Riccardo Bonalli
Riccardo is a postdoctoral researcher at Stanford’s Department of Aeronautics and Astronautics. He obtained his Ph.D. in Applied Mathematics at Sorbonne Université, Paris in 2018 under a collaboration with ONERA - The French Aerospace Lab, Palaiseau, and received both his B.Sc. in Physical Engineering in 2011 and his M.Sc. in Mathematical Engineering in 2014 from Politecnico di Milano, Milan.
Riccardo’s research interests include differential geometry and Lie groups theory applied to nonlinear control systems, theoretical and numerical optimal control and optimization, homotopy and shooting algorithms, aerospace rendezvous problems, motion planning and trajectory optimization. Under a NASA grant, he is currently focusing on developing fast and robust algorithms for the optimal control of robots operating in microgravity environments.
In his free time, Riccardo enjoys skiing, political philosophy and viticulture.
Awards:
- 2018 Best Ph.D. thesis at ONERA, TIS Department
Currently at CNRS
ASL Publications
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T. Lew, R. Bonalli, L. Janson, and M. Pavone, “Estimating the convex hull of the image of a set with smooth boundary: error bounds and applications,” Discrete & Computational Geometry, pp. 1–39, Aug. 2024.
Abstract: We study the problem of estimating the convex hull of the image f(X)⊂\mathbbR^n of a compact set X⊂\mathbbR^m with smooth boundary through a smooth function f:\mathbbR^m\to\mathbbR^n. Assuming that f is a diffeomorphism or a submersion, we derive new bounds on the Hausdorff distance between the convex hull of f(X) and the convex hull of the images f(x_i) of M samples x_i on the boundary of X. When applied to the problem of geometric inference from random samples, our results give tighter and more general error bounds than the state of the art. We present applications to the problems of robust optimization, of reachability analysis of dynamical systems, and of robust trajectory optimization under bounded uncertainty.
@article{LewBonalliJansonPavone2024, author = {Lew, T. and Bonalli, R. and Janson, L. and Pavone, M.}, title = {Estimating the convex hull of the image of a set with smooth boundary: error bounds and applications}, journal = {{Discrete \& Computational Geometry}}, year = {2024}, volume = {}, number = {}, pages = {1--39}, month = aug, doi = {10.1007/s00454-024-00683-5}, url = {https://arxiv.org/abs/2302.13970}, owner = {lew}, timestamp = {2023-02-27} } -
T. Lew, R. Bonalli, and M. Pavone, “Sample Average Approximation for Stochastic Programming with Equality Constraints,” SIAM Journal on Optimization, vol. 34, no. 4, pp. 3506–3533, 2024.
Abstract: We revisit the sample average approximation (SAA) approach for general non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic optimality guarantees as the number of samples increases. To address this issue, we relax the equality constraints. Then, we prove the asymptotic optimality of the modified SAA approach under mild smoothness and boundedness conditions on the equality constraint functions. Our analysis uses random set theory and concentration inequalities to characterize the approximation error from the sampling procedure. We apply our approach to the problem of stochastic optimal control for nonlinear dynamical systems subject to external disturbances modeled by a Wiener process. We verify our approach on a rocket-powered descent problem and show that our computed solutions allow for significant uncertainty reduction.
@article{LewBonalliPavone2024, author = {Lew, T. and Bonalli, R. and Pavone, M.}, title = {Sample Average Approximation for Stochastic Programming with Equality Constraints}, journal = {{SIAM Journal on Optimization}}, year = {2024}, volume = {34}, number = {4}, pages = {3506--3533}, doi = {doi.org/10.1137/23M1573227}, owner = {jthluke}, timestamp = {2024-10-30}, url = {https://arxiv.org/abs/2206.09963} } -
T. Lew, R. Bonalli, and M. Pavone, “Convex Hulls of Reachable Sets,” IEEE Transactions on Automatic Control, 2024. (Submitted)
Abstract: We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation with initial conditions on the sphere. This finite-dimensional characterization unlocks an efficient sampling-based estimation algorithm to accurately over-approximate reachable sets. We also study the structure of the boundary of the reachable convex hulls and derive error bounds for the estimation algorithm. We give applications to neural feedback loop analysis and robust MPC.
@article{LewBonalliPavoneTAC2024, author = {Lew, T. and Bonalli, R. and Pavone, M.}, title = {Convex Hulls of Reachable Sets}, journal = {{IEEE Transactions on Automatic Control}}, year = {2024}, note = {Submitted}, url = {https://arxiv.org/abs/2303.17674}, keywords = {sub}, owner = {lew}, timestamp = {2024-03-01} } -
T. Lew, R. Bonalli, and M. Pavone, “Risk-Averse Trajectory Optimization via Sample Average Approximation,” IEEE Robotics and Automation Letters, vol. 9, no. 2, pp. 1500–1507, 2023.
Abstract: Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations, nonlinear dynamics, and non-convex constraints. In this work, we first introduce a continuous-time planning formulation with an average-value-at-risk constraint over the entire planning horizon. Then, we propose a sample-based approximation that unlocks an efficient, general-purpose, and time-consistent algorithm for risk-averse trajectory optimization. We prove that the method is asymptotically optimal and derive finite-sample error bounds. Simulations demonstrate the high speed and reliability of the approach on problems with stochasticity in nonlinear dynamics, obstacle fields, interactions, and terrain parameters.
@article{LewBonalliPavone2023, author = {Lew, T. and Bonalli, R. and Pavone, M.}, title = {Risk-Averse Trajectory Optimization via Sample Average Approximation}, journal = {{IEEE Robotics and Automation Letters}}, volume = {9}, number = {2}, pages = {1500--1507}, year = {2023}, url = {https://arxiv.org/abs/2307.03167}, keywords = {pub}, owner = {lew}, timestamp = {2024-02-29} } -
T. Lew, R. Bonalli, and M. Pavone, “Exact Characterization of the Convex Hulls of Reachable Sets,” in Proc. IEEE Conf. on Decision and Control, Singapore, 2023.
Abstract: We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we exactly characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation from all possible initial values of the disturbances. This finite-dimensional characterization unlocks a tight estimation algorithm to over-approximate reachable sets that is significantly faster and more accurate than existing methods. We present applications to neural feedback loop analysis and robust model predictive control.
@inproceedings{LewBonalliEtAl2023, author = {Lew, T. and Bonalli, R. and Pavone, M.}, title = {Exact Characterization of the Convex Hulls of Reachable Sets}, booktitle = {{Proc. IEEE Conf. on Decision and Control}}, year = {2023}, address = {Singapore}, doi = {10.1109/CDC49753.2023.10383902}, owner = {lew}, timestamp = {2023-04-03}, url = {https://ieeexplore.ieee.org/document/10383902} } -
R. Bonalli, T. Lew, and M. Pavone, “Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control,” IEEE Transactions on Automatic Control, vol. 68, no. 8, pp. 4570–4585, 2023.
Abstract: Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of SCP has received comparatively limited attention, and it is often restricted to discrete-time formulations. In this paper, we present a unifying theoretical analysis of a fairly general class of SCP procedures for continuous-time optimal control problems. In addition to the derivation of convergence guarantees in a continuous-time setting, our analysis reveals two new numerical and practical insights. First, we show how one can more easily account for manifold-type constraints, which are a defining feature of optimal control of mechanical systems. Second, we show how our theoretical analysis can be leveraged to accelerate SCP-based optimal control methods by infusing techniques from indirect optimal control.
@article{BonalliLewEtAl2023, author = {Bonalli, R. and Lew, T. and Pavone, M.}, title = {Analysis of Theoretical and Numerical Properties of Sequential Convex Programming for Continuous-Time Optimal Control}, journal = {{IEEE Transactions on Automatic Control}}, volume = {68}, number = {8}, year = {2023}, pages = {4570--4585}, keywords = {pub}, owner = {lew}, timestamp = {2023-09-12}, url = {https://arxiv.org/abs/2009.05038} } -
T. Lew, L. Janson, R. Bonalli, and M. Pavone, “A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis,” in Learning for Dynamics & Control Conference, 2022.
Abstract: In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of dynamical systems. By sampling inputs, evaluating their images in the true reachable set, and taking their ε-padded convex hull as a set estimator, this algorithm applies to general problem settings and is simple to implement. Our main contribution is the derivation of asymptotic and finite-sample accuracy guarantees using random set theory. This analysis informs algorithmic design to obtain an ε-close reachable set approximation with high probability, provides insights into which reachability problems are most challenging, and motivates safety-critical applications of the technique. On a neural network verification task, we show that this approach is more accurate and significantly faster than prior work. Informed by our analysis, we also design a robust model predictive controller that we demonstrate in hardware experiments.
@inproceedings{LewJansonEtAl2022, author = {Lew, T. and Janson, L. and Bonalli, R. and Pavone, M.}, title = {A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis}, year = {2022}, booktitle = {{Learning for Dynamics \& Control Conference}}, month = mar, url = {https://arxiv.org/abs/2112.05745}, keywords = {pub}, owner = {lew}, timestamp = {2022-03-01} } -
D. Malyuta, T. P. Reynolds, M. Szmuk, T. Lew, R. Bonalli, M. Pavone, and B. Acikmese, “Convex Optimization for Trajectory Generation,” IEEE Control Systems Magazine, vol. 42, no. 5, pp. 40–113, Jan. 2022.
Abstract: Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems of tomorrow. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory generation methods: lossless convexification (LCvx), and two sequential convex programming algorithms known as SCvx and GuSTO. In this article, trajectory generation is the computation of a dynamically feasible state and control signal that satisfies a set of constraints while optimizing key mission objectives. The trajectory generation problem is almost always nonconvex, which typically means that it is not readily amenable to efficient and reliable solution onboard an autonomous vehicle. The three algorithms that we discuss use problem reformulation and a systematic algorithmic strategy to nonetheless solve nonconvex trajectory generation tasks through the use of a convex optimizer. The theoretical guarantees and computational speed offered by convex optimization have made the algorithms popular in both research and industry circles. To date, the list of applications include rocket landing, spacecraft hypersonic reentry, spacecraft rendezvous and docking, aerial motion planning for fixed-wing and quadrotor vehicles, robot motion planning, and more. Among these applications are high-profile rocket flights conducted by organizations like NASA, Masten Space Systems, SpaceX, and Blue Origin. This article aims to give the reader the tools and understanding necessary to work with each algorithm, and to know what each method can and cannot do. A publicly available source code repository supports the numerical examples provided at the end of this article. By the end of the article, the reader should be ready to use each method, to extend them, and to contribute to their many exciting modern applications.
@article{MalyutaEtAl2022, author = {Malyuta, D. and Reynolds, T.~P. and Szmuk, M. and Lew, T. and Bonalli, R. and Pavone, M. and Acikmese, B.}, title = {Convex Optimization for Trajectory Generation}, year = {2022}, journal = {{IEEE Control Systems Magazine}}, volume = {42}, number = {5}, pages = {40--113}, month = jan, url = {https://arxiv.org/abs/2106.09125}, keywords = {pub}, owner = {lew}, timestamp = {2022-01-30} } -
F. Mahlknecht, J. I. Alora, S. Jain, E. Schmerling, R. Bonalli, G. Haller, and M. Pavone, “Using Spectral Submanifolds for Nonlinear Periodic Control,” in Proc. IEEE Conf. on Decision and Control, 2022.
Abstract: Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element methods. The complexity of these systems present computational challenges for direct application to automatic control. While model reduction has seen ubiquitous applications in control, the use of nonlinear model reduction methods in this setting remains difficult. The problem lies in preserving the structure of the nonlinear dynamics in the reduced order model for high-fidelity control. In this work, we leverage recent advances in Spectral Submanifold (SSM) theory to enable model reduction under well-defined assumptions for the purpose of efficiently synthesizing feedback controllers.
@inproceedings{MahlknechtAloraEtAl2022, author = {Mahlknecht, F. and Alora, J.I. and Jain, S. and Schmerling, E. and Bonalli, R. and Haller, G. and Pavone, M.}, booktitle = {{Proc. IEEE Conf. on Decision and Control}}, title = {Using Spectral Submanifolds for Nonlinear Periodic Control}, year = {2022}, keywords = {pub}, owner = {jjalora}, timestamp = {2022-11-22}, url = {https://arxiv.org/abs/2209.06573} } -
R. Bonalli, T. Lew, and M. Pavone, “Sequential Convex Programming For Non-Linear Stochastic Optimal Control,” ESAIM: Control, Optimisation & Calculus of Variations, vol. 28, 2022.
Abstract:
@article{BonalliLewESAIM2022, author = {Bonalli, R. and Lew, T. and Pavone, M.}, title = {Sequential Convex Programming For Non-Linear Stochastic Optimal Control}, journal = {{ESAIM: Control, Optimisation \& Calculus of Variations}}, volume = {28}, year = {2022}, owner = {lew}, timestamp = {2022-01-29}, url = {https://arxiv.org/abs/2009.05182} } -
A. Bylard, R. Bonalli, and M. Pavone, “Composable Geometric Motion Policies using Multi-Task Pullback Bundle Dynamical Systems,” in Proc. IEEE Conf. on Robotics and Automation, Xi’an, China, 2021.
Abstract: Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This work presents a principled method for designing and fusing desired robot task behaviors into a stable robot motion policy, leveraging the geometric structure of non-Euclidean manifolds, which are prevalent in robot configuration and task spaces. Our Pullback Bundle Dynamical Systems (PBDS) framework drives desired task behaviors and prioritizes tasks using separate position-dependent and position/velocity-dependent Riemannian metrics, respectively, thus simplifying individual task design and modular composition of tasks. For enforcing constraints, we provide a class of metric-based tasks, eliminating local minima by imposing non-conflicting potential functions only for goal region attraction. We also provide a geometric optimization problem for combining tasks inspired by Riemannian Motion Policies (RMPs) that reduces to a simple least-squares problem, and we show that our approach is geometrically well-defined. We demonstrate the PBDS framework on the sphere S2 and at 300-500 Hz on a manipulator arm, and we provide task design guidance and an open-source Julia library implementation. Overall, this work presents a fast, easy-to-use framework for generating motion policies without unwanted potential function local minima on general manifolds.
@inproceedings{BylardBonalliEtAl2021, author = {Bylard, A. and Bonalli, R. and Pavone, M.}, title = {Composable Geometric Motion Policies using Multi-Task Pullback Bundle Dynamical Systems}, booktitle = {{Proc. IEEE Conf. on Robotics and Automation}}, year = {2021}, address = {Xi'an, China}, month = may, owner = {jthluke}, timestamp = {2024-10-28}, url = {https://arxiv.org/abs/2101.01297} } -
M. P. Chapman, R. Bonalli, K. M. Smith, I. Yang, M. Pavone, and C. J. Tomlin, “Risk-sensitive safety analysis using Conditional Value-at-Risk,” IEEE Transactions on Automatic Control, vol. 67, no. 12, pp. 6521–6536, 2021.
Abstract:
@article{ChapmanBonalliEtAlTAC2021, author = {Chapman, M. P. and Bonalli, R. and Smith, K. M. and Yang, I. and Pavone, M. and Tomlin, C. J.}, title = {Risk-sensitive safety analysis using Conditional Value-at-Risk}, journal = {{IEEE Transactions on Automatic Control}}, volume = {67}, number = {12}, pages = {6521-6536}, year = {2021}, keywords = {pub}, owner = {bonalli}, timestamp = {2021-03-23}, url = {https://arxiv.org/abs/2101.12086} } -
T. Lew, R. Bonalli, and M. Pavone, “Chance-Constrained Sequential Convex Programming for Robust Trajectory Optimization,” in European Control Conference, St. Petersburg, Russia, 2020.
Abstract: Planning safe trajectories for nonlinear dynamical systems subject to model uncertainty and disturbances is challenging. In this work, we present a novel approach to tackle chance-constrained trajectory planning problems with nonconvex constraints, whereby obstacle avoidance chance constraints are reformulated using the signed distance function. We propose a novel sequential convex programming algorithm and prove that under a discrete time problem formulation, it is guaranteed to converge to a solution satisfying first-order optimality conditions. We demonstrate the approach on an uncertain 6 degrees of freedom spacecraft system and show that the solutions satisfy a given set of chance constraints.
@inproceedings{LewBonalliEtAl2020, author = {Lew, T. and Bonalli, R. and Pavone, M.}, title = {Chance-Constrained Sequential Convex Programming for Robust Trajectory Optimization}, booktitle = {{European Control Conference}}, year = {2020}, address = {St. Petersburg, Russia}, month = may, url = {/wp-content/papercite-data/pdf/Lew.Bonalli.Pavone.ECC20.pdf}, owner = {lew}, timestamp = {2020-03-16} } -
S. Banerjee, T. Lew, R. Bonalli, A. Alfaadhel, I. A. Alomar, H. M. Shageer, and M. Pavone, “Learning-based Warm-Starting for Fast Sequential Convex Programming and Trajectory Optimization,” in IEEE Aerospace Conference, Big Sky, Montana, 2020.
Abstract: Sequential convex programming (SCP) has recently emerged as an effective tool to quickly compute locally optimal trajectories for robotic and aerospace systems alike, even when initialized with an unfeasible trajectory. In this paper, by focusing on the Guaranteed Sequential Trajectory Optimization (GuSTO) algorithm, we propose a methodology to accelerate SCP-based algorithms through warm-starting. Specifically, leveraging a dataset of expert trajectories from GuSTO, we devise a neural-network-based approach to predict a locally optimal state and control trajectory, which is used to warm-start the SCP algorithm. This approach allows one to retain all the theoretical guarantees of GuSTO while simultaneously taking advantage of the fast execution of the neural network and reducing the time and number of iterations required for GuSTO to converge. The result is a faster and theoretically guaranteed trajectory optimization algorithm.
@inproceedings{BanerjeeEtAl2020, author = {Banerjee, S. and Lew, T. and Bonalli, R. and Alfaadhel, A. and Alomar, I. A. and Shageer, H. M. and Pavone, M.}, title = {Learning-based Warm-Starting for Fast Sequential Convex Programming and Trajectory Optimization}, booktitle = {{IEEE Aerospace Conference}}, year = {2020}, address = {Big Sky, Montana}, month = mar, url = {https://ieeexplore.ieee.org/abstract/document/9172293/}, owner = {lew}, timestamp = {2020-01-09} } -
R. Bonalli, A. Bylard, A. Cauligi, T. Lew, and M. Pavone, “Trajectory Optimization on Manifolds: A Theoretically-Guaranteed Embedded Sequential Convex Programming Approach,” in Robotics: Science and Systems, Freiburg im Breisgau, Germany, 2019.
Abstract: Sequential Convex Programming (SCP) has recently gain popularity as a tool for trajectory optimization, due to its sound theoretical properties and practical performance. Yet, most SCP-based methods for trajectory optimization are restricted to Euclidean settings, which precludes their application to problem instances where one needs to reason about manifold-type constraints (that is, constraints, such as loop closure, which restrict the motion of a system to a subset of the ambient space). The aim of this paper is to fill this gap by extending SCP-based trajectory optimization methods to a manifold setting. The key insight is to leverage geometric embeddings to lift a manifold-constrained trajectory optimization problem into an equivalent problem defined over a space enjoying Euclidean structure. This insight allows one to extend existing SCP methods to a manifold setting in a fairly natural way. In particular, we present an SCP algorithm for manifold problems with theoretical guarantees that resemble those derived for the Euclidean setting, and demonstrate its practical performance via numerical experiments.
@inproceedings{BonalliBylardEtAl2019, author = {Bonalli, R. and Bylard, A. and Cauligi, A. and Lew, T. and Pavone, M.}, title = {Trajectory Optimization on Manifolds: {A} Theoretically-Guaranteed Embedded Sequential Convex Programming Approach}, booktitle = {{Robotics: Science and Systems}}, year = {2019}, address = {Freiburg im Breisgau, Germany}, month = jun, url = {https://arxiv.org/pdf/1905.07654.pdf}, owner = {bylard}, timestamp = {2019-05-01} } -
R. Bonalli, A. Cauligi, A. Bylard, and M. Pavone, “GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming,” in Proc. IEEE Conf. on Robotics and Automation, Montreal, Canada, 2019.
Abstract: Sequential Convex Programming (SCP) has recently seen a surge of interest as a tool for trajectory optimization. Yet, most available methods lack rigorous performance guarantees and are often tailored to specific optimal control setups. In this paper, we present GuSTO (Guaranteed Sequential Trajectory Optimization), an algorithmic framework to solve trajectory optimization problems for control-affine systems with drift. GuSTO generalizes earlier SCP-based methods for trajectory optimization (by addressing, for example, goal region constraints and problems with either fixed or free final time), and enjoys theoretical convergence guarantees in terms of convergence to, at least, a stationary point. The theoretical analysis is further leveraged to devise an accelerated implementation of GuSTO, which originally infuses ideas from indirect optimal control into an SCP context. Numerical experiments on a variety of trajectory optimization setups show that GuSTO generally outperforms current state-of-the-art approaches in terms of success rates, solution quality, and computation times.
@inproceedings{BonalliCauligiEtAl2019, author = {Bonalli, R. and Cauligi, A. and Bylard, A. and Pavone, M.}, title = {{GuSTO:} Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming}, booktitle = {{Proc. IEEE Conf. on Robotics and Automation}}, year = {2019}, address = {Montreal, Canada}, month = may, url = {https://arxiv.org/pdf/1903.00155.pdf}, owner = {bylard}, timestamp = {2018-10-04} }