Showing papers by "Brian D. O. Anderson published in 2022"

Topological Analysis of Vector-Field Guided Path Following on Manifolds

Abstract: A path-following control algorithm enables a system’s trajectories under its guidance to converge to and evolve along a given geometric desired path. There exist various such algorithms, but many of them can only guarantee local convergence to the desired path in its neighborhood. In contrast, the control algorithms using a well-designed guiding vector field can ensure almost global convergence of trajectories to the desired path; here, “almost” means that in some cases, a measure-zero set of trajectories converge to the singular set where the vector field becomes zero (with all other trajectories converging to the desired path). In this article, we first generalize the guiding vector field from the Euclidean space to a general smooth Riemannian manifold. This generalization can deal with path-following in some abstract configuration space (such as robot arm joint space). Then, we show several theoretical results from a topological viewpoint. Specifically, we are motivated by the observation that singular points of the guiding vector field exist in many examples where the desired path is homeomorphic to the unit circle, but it is unknown whether the existence of singular points always holds in general (i.e., is inherent in the topology of the desired path). In the $n$-dimensional Euclidean space, we provide an affirmative answer, and conclude that it is not possible to guarantee global convergence to desired paths that are homeomorphic to the unit circle. Furthermore, we show that there always exist nonpath-converging trajectories (i.e., trajectories that do not converge to the desired path) starting from the boundary of a ball containing the desired path in an $n$-dimensional Euclidean space where $n \geq 3$. Examples are provided to illustrate the theoretical results.

Guiding Vector Fields for Following Occluded Paths

Abstract: Accurately following a geometric desired path in a two-dimensional (2-D) space is a fundamental task for many engineering systems, in particular mobile robots. When the desired path is occluded by obstacles, it is necessary and crucial to temporarily deviate from the path for obstacle/collision avoidance. In this article, we develop a composite guiding vector field via the use of smooth bump functions and provide theoretical guarantees that the integral curves of the vector field can follow an arbitrary sufficiently smooth desired path and avoid collision with obstacles of arbitrary shapes. These two behaviors are reactive since path (re)planning and global map construction are not involved. To deal with the common deadlock problem, we introduce a switching vector field, and the Zeno behavior is excluded. Simulations are conducted to support the theoretical results.

Distributed Optimization for Graph Matching

Abstract: Graph matching, or the determination of the vertex correspondences between a pair of graphs, is a crucial task in various problems in different science and engineering disciplines. This article aims to propose a distributed optimization approach for graph matching (GM) between two isomorphic graphs over multiagent networks. For this, we first show that for a class of asymmetric graphs, GM of two isomorphic graphs is equivalent to a convex relaxation where the set of permutation matrices is replaced by the set of pseudostochastic matrices. Then, we formulate GM as a distributed convex optimization problem with equality constraints and a set constraint, over a network of multiple agents. For arbitrary labelings of the vertices, each agent only has information about just one vertex and its neighborhood, and can exchange information with its neighbors. A projected primal-dual gradient method is developed to solve the constrained optimization problem, and globally exponential convergence of the agents’ states to the optimal permutation is achieved. Finally, we illustrate the effectiveness of the algorithm through simulation examples.

Cooperative Tuning of Multi-Agent Optimal Control Systems

Abstract: This paper investigates the problem of cooperative tuning of multi-agent optimal control systems, where a network of agents (i.e. multiple coupled optimal control systems) adjusts parameters in their dynamics, objective functions, or controllers in a coordinated way to minimize the sum of their loss functions. Different from classical techniques for tuning parameters in a controller, we allow tunable parameters appearing in both the system dynamics and the objective functions of each agent. A framework is developed to allow all agents to reach a consensus on the tunable parameter, which minimizes team loss. The key idea of the proposed algorithm rests on the integration of consensus-based distributed optimization for a multi-agent system and a gradient generator capturing the optimal performance as a function of the parameter in the feedback loop tuning the parameter for each agent. Both theoretical results and simulations for a synchronous multi-agent rendezvous problem are provided to validate the proposed method for cooperative tuning of multi-agent optimal control.

Linear System Challenges of Dynamic Factor Models

Abstract: A survey is provided dealing with the formulation of modelling problems for dynamic factor models, and the various algorithm possibilities for solving these modelling problems. Emphasis is placed on understanding requirements for the handling of errors, noting the relevance of the proposed application of the model, be it for example prediction or business cycle determination. Mixed frequency problems are also considered, in which certain entries of an underlying vector process are only available for measurement at a submultiple frequency of the original process. Certain classes of processes are shown to be generically identifiable, and others not to have this property.

Wisconsin Forests 2019

Abstract: This summary report provides results of the ninth forest inventory of the forests of Wisconsin conducted by the USDA Forest Service, Forest Inventory and Analysis program. There are an estimated 17 million acres of forest land across the State which is a small decrease from the 2014 estimate. There are 11.5 billion live trees at least 1 inch diameter at breast height (d.b.h.)/diameter at root collar (d.r.c.) on this forest land. Growing-stock volume on timberland totaled 22.4 billion cubic feet, led by sugar maple and red maple with 2.5 billion cubic feet and 2.3 billion cubic feet, respectively. By forest type, white oak/red oak/hickory is the most abundant at 4.1 billion cubic feet with the next most common forest type being sugar maple/beech/yellow birch at 3.5 billion cubic feet. The full, interactive report is available at https://doi.org/10.2737/NRS-RB-127-INT.

Cooperative constrained motion coordination of networked heterogeneous vehicles

Abstract: We consider the problem of cooperative motion coordination for multiple heterogeneous mobile vehicles subject to various constraints. These include nonholonomic motion constraints, constant speed constraints, holonomic coordination constraints, and equality/inequality geometric constraints. We develop a general framework involving differential-algebraic equations and viability theory to determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination task constraints. If a coordinated motion solution exists for the derived differential-algebraic equations and/or inequalities, a constructive algorithm is proposed to derive an equivalent dynamical system that generates a set of feasible coordinated motions for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. The motion generation algorithm is well-backed by simulation data for a wide variety of coordination situations involving heterogeneous vehicles. We then extend the vehicle control framework to deal with the cooperative coordination problem with timevarying coordination tasks and leader-follower structure. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.

Distributed State Estimation for Linear Systems

Abstract: This paper studies a distributed state estimation problem for both continuous- and discrete-time linear systems. A simply structured distributed estimator is first described for estimating the state of a continuous-time, jointly observable, input free, multi-channel linear system whose sensed outputs are distributed across a fixed multi-agent network. The estimator is then extended to non-stationary networks whose graphs switch according to a switching signal with a fixed dwell time or a variable but with fixed average dwell time, or switch arbitrarily under appropriate assumptions. The estimator is guaranteed to solve the problem, provided a network-widely shared gain is sufficiently large. As an alternative to sharing a common gain across the network, a fully distributed version of the estimator is thus studied in which each agent adaptively adjusts a local gain though the practicality of this approach is subject to a robustness issue common to adaptive control. A discrete-time version of the distributed state estimation problem is also studied, and a corresponding estimator is proposed for time-varying networks. For each scenario, it is explained how to construct the estimator so that its state estimation errors all converge to zero exponentially fast at a fixed but arbitrarily chosen rate, provided the network’s graph is strongly connected for all time. This is accomplished by appealing to the “split-spectrum” approach and exploiting several well-known properties of invariant subspace. The proposed estimators are inherently resilient to abrupt changes in the number of agents and communication links in the inter-agent communication graph upon which the algorithms depend, provided the network is redundantly strongly connected and redundantly jointly observable.