Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2002.03036

Scalable Vehicle Team Continuum Deformation Coordination with Eigen Decomposition

Hossein Rastgoftar·Ella M. Atkins·Ilya Kolmanovsky
View original source ↗Read source document ↗Export metadata ↓

Abstract

The continuum deformation leader-follower cooperative control strategy models vehicles in a multi-agent system as particles of a deformable body. A desired continuum deformation is defined based on leaders' trajectories and acquired by followers in real-time through local communication. The existing continuum deformation theory requires followers to be placed inside the convex simplex defined by leaders. This constraint is relaxed in this paper. We prove that under suitable assumptions any (n+1)(n=1,2,3) vehicles forming an n-D simplex can be selected as leaders while followers, arbitrarily positioned inside or outside the leading simplex, can acquire a desired continuum deformation in a decentralized fashion. The paper's second contribution is to assign a one-to-one mapping between leaders' smooth trajectories and homogeneous deformation features obtained by continuum deformation eigen-decomposition. Therefore, a safe and smooth continuum deformation coordination can be planned either by shaping homogeneous transformation features or by choosing appropriate leader trajectories. This is beneficial to efficiently plan and guarantee inter-agent collision avoidance in a large-scale group. A simulation case study is reported in which a virtual convex simplex contains a quadcopter vehicle team at any time t; A* search is applied to optimize quadcopter team continuum deformation in an obstacle-laden environment.

Explore related subjects

eess.SYcs.SY

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Hossein Rastgoftar, Ella M. Atkins, Ilya Kolmanovsky. 2020-02-07. Scalable Vehicle Team Continuum Deformation Coordination with Eigen Decomposition. https://arxiv.org/abs/2002.03036

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

This paper presents a two-stage framework for constrained feedback control of input-affine nonlinear systems. Offline, an approximate value function for the unconstrained problem is computed, for example using Hamilton--Jacobi--Bellman (HJB)-based policy iteration. Online, the proposed quadratic program (QP) minimizes the pre-Hamiltonian evaluated using the approximate value-function gradient subject to safety constraints enforced by control barrier functions (CBFs). This architecture decouples performance optimization from constraint enforcement, allowing constraints to be modified without recomputing the value function. As in CBF-QP architectures based on control Lyapunov functions (CLFs), safety is enforced as a hard constraint; however, the performance objective targets approximate optimality rather than a prescribed Lyapunov decay. Numerical results on a linear 2-state hovercraft and a nonlinear 9-state spacecraft attitude-control problem show agreement with the constrained open-loop optimal control problem (OCP) benchmark in the linear case, and performance close to the OCP benchmark, improving on CLF-based controllers, in the nonlinear case.

eess.SY↗
arXiv2026

Rao-Blackwellized Stein Gradient Descent for Joint State-Parameter Estimation

We present a filtering framework for online joint state estimation and parameter identification in nonlinear, time-varying systems. The algorithm uses a Rao-Blackwellization technique to infer joint state-parameter posteriors efficiently. In particular, conditional state distributions are computed analytically via Kalman filtering, while model parameters, including the measurement-noise covariance, are approximated using particle-based Stein Variational Gradient Descent (SVGD), enabling stable real-time inference. To handle parameters subject to physical constraints, we further introduce constrained variants that enforce them through an alternating direction method of multipliers (ADMM) splitting of the SVGD update, including nonlinear equality constraints that standard particle filters cannot readily handle. We derive a stability bound that relates the approximation error in the parameter posterior to the resulting error in the marginal state distribution. Performance of the proposed filters is validated on three case studies: a fed-batch bioreactor with Haldane kinetics and a damped pendulum, both under physical constraints, and a neural-network-augmented dynamic system. The examples cover parameter estimation under inequality and equality constraints and online neural-network training within a dynamical model.

eess.SY↗
arXiv2026

Firing Rate Neural Network Implementations of Model Predictive Control

Human and animal brains perform planning to enable complex movements and behaviors, a process that can be effectively described using model predictive control (MPC). How could the brain physically implement MPC? In this work, we translate model predictive controllers into firing rate neural networks, offering insights into the nonlinear neural dynamics that underpin planning. We propose a constructive method; no training is required. This is done first applying the projected gradient method to the dual problem to derive a baseline neural network implementation. We then use factorization and contraction analysis to systematically generate alternative network architectures; in other words, we systematically generate hypotheses for how planning is done in the brain via neural dynamics. Finally, we present numerical simulations to study different neural networks performing MPC to balance an inverted pendulum on a cart (i.e., balancing a stick on a hand), including one example in which imposing sparse connectivity (a property observed in brain networks) does not degrade control performance.

eess.SY↗