arXiv subjects

Ian R. Manchester

Publications and source records attributed to Ian R. Manchester.

At least 37 records · Page 2Linked to original sources

arXiv2025

Training Trajectory Predictors Without Ground-Truth Data

This paper presents a framework capable of accurately and smoothly estimating position, heading, and velocity. Using this high-quality input, we propose a system based on Trajectron++, able to consistently generate precise trajectory predictions. Unlike conventional models that require ground-truth data for training, our approach eliminates this dependency. Our analysis demonstrates that poor quality input leads to noisy and unreliable predictions, which can be detrimental to navigation modules. We evaluate both input data quality and model output to illustrate the impact of input noise. Furthermore, we show that our estimation system enables effective training of trajectory prediction models even with limited data, producing robust predictions across different environments. Accurate estimations are crucial for deploying trajectory prediction models in real-world scenarios, and our system ensures meaningful and reliable results across various application contexts.

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arXiv2025

On Robust Reinforcement Learning with Lipschitz-Bounded Policy Networks

This paper presents a study of robust policy networks in deep reinforcement learning. We investigate the benefits of policy parameterizations that naturally satisfy constraints on their Lipschitz bound, analyzing their empirical performance and robustness on two representative problems: pendulum swing-up and Atari Pong. We illustrate that policy networks with smaller Lipschitz bounds are more robust to disturbances, random noise, and targeted adversarial attacks than unconstrained policies composed of vanilla multi-layer perceptrons or convolutional neural networks. However, the structure of the Lipschitz layer is important. We find that the widely-used method of spectral normalization is too conservative and severely impacts clean performance, whereas more expressive Lipschitz layers such as the recently-proposed Sandwich layer can achieve improved robustness without sacrificing clean performance.

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arXiv2024

Learning Stable and Passive Neural Differential Equations

In this paper, we introduce a novel class of neural differential equation, which are intrinsically Lyapunov stable, exponentially stable or passive. We take a recently proposed Polyak Lojasiewicz network (PLNet) as an Lyapunov function and then parameterize the vector field as the descent directions of the Lyapunov function. The resulting models have a same structure as the general Hamiltonian dynamics, where the Hamiltonian is lower- and upper-bounded by quadratic functions. Moreover, it is also positive definite w.r.t. either a known or learnable equilibrium. We illustrate the effectiveness of the proposed model on a damped double pendulum system.

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arXiv2024

Real-time Coupled Centroidal Motion and Footstep Planning for Biped Robots

This paper presents an algorithm that finds a centroidal motion and footstep plan for a Spring-Loaded Inverted Pendulum (SLIP)-like bipedal robot model substantially faster than real-time. This is achieved with a novel representation of the dynamic footstep planning problem, where each point in the environment is considered a potential foothold that can apply a force to the center of mass to keep it on a desired trajectory. For a biped, up to two such footholds per time step must be selected, and we approximate this cardinality constraint with an iteratively reweighted $l_1$-norm minimization. Along with a linearizing approximation of an angular momentum constraint, this results in a quadratic program can be solved for a contact schedule and center of mass trajectory with automatic gait discovery. A 2 s planning horizon with 13 time steps and 20 surfaces available at each time is solved in 142 ms, roughly ten times faster than comparable existing methods in the literature. We demonstrate the versatility of this program in a variety of simulated environments.

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arXiv2024

Path-Parameterised RRTs for Underactuated Systems

We present a sample-based motion planning algorithm specialised to a class of underactuated systems using path parameterisation. The structure this class presents under a path parameterisation enables the trivial computation of dynamic feasibility along a path. Using this, a specialised state-based steering mechanism within an RRT motion planning algorithm is developed, enabling the generation of both geometric paths and their time parameterisations without introducing excessive computational overhead. We find with two systems that our algorithm computes feasible trajectories with higher rates of success and lower mean computation times compared to existing approaches.

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arXiv2024

Monotone, Bi-Lipschitz, and Polyak-Lojasiewicz Networks

This paper presents a new bi-Lipschitz invertible neural network, the BiLipNet, which has the ability to smoothly control both its Lipschitzness (output sensitivity to input perturbations) and inverse Lipschitzness (input distinguishability from different outputs). The second main contribution is a new scalar-output network, the PLNet, which is a composition of a BiLipNet and a quadratic potential. We show that PLNet satisfies the Polyak-Lojasiewicz condition and can be applied to learn non-convex surrogate losses with a unique and efficiently-computable global minimum. The central technical element in these networks is a novel invertible residual layer with certified strong monotonicity and Lipschitzness, which we compose with orthogonal layers to build the BiLipNet. The certification of these properties is based on incremental quadratic constraints, resulting in much tighter bounds than can be achieved with spectral normalization. Moreover, we formulate the calculation of the inverse of a BiLipNet -- and hence the minimum of a PLNet -- as a series of three-operator splitting problems, for which fast algorithms can be applied.

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arXiv2024

Control contraction metrics on Lie groups

In this paper, we extend the control contraction metrics (CCM) approach, which was originally proposed for the universal tracking control of nonlinear systems, to those that evolves on Lie groups. Our idea is to view the manifold as a constrained set that is embedded in Euclidean space, and then propose the sufficient conditions for the existence of a CCM and the associated controller design. Notably, we demonstrate that the search for CCM on Lie groups can be reformulated as convex conditions. The results extend the applicability of the CCM approach and provide a framework for analyzing the behavior of control systems with Lie group structures.

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arXiv2024

Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian

We establish a layer-wise parameterization for 1D convolutional neural networks (CNNs) with built-in end-to-end robustness guarantees. In doing so, we use the Lipschitz constant of the input-output mapping characterized by a CNN as a robustness measure. We base our parameterization on the Cayley transform that parameterizes orthogonal matrices and the controllability Gramian of the state space representation of the convolutional layers. The proposed parameterization by design fulfills linear matrix inequalities that are sufficient for Lipschitz continuity of the CNN, which further enables unconstrained training of Lipschitz-bounded 1D CNNs. Finally, we train Lipschitz-bounded 1D CNNs for the classification of heart arrythmia data and show their improved robustness.

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arXiv2023

Learning Over Contracting and Lipschitz Closed-Loops for Partially-Observed Nonlinear Systems (Extended Version)

This paper presents a policy parameterization for learning-based control on nonlinear, partially-observed dynamical systems. The parameterization is based on a nonlinear version of the Youla parameterization and the recently proposed Recurrent Equilibrium Network (REN) class of models. We prove that the resulting Youla-REN parameterization automatically satisfies stability (contraction) and user-tunable robustness (Lipschitz) conditions on the closed-loop system. This means it can be used for safe learning-based control with no additional constraints or projections required to enforce stability or robustness. We test the new policy class in simulation on two reinforcement learning tasks: 1) magnetic suspension, and 2) inverting a rotary-arm pendulum. We find that the Youla-REN performs similarly to existing learning-based and optimal control methods while also ensuring stability and exhibiting improved robustness to adversarial disturbances.

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arXiv2023

On the equivalence of contraction and Koopman approaches for nonlinear stability and control

In this paper we prove new connections between two frameworks for analysis and control of nonlinear systems: the Koopman operator framework and contraction analysis. Each method, in different ways, provides exact and global analyses of nonlinear systems by way of linear systems theory. The main results of this paper show equivalence between contraction and Koopman approaches for a wide class of stability analysis and control design problems. In particular: stability or stablizability in the Koopman framework implies the existence of a contraction metric (resp. control contraction metric) for the nonlinear system. Further in certain cases the converse holds: contraction implies the existence of a set of observables with which stability can be verified via the Koopman framework. We provide results for the cases of autonomous and time-varying systems, as well as orbital stability of limit cycles. Furthermore, the converse claims are based on a novel relation between the Koopman method and construction of a Kazantzis-Kravaris-Luenberger observer. We also provide a byproduct of the main results, that is, a new method to learn contraction metrics from trajectory data via linear system identification.

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arXiv2023

Unconstrained Parametrization of Dissipative and Contracting Neural Ordinary Differential Equations

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.

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arXiv2023

Virtual Control Contraction Metrics: Convex Nonlinear Feedback Design via Behavioral Embedding

This paper presents a systematic approach to nonlinear state-feedback control design that has three main advantages: (i) it ensures exponential stability and $ \mathcal{L}_2 $-gain performance with respect to a user-defined set of reference trajectories, and (ii) it provides constructive conditions based on convex optimization and a path-integral-based control realization, and (iii) it is less restrictive than previous similar approaches. In the proposed approach, first a virtual representation of the nonlinear dynamics is constructed for which a behavioral (parameter-varying) embedding is generated. Then, by introducing a virtual control contraction metric, a convex control synthesis formulation is derived. Finally, a control realization with a virtual reference generator is computed, which is guaranteed to achieve exponential stability and $ \mathcal{L}_2 $-gain performance for all trajectories of the targeted reference behavior. We show that the proposed methodology is a unified generalization of the two distinct categories of linear-parameter-varying (LPV) state-feedback control approaches: global and local methods. Moreover, it provides rigorous stability and performance guarantees as a method for nonlinear tracking control, while such properties are not guaranteed for tracking control using standard LPV approaches.

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arXiv2023

Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness

This paper introduces recurrent equilibrium networks (RENs), a new class of nonlinear dynamical models} for applications in machine learning, system identification and control. The new model class admits ``built in'' behavioural guarantees of stability and robustness. All models in the proposed class are contracting -- a strong form of nonlinear stability -- and models can satisfy prescribed incremental integral quadratic constraints (IQC), including Lipschitz bounds and incremental passivity. RENs are otherwise very flexible: they can represent all stable linear systems, all previously-known sets of contracting recurrent neural networks and echo state networks, all deep feedforward neural networks, and all stable Wiener/Hammerstein models, and can approximate all fading-memory and contracting nonlinear systems. RENs are parameterized directly by a vector in R^N, i.e. stability and robustness are ensured without parameter constraints, which simplifies learning since \HL{generic methods for unconstrained optimization such as stochastic gradient descent and its variants can be used}. The performance and robustness of the new model set is evaluated on benchmark nonlinear system identification problems, and the paper also presents applications in data-driven nonlinear observer design and control with stability guarantees.

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arXiv2023

On IMU preintegration: A nonlinear observer viewpoint and its application

The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear observer perspective, specifically the parameter estimation-based observer (PEBO). We demonstrate that the preintegration approach can be viewed as recursive implementation of PEBO in moving horizons, and that the two approaches are equivalent in the case of perfect measurements. We then discuss how these findings can be used to tackle practical challenges in estimation problems. As byproducts, our results lead to a novel hybrid sampled-data observer design and an approach to address statistical optimality for PEBO in presence of noise.

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arXiv2023

PEBO-SLAM: Observer design for visual inertial SLAM with convergence guarantees

This paper introduces a new linear parameterization to the problem of visual inertial simultaneous localization and mapping (VI-SLAM) -- without any approximation -- for the case only using information from a single monocular camera and an inertial measurement unit. In this problem set, the system state evolves on the nonlinear manifold $SE(3)\times \mathbb{R}^{3n}$, on which we design dynamic extensions carefully to generate invariant foliations, such that the problem can be reformulated into online \emph{constant parameter} identification, then interestingly with linear regression models obtained. It demonstrates that VI-SLAM can be translated into a linear least squares problem, in the deterministic sense, \emph{globally} and \emph{exactly}. Based on this observation, we propose a novel SLAM observer, following the recently established parameter estimation-based observer (PEBO) methodology. A notable merit is that the proposed observer enjoys almost global asymptotic stability, requiring neither persistency of excitation nor uniform complete observability, which, however, are widely adopted in most existing works with provable stability but can hardly be assured in many practical scenarios.

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arXiv2023

Direct Parameterization of Lipschitz-Bounded Deep Networks

This paper introduces a new parameterization of deep neural networks (both fully-connected and convolutional) with guaranteed $\ell^2$ Lipschitz bounds, i.e. limited sensitivity to input perturbations. The Lipschitz guarantees are equivalent to the tightest-known bounds based on certification via a semidefinite program (SDP). We provide a ``direct'' parameterization, i.e., a smooth mapping from $\mathbb R^N$ onto the set of weights satisfying the SDP-based bound. Moreover, our parameterization is complete, i.e. a neural network satisfies the SDP bound if and only if it can be represented via our parameterization. This enables training using standard gradient methods, without any inner approximation or computationally intensive tasks (e.g. projections or barrier terms) for the SDP constraint. The new parameterization can equivalently be thought of as either a new layer type (the \textit{sandwich layer}), or a novel parameterization of standard feedforward networks with parameter sharing between neighbouring layers. A comprehensive set of experiments on image classification shows that sandwich layers outperform previous approaches on both empirical and certified robust accuracy. Code is available at \url{https://github.com/acfr/LBDN}.

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arXiv2023

Structured linear quadratic control computations over 2D grids

In this paper, we present a structured solver based on the preconditioned conjugate gradient method (PCGM) for solving the linear quadratic (LQ) optimal control problem for $K \times N$ sub-systems connected in a two-dimensional (2D) grid structure. Our main contribution is the development of a structured preconditioner based on a fixed number of inner-outer iterations of the nested block Jacobi method. We establish that the proposed preconditioner is positive-definite. Moreover, the proposed approach retains structure in both spatial dimensions as well as in the temporal dimension of the problem. The arithmetic complexity of each PCGM step scales as $O(KNT)$, where $T$ is the length of the time horizon. The computations involved at each step of the proposed PCGM are decomposable and amenable to distributed implementation on parallel processors connected in a 2D grid structure with localized data exchange. We also provide results of numerical experiments performed on two example systems.

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arXiv2023

Sparse Resource Allocation for Spreading Processes on Temporal-Switching Networks

Spreading processes, e.g. epidemics, wildfires and rumors, are often modeled on static networks. However, their underlying network structures, e.g. changing contacts in social networks, different weather forecasts for wildfires, are due to ever-changing circumstances inherently time-varying in nature. In this paper, we therefore, propose an optimization framework for sparse resource allocation for control of spreading processes over temporal networks with known connectivity patterns. We use convex optimization, in particular exponential cone programming, and dynamic programming techniques to bound and minimize the risk of an undetected outbreak by allocating budgeted resources each time step. We demonstrate with misinformation, epidemic and wildfire examples how the method can provide targeted allocation of resources.

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