arXiv subjects

Tyler Summers

Publications and source records attributed to Tyler Summers.

At least 19 recordsLinked to original sources

arXiv2026

Augmented Graphs of Convex Sets and the Traveling Salesman Problem

We present a trajectory optimization algorithm for the traveling salesman problem (TSP) in graphs of convex sets (GCS). Our framework uses an augmented graph of convex sets to encode the TSP specification and solve it exactly as a shortest path problem in GCS. We establish a precise relationship between the landmark Bellman-Held-Karp algorithm and the augmented graph of convex sets with a TSP specification. Additionally, we present a branch and bound heuristic that uses minimum 1-trees to obtain certifiably optimal or near optimal solutions and scales to problems far larger than the exact framework can handle. To assess and certify performance, we explore several alternative lower bounds.

eess.SY↗

arXiv2026

Forward-Backward Dynamic Programming for LQG Dynamic Games with Partial and Asymmetric Information

We formulate and study a class of two-player zero-sum stochastic dynamic games with partial and asymmetric information. Information asymmetry introduces fundamental challenges involving \emph{belief representation} and \emph{theory of mind} issues, where agents must impute belief states and estimates of other agents to inform their own strategy. To avoid an infinite regress of higher-order beliefs amongst agents and obtain computationally implementable results, we focus on a linear quadratic Gaussian (LQG) model and consider strategies with limited internal state dimension. We present a novel iterative forward-backward algorithm to jointly compute belief states and equilibrium strategies and value functions for a finite-horizon problem. We also present a value iteration-like algorithm to jointly compute stationary belief states and equilibrium strategies for an average-cost infinite-horizon problem. An open-source implementation of the algorithms is provided, and we demonstrate the effectiveness of the proposed algorithms in numerical experiments.

math.OC↗

arXiv2026

Optimizing Weighted Hodge Laplacian Flows on Simplicial Complexes

Simplicial complexes are generalizations of graphs that describe higher-order network interactions among nodes in the graph. Network dynamics described by graph Laplacian flows have been widely studied in network science and control theory, and these can be generalized to simplicial complexes using Hodge Laplacians. We study weighted Hodge Laplacian flows on simplicial complexes. In particular, we develop a framework for weighted consensus dynamics based on weighted Hodge Laplacian flows and show some decomposition results for weighted Hodge Laplacians. We then show that two key spectral functions of the weighted Hodge Laplacians, the trace of the pseudoinverse and the smallest non-zero eigenvalue, are jointly convex in upper and lower simplex weights and can be formulated as semidefinite programs. Thus, globally optimal weights can be efficiently determined to optimize flows in terms of these functions. Numerical experiments demonstrate that optimal weights can substantially improve these metrics compared to uniform weights.

math.OC↗

arXiv2026

Solving the Offline and Online Min-Max Problem of Non-smooth Submodular-Concave Functions: A Zeroth-Order Approach

We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser. We investigate the performance of a zeroth-order method applied to this problem. The method is based on the subgradient of the Lov\'asz extension of the objective function with respect to the minimiser and based on Gaussian smoothing to estimate the smoothed function gradient with respect to the maximiser. In expectation sense, we prove the convergence of the algorithm to an $\epsilon$-saddle point in the offline case. Moreover, we show that, in the expectation sense, in the online setting, the algorithm achieves $O(\sqrt{N(1+\bar{P}_N)})$ online duality gap, where $N$ is the number of iterations and $\bar{P}_N$ is the path length of the sequence of optimal decisions. The complexity analysis and hyperparameter selection are presented for all the cases. The theoretical results are illustrated via numerical examples.

math.OC↗

arXiv2025

Motion Planning with Precedence Specifications via Augmented Graphs of Convex Sets

We present an algorithm for planning trajectories that avoid obstacles and satisfy key-door precedence specifications expressed with a fragment of signal temporal logic. Our method includes a novel exact convex partitioning of the obstacle free space that encodes connectivity among convex free space sets, key sets, and door sets. We then construct an augmented graph of convex sets that exactly encodes the key-door precedence specifications. By solving a shortest path problem in this augmented graph of convex sets, our pipeline provides an exact solution up to a finite parameterization of the trajectory. To illustrate the effectiveness of our approach, we present a method to generate key-door mazes that provide challenging problem instances, and we perform numerical experiments to evaluate the proposed pipeline. Our pipeline is faster by several orders of magnitude than recent state-of-the art methods that use general purpose temporal logic tools.

eess.SY↗

arXiv2025

HRT1: One-Shot Human-to-Robot Trajectory Transfer for Mobile Manipulation

We introduce a novel system for human-to-robot trajectory transfer that enables robots to manipulate objects by learning from human demonstration videos. The system consists of four modules. The first module is a data collection module that is designed to collect human demonstration videos from the point of view of a robot using an AR headset. The second module is a video understanding module that detects objects and extracts 3D human-hand trajectories from demonstration videos. The third module transfers a human-hand trajectory into a reference trajectory of a robot end-effector in 3D space. The last module utilizes a trajectory optimization algorithm to solve a trajectory in the robot configuration space that can follow the end-effector trajectory transferred from the human demonstration. Consequently, these modules enable a robot to watch a human demonstration video once and then repeat the same mobile manipulation task in different environments, even when objects are placed differently from the demonstrations. Experiments of different manipulation tasks are conducted on a mobile manipulator to verify the effectiveness of our system

cs.RO↗

arXiv2025

Minimisation of Submodular Functions Using Gaussian Zeroth-Order Random Oracles

We consider the minimisation problem of submodular functions and investigate the application of a zeroth-order method to this problem. The method is based on exploiting a Gaussian smoothing random oracle to estimate the smoothed function gradient. We prove the convergence of the algorithm to a global $\epsilon$-approximate solution in the offline case and show that the algorithm is Hannan-consistent in the online case with respect to static regret. Moreover, we show that the algorithm achieves $O(\sqrt{NP_N^\ast})$ dynamic regret, where $N$ is the number of iterations and $P_N^\ast$ is the path length. The complexity analysis and hyperparameter selection are presented for all the cases. The theoretical results are illustrated via numerical examples.

math.OC↗

arXiv2024

Build Once, Monitor Continuously: Persistent Semantic Mapping via Autonomous Exploration and Open-Vocabulary Object Updates

Persistent semantic monitoring of indoor spaces such as warehouses, hospitals, and offices requires a robot to repeatedly monitor an environment and track how objects change over time. Running full simultaneous localization and mapping (SLAM) with dense semantic reconstruction from scratch on every visit is redundant when the environment geometry stays the same and only the objects move. We present a modular two-stage system that separates geometric mapping from semantic updating. In the first stage, a frontier-based exploration method with a dynamic search window builds a 2D occupancy grid. In the second stage, the robot relocalizes in this map and builds a semantic object graph using an open-vocabulary object detector and a promptable segmentation model. Only the lightweight semantic stage is repeated on later visits, so the system scales well to frequent revisits. The object graph uses a category and distance based association rule to update objects, which lets the map reflect both intra-session changes (object changes within a single traversal) and inter-session changes (changes across revisits), such as objects being moved, removed, or added. We validate the system on a Fetch robot in two real indoor environments of about 8,500 sq.m and 117 sq.m, and report precision, recall, and F1 scores across multiple update iterations.

cs.RO↗

arXiv2024

Grasping Trajectory Optimization with Point Clouds

We introduce a new trajectory optimization method for robotic grasping based on a point-cloud representation of robots and task spaces. In our method, robots are represented by 3D points on their link surfaces. The task space of a robot is represented by a point cloud that can be obtained from depth sensors. Using the point-cloud representation, goal reaching in grasping can be formulated as point matching, while collision avoidance can be efficiently achieved by querying the signed distance values of the robot points in the signed distance field of the scene points. Consequently, a constrained nonlinear optimization problem is formulated to solve the joint motion and grasp planning problem. The advantage of our method is that the point-cloud representation is general to be used with any robot in any environment. We demonstrate the effectiveness of our method by performing experiments on a tabletop scene and a shelf scene for grasping with a Fetch mobile manipulator and a Franka Panda arm. The project page is available at \url{https://irvlutd.github.io/GraspTrajOpt}

cs.RO↗

arXiv2024

CLIPPER+: A Fast Maximal Clique Algorithm for Robust Global Registration

We present CLIPPER+, an algorithm for finding maximal cliques in unweighted graphs for outlier-robust global registration. The registration problem can be formulated as a graph and solved by finding its maximum clique. This formulation leads to extreme robustness to outliers; however, finding the maximum clique is an NP-hard problem, and therefore approximation is required in practice for large-size problems. The performance of an approximation algorithm is evaluated by its computational complexity (the lower the runtime, the better) and solution accuracy (how close the solution is to the maximum clique). Accordingly, the main contribution of CLIPPER+ is outperforming the state-of-the-art in accuracy while maintaining a relatively low runtime. CLIPPER+ builds on prior work (CLIPPER [1] and PMC [2]) and prunes the graph by removing vertices that have a small core number and cannot be a part of the maximum clique. This will result in a smaller graph, on which the maximum clique can be estimated considerably faster. We evaluate the performance of CLIPPER+ on standard graph benchmarks, as well as synthetic and real-world point cloud registration problems. These evaluations demonstrate that CLIPPER+ has the highest accuracy and can register point clouds in scenarios where over $99\%$ of associations are outliers. Our code and evaluation benchmarks are released at https://github.com/ariarobotics/clipperp.

cs.RO↗

arXiv2024

Self-Tuning Network Control Architectures with Joint Sensor and Actuator Selection

We formulate a mathematical framework for designing a self-tuning network control architecture, and propose a computationally-feasible greedy algorithm for online architecture optimization. In this setting, the locations of active sensors and actuators in the network, as well as the feedback control policy are jointly adapted using all available information about the network states and dynamics to optimize a performance criterion. We show that the case with full-state feedback can be solved with dynamic programming, and in the linear-quadratic setting, the optimal cost functions and policies are piecewise quadratic and piecewise linear, respectively. Our framework is extended for joint sensor and actuator selection for dynamic output feedback control with both control performance and architecture costs. For large networks where exhaustive architecture search is prohibitive, we describe a greedy heuristic for actuator selection and propose a greedy swapping algorithm for joint sensor and actuator selection. Via numerical experiments, we demonstrate a dramatic performance improvement of greedy self-tuning architectures over fixed architectures. Our general formulation provides an extremely rich and challenging problem space with opportunities to apply a wide variety of approximation methods from stochastic control, system identification, reinforcement learning, and static architecture design for practical model-based control.

eess.SY↗

arXiv2023

Regret Analysis of Online LQR Control via Trajectory Prediction and Tracking: Extended Version

In this paper, we propose and analyze a new method for online linear quadratic regulator (LQR) control with a priori unknown time-varying cost matrices. The cost matrices are revealed sequentially with the potential for future values to be previewed over a short window. Our novel method involves using the available cost matrices to predict the optimal trajectory, and a tracking controller to drive the system towards it. We adopted the notion of dynamic regret to measure the performance of this proposed online LQR control method, with our main result being that the (dynamic) regret of our method is upper bounded by a constant. Moreover, the regret upper bound decays exponentially with the preview window length, and is extendable to systems with disturbances. We show in simulations that our proposed method offers improved performance compared to other previously proposed online LQR methods.

math.OC↗

arXiv2023

Self-Tuning Network Control Architectures

We formulate a general mathematical framework for self-tuning network control architecture design. This problem involves jointly adapting the locations of active sensors and actuators in the network and the feedback control policy to all available information about the time-varying network state and dynamics to optimize a performance criterion. We propose a general solution structure analogous to the classical self-tuning regulator from adaptive control. We show that a special case with full-state feedback can be solved in principle with dynamic programming, and in the linear quadratic setting the optimal cost functions and policies are piecewise quadratic and piecewise linear, respectively. For large networks where exhaustive architecture search is prohibitive, we describe a greedy heuristic for joint architecture-policy design. We demonstrate in numerical experiments that self-tuning architectures can provide dramatically improved performance over fixed architectures. Our general formulation provides an extremely rich and challenging problem space with opportunities to apply a wide variety of approximation methods from stochastic control, system identification, reinforcement learning, and static architecture design.

math.OC↗

arXiv2022

Data-driven distributionally robust MPC for systems with uncertain dynamics

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected data and an approximate model of the dynamics to formulate a finite-horizon optimization problem. To account for both the uncertainty related to the dynamics and the disturbance acting on the system, we resort to a distributionally robust formulation that optimizes the cost expectation while satisfying Conditional Value-at-Risk constraints with respect to the worst-case probability distributions of the uncertainties within an ambiguity set defined using the Wasserstein metric. Using results from the distributionally robust optimization literature we derive a tractable finite-dimensional convex optimization problem with finite-sample guarantees for the class of convex piecewise affine cost and constraint functions. The performance of the proposed algorithm is demonstrated in closed-loop simulation on a simple numerical example.

math.OC↗

arXiv2022

Sparse Structure Design for Stochastic Linear Systems via a Linear Matrix Inequality Approach

In this paper, we propose a sparsity-promoting feedback control design for stochastic linear systems with multiplicative noise. The objective is to identify a sparse control architecture that optimizes the closed-loop performance while stabilizing the system in the mean-square sense. The proposed approach approximates the nonconvex combinatorial optimization problem by minimizing various matrix norms subject to the Linear Matrix Inequality (LMI) stability condition. We present two design problems to reduce the number of actuators via the static state-feedback and a low-dimensional output. A regularized linear quadratic regulator with multiplicative noise (LQRm) optimal control problem and its convex relaxation are presented to demonstrate the tradeoff between the suboptimal closed-loop performance and the sparsity degree of control structure. Case studies on power grids for wide-area frequency control show that the proposed sparsity-promoting control can considerably reduce the number of actuators without significant loss in system performance. The sparse control architecture is robust to substantial system-level disturbances while achieving mean-square stability.

math.OC↗

arXiv2022

Robust Data-Driven Output Feedback Control via Bootstrapped Multiplicative Noise

We propose a robust data-driven output feedback control algorithm that explicitly incorporates inherent finite-sample model estimate uncertainties into the control design. The algorithm has three components: (1) a subspace identification nominal model estimator; (2) a bootstrap resampling method that quantifies non-asymptotic variance of the nominal model estimate; and (3) a non-conventional robust control design method comprising a coupled optimal dynamic output feedback filter and controller with multiplicative noise. A key advantage of the proposed approach is that the system identification and robust control design procedures both use stochastic uncertainty representations, so that the actual inherent statistical estimation uncertainty directly aligns with the uncertainty the robust controller is being designed against. Moreover, the control design method accommodates a highly structured uncertainty representation that can capture uncertainty shape more effectively than existing approaches. We show through numerical experiments that the proposed robust data-driven output feedback controller can significantly outperform a certainty equivalent controller on various measures of sample complexity and stability robustness.

eess.SY↗

arXiv2022

Dynamic Programming Through the Lens of Semismooth Newton-Type Methods (Extended Version)

Policy iteration and value iteration are at the core of many (approximate) dynamic programming methods. For Markov Decision Processes with finite state and action spaces, we show that they are instances of semismooth Newton-type methods to solve the Bellman equation. In particular, we prove that policy iteration is equivalent to the exact semismooth Newton method and enjoys local quadratic convergence rate. This finding is corroborated by extensive numerical evidence in the fields of control and operations research, which confirms that policy iteration generally requires few iterations to achieve convergence even when the number of policies is vast. We then show that value iteration is an instance of the fixed-point iteration method. In this spirit, we develop a novel locally accelerated version of value iteration with global convergence guarantees and negligible extra computational costs.

math.OC↗

arXiv2022

Probabilistic Data Association for Semantic SLAM at Scale

With advances in image processing and machine learning, it is now feasible to incorporate semantic information into the problem of simultaneous localisation and mapping (SLAM). Previously, SLAM was carried out using lower level geometric features (points, lines, and planes) which are often view-point dependent and error prone in visually repetitive environments. Semantic information can improve the ability to recognise previously visited locations, as well as maintain sparser maps for long term SLAM applications. However, SLAM in repetitive environments has the critical problem of assigning measurements to the landmarks which generated them. In this paper, we use k-best assignment enumeration to compute marginal assignment probabilities for each measurement landmark pair, in real time. We present numerical studies on the KITTI dataset to demonstrate the effectiveness and speed of the proposed framework.

cs.RO↗