of constraints generates a set of candidate optimal strategies. Stochastic Dynamic Programming is finally implemented to choose the best strategy considering competitors, whose motion is generated by the MC simulator. Our approach, validated on data from a real stint of race, allows to significantly reduce the lap time.

Extended Object Tracking in Curvilinear Road Coordinates for Autonomous Driving

In literature, Extended Object Tracking (EOT) algorithms developed for autonomous driving predominantly provide obstacles state estimation in cartesian coordinates in the Vehicle Reference Frame. However, in many scenarios, state representation in road-aligned curvilinear coordinates is preferred when implementing autonomous driving subsystems like cruise control, lane-keeping assist, platooning, etc. This paper proposes a Gaussian Mixture Probability Hypothesis Density~(GM-PHD) filter with an Unscented Kalman Filter~(UKF) estimator that provides obstacle state estimates in curvilinear road coordinates. We employ a hybrid sensor fusion architecture between Lidar and Radar sensors to obtain rich measurement point representations for EOT. The measurement model for the UKF estimator is developed with the integration of coordinate conversion from curvilinear road coordinates to cartesian coordinates by using cubic hermit spline road model. The proposed algorithm is validated through Matlab Driving Scenario Designer simulation and experimental data collected at Monza Eni Circuit.