Search

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution operator for different computational domains is a problem of general importance for a variety of engineering applications. To this end, we propose a physics-informed deep operator network (DeepONet) capable of predicting the scattered pressure field for arbitrarily shaped scatterers using a geometric parameterization approach based on non-uniform rational B-splines (NURBS). This approach also results in parsimonious representations of non-trivial scatterer geometries. In contrast to existing physics-based approaches that require model re-evaluation when changing the computational domains, our trained model is capable of learning solution operator that can approximate physically-consistent scattered pressure field in just a few seconds for arbitrary rigid scatterer shapes; it follows that the computational time for forward simulations can improve (i.e. be reduced) by orders of magnitude in comparison to the traditional forward solvers. In addition, this approach can evaluate the scattered pressure field without the need for labeled training data. After presenting the theoretical approach, a comprehensive numerical study is also provided to illustrate the remarkable ability of this approach to simulate the acoustic pressure fields resulting from arbitrary combinations of arbitrary scatterer geometries. These results highlight the unique generalization capability of the proposed operator learning approach., Comment: 20 pages of main text, 9 figures

Multi-Objective Learning Model Predictive Control is a novel data-driven control scheme which improves a linear system's closed-loop performance with respect to several convex control objectives over iterations of a repeated task. At each task iteration, collected system data is used to construct terminal components of a Model Predictive Controller. The formulation presented in this paper ensures that closed-loop control performance improves between successive iterations with respect to each objective. We provide proofs of recursive feasibility and performance improvement, and show that the converged policy is Pareto optimal. Simulation results demonstrate the applicability of the proposed approach.

This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the concept of super finite network element, this paper provides the necessary foundation to extend FENA to linear time-transient simulations for both homogeneous and inhomogeneous domains. The concept of neural network concatenation, originally formulated to combine networks representative of different structural components in space, is extended to the time domain. Network concatenation in time enables training neural network models based on data available in a limited time frame and then using the trained networks to simulate the system evolution beyond the initial time window characteristic of the training data set. The proposed methodology is validated by applying FENA to the transient simulation of one-dimensional structural elements (such as rods and beams) and by comparing the results with either analytical or finite element solutions. Results confirm that FENA accurately predicts the dynamic response of the physical system and, while introducing an error on the order of 1% (compared to analytical or computational solutions of the governing differential equations), it is capable of delivering extreme computational efficiency.

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based on the physics of the scattering problem as well as a tailored network structure that embodies the concept of the superposition principle of linear wave interaction. The framework can also simulate the scattered field due to rigid scatterers having arbitrary shape as well as high-frequency problems. Unlike conventional data-driven neural networks, the PINN is trained by directly enforcing the governing equations describing the underlying physics, hence without relying on any labeled training dataset. Remarkably, the network model has significantly lower discretization dependence and offers simulation capabilities akin to parallel computation. This feature is particularly beneficial to address computational challenges typically associated with conventional mesh-dependent simulation methods. The performance of the network is investigated via a comprehensive numerical study that explores different application scenarios based on acoustic scattering., Comment: 23 pages of main text, 9 figures

We propose a hierarchical architecture designed for scalable real-time Model Predictive Control (MPC) in complex, multi-modal traffic scenarios. This architecture comprises two key components: 1) RAID-Net, a novel attention-based Recurrent Neural Network that predicts relevant interactions along the MPC prediction horizon between the autonomous vehicle and the surrounding vehicles using Lagrangian duality, and 2) a reduced Stochastic MPC problem that eliminates irrelevant collision avoidance constraints, enhancing computational efficiency. Our approach is demonstrated in a simulated traffic intersection with interactive surrounding vehicles, showcasing a 12x speed-up in solving the motion planning problem. A video demonstrating the proposed architecture in multiple complex traffic scenarios can be found here: https://youtu.be/-pRiOnPb9_c. GitHub: https://github.com/MPC-Berkeley/hmpc_raidnet, Comment: Accepted at IEEE Intelligent Vehicles Symposium 2024

We propose a Stochastic MPC (SMPC) formulation for path planning with autonomous vehicles in scenarios involving multiple agents with multi-modal predictions. The multi-modal predictions capture the uncertainty of urban driving in distinct modes/maneuvers (e.g., yield, keep speed) and driving trajectories (e.g., speed, turning radius), which are incorporated for multi-modal collision avoidance chance constraints for path planning. In the presence of multi-modal uncertainties, it is challenging to reliably compute feasible path planning solutions at real-time frequencies ($\geq$ 10 Hz). Our main technological contribution is a convex SMPC formulation that simultaneously (1) optimizes over parameterized feedback policies and (2) allocates risk levels for each mode of the prediction. The use of feedback policies and risk allocation enhances the feasibility and performance of the SMPC formulation against multi-modal predictions with large uncertainty. We evaluate our approach via simulations and road experiments with a full-scale vehicle interacting in closed-loop with virtual vehicles. We consider distinct, multi-modal driving scenarios: 1) Negotiating a traffic light and a fast, tailgating agent, 2) Executing an unprotected left turn at a traffic intersection, and 3) Changing lanes in the presence of multiple agents. For all of these scenarios, our approach reliably computes multi-modal solutions to the path-planning problem at real-time frequencies., Comment: The first three authors contributed equally

We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions. Inspired by Branch-and-Bound techniques, the key idea is to train a Neural Network/Random Forest, which for a given parameter, predicts a strategy consisting of (1) a set of Linear Programs (LPs) such that their feasible sets form a partition of the feasible set of the MILP and (2) a candidate integer solution. For control computation and sub-optimality quantification, we solve a set of LPs online in parallel. We demonstrate our approach for a motion planning example and compare against various commercial and open-source mixed-integer programming solvers., Comment: First two authors contributed equally

We propose an iterative approach for designing Robust Learning Model Predictive Control (LMPC) policies for a class of nonlinear systems with additive, unmodelled dynamics. The nominal dynamics are assumed to be difference flat, i.e., the state and input can be reconstructed using flat output sequences. For the considered class of systems, we synthesize Robust MPC policies and show how to use historical trajectory data collected during iterative tasks to 1) obtain bounds on the unmodelled dynamics and 2) construct a convex value function approximation along with a convex safe set in the space of output sequences for designing terminal components in the Robust MPC design. We show that the proposed strategy guarantees robust constraint satisfaction, asymptotic convergence to a desired subset of the state space, and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a minimum time control problem using a constrained nonlinear and uncertain vehicle model.

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. An extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design., Comment: 23 pages of main text, 10 figures

Motion planning for autonomous vehicles sharing the road with human drivers remains challenging. The difficulty arises from three challenging aspects: human drivers are 1) multi-modal, 2) interacting with the autonomous vehicle, and 3) actively making decisions based on the current state of the traffic scene. We propose a motion planning framework based on Branch Model Predictive Control to deal with these challenges. The multi-modality is addressed by considering multiple future outcomes associated with different decisions taken by the human driver. The interactive nature of humans is considered by modeling them as reactive agents impacted by the actions of the autonomous vehicle. Finally, we consider a model developed in human neuroscience studies as a possible way of encoding the decision making process of human drivers. We present simulation results in various scenarios, showing the advantages of the proposed method and its ability to plan assertive maneuvers that convey intent to humans., Comment: 8 pages, 10 figures

In this report, we analyze and design feedback policies for discrete-time Piecewise-Affine (PWA) systems with uncertainty in both the affine dynamics and the polytopic partition. The main idea is to utilise the Difference-of-Convex (DC) decomposition of continuous PWA systems to derive quadratic Lyapunov functions as stability certificates and stabilizing affine policies in a higher dimensional space. When projected back to the state space, we obtain time-varying PWQ Lyapunov functions and time-varying PWA feedback policies., Comment: Extended project report

We propose a Model Predictive Control (MPC) for collision avoidance between an autonomous agent and dynamic obstacles with uncertain predictions. The collision avoidance constraints are imposed by enforcing positive distance between convex sets representing the agent and the obstacles, and tractably reformulating them using Lagrange duality. This approach allows for smooth collision avoidance constraints even for polytopes, which otherwise require mixed-integer or non-smooth constraints. We consider three widely used descriptions of the uncertain obstacle position: 1) Arbitrary distribution with polytopic support, 2) Gaussian distributions and 3) Arbitrary distribution with first two moments known. For each case we obtain deterministic reformulations of the collision avoidance constraints. The proposed MPC formulation optimizes over feedback policies to reduce conservatism in satisfying the collision avoidance constraints. The proposed approach is validated using simulations of traffic intersections in CARLA., Comment: Accepted to CDC'22

We propose a Stochastic MPC (SMPC) approach for autonomous driving which incorporates multi-modal, interaction-aware predictions of surrounding vehicles. For each mode, vehicle motion predictions are obtained by a control model described using a basis of fixed features with unknown weights. The proposed SMPC formulation finds optimal controls which serves two purposes: 1) reducing conservatism of the SMPC by optimizing over parameterized control laws and 2) prediction and estimation of feature weights used in interaction-aware modeling using Kalman filtering. The proposed approach is demonstrated on a longitudinal control example, with uncertainties in predictions of the autonomous and surrounding vehicles., Comment: Accepted to AVEC'22

We propose a Stochastic MPC (SMPC) formulation for autonomous driving at traffic intersections which incorporates multi-modal predictions of surrounding vehicles for collision avoidance constraints. The multi-modal predictions are obtained with Gaussian Mixture Models (GMM) and constraints are formulated as chance-constraints. Our main theoretical contribution is a SMPC formulation that optimizes over a novel feedback policy class designed to exploit additional structure in the GMM predictions, and that is amenable to convex programming. The use of feedback policies for prediction is motivated by the need for reduced conservatism in handling multi-modal predictions of the surrounding vehicles, especially prevalent in traffic intersection scenarios. We evaluate our algorithm along axes of mobility, comfort, conservatism and computational efficiency at a simulated intersection in CARLA. Our simulations use a kinematic bicycle model and multimodal predictions trained on a subset of the Lyft Level 5 prediction dataset. To demonstrate the impact of optimizing over feedback policies, we compare our algorithm with two SMPC baselines that handle multi-modal collision avoidance chance constraints by optimizing over open-loop sequences., Comment: Extended version of ITSC 2022 submission

We propose a computationally efficient Learning Model Predictive Control (LMPC) scheme for constrained optimal control of a class of nonlinear systems where the state and input can be reconstructed using lifted outputs. For the considered class of systems, we show how to use historical trajectory data collected during iterative tasks to construct a convex value function approximation along with a convex safe set in a lifted space of virtual outputs. These constructions are iteratively updated with historical data and used to synthesize predictive control policies. We show that the proposed strategy guarantees recursive constraint satisfaction, asymptotic stability and non-decreasing closed-loop performance at each policy update. Finally, simulation results demonstrate the effectiveness of the proposed strategy on a piecewise affine (PWA) system, kinematic unicycle and bilinear DC motor.

We propose an Adaptive MPC framework for uncertain linear systems to achieve robust satisfaction of state and input constraints. The uncertainty in the system is assumed additive, state dependent, and globally Lipschitz with a known Lipschitz constant. We use a non-parametric technique for online identification of the system uncertainty by approximating its graph via envelopes defined by quadratic constraints. At any given time, by solving a set of convex optimization problems, the MPC controller guarantees robust constraint satisfaction for the closed loop system for all possible values of system uncertainty modeled by the envelope. The uncertainty envelope is refined with data using Set Membership Methods. We highlight the efficacy of the proposed framework via a detailed numerical example., Comment: Accepted for European Control Conference (ECC), May 2020, Saint Petersburg, Russia

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.

We propose a high-level planner for a multirotor to chase a ground vehicle, while simultaneously respecting various state and input constraints. Assuming a minimal kinematic model for the ground vehicle, we use data collected online to generate predictions for our planner within a model predictive control framework. Our solution is demonstrated, both via simulations and experiments on a stable quadcopter platform.

Recent results in control systems and numerical integration literature utilize invariant set theory to lift dynamical systems evolving on nonlinear manifolds to those evolving on vector spaces. We leverage this technique to propose an algorithm to solve a class of constrained optimization problems as unconstrained problems., Comment: Withdrawn for revision

This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and subsequently solved using variational principles again, to obtain necessary conditions that characterize optimal trajectories. The proposed approach is demonstrated on benchmark underactuated systems and accompanied by numerical simulations.

The paper presents a systematic strategy for implementing Hilbert's space filling curve for use in online exploration tasks and addresses its application in scenarios wherein the space to be searched obstacles (or holes) whose locations are not known a priori. Using the self-similarity and locality preserving properties of Hilbert's space filling curve, a set of evasive maneuvers are prescribed and characterized for online implementation. Application of these maneuvers in the case of non-uniform coverage of spaces and for obstacles of varying sizes is also presented. The results are validated with representative simulations demonstrating the deployment of the approach., Comment: Accepted for presentation at the 56th IEEE Conference on Decision and Control 2017

This paper considers the problem of achieving attitude consensus in spacecraft formations with bounded, time-varying communication delays between spacecraft connected as specified by a strongly connected topology. A state feedback con- troller is proposed and investigated using a time domain approach (via LMIs) and a frequency domain approach (via the small-gain theorem) to obtain delay depen- dent stability criteria to achieve the desired consensus. Simulations are presented to demonstrate the application of the strategy in a specific scenario., Comment: Presented at the 27th AAS/AIAA Space Flight Mechanics Meeting, February 2017, San Antonio, TX, USA

This article studies the dynamics and control of a novel underactuated system, wherein a plate suspended by cables and with a freely moving mass on top, whose other ends are attached to three quadrotors, is sought to be horizontally stabilized at a certain height, with the ball positioned at the center of mass of the plate. The freely moving mass introduces a 2-degree of underactuation into the system. The design proceeds through a decoupling of the quadrotors and the plate dynamics. Through a partial feedback linearization approach, the attitude of the plate and the translational height of the plate is initially controlled, while maintaining a bounded velocity along the $y$ and $x$ directions. These inputs are then synthesized through the quadrotors with a backstepping and timescale separation argument based on Tikhonov's theorem.