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The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…
Solving inverse problems and achieving statistical rigour in landscape evolution models requires running many model realizations. Parallel computation is necessary to achieve this in a reasonable time. However, no previous algorithm is…
Generative planners based on flow matching (FM) produce high-quality paths in a single or a few ODE steps, but their sampling dynamics offer no formal safety guarantees and can yield incomplete paths near constraints. We present…
Motion planning is a fundamental problem in robotics that involves generating feasible trajectories for a robot to follow. Recent advances in parallel computing, particularly through CPU and GPU architectures, have significantly reduced…
Sequential Convex Programming (SCP) has recently seen a surge of interest as a tool for trajectory optimization. However, most available methods lack rigorous performance guarantees and they are often tailored to specific optimal control…
This thesis presents novel contributions in two primary areas: advancing the efficiency of generative models, particularly normalizing flows, and applying generative models to solve real-world computer vision challenges. The first part…
This paper presents a novel method for accelerating path-planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of…
Maxflow is a fundamental problem in graph theory and combinatorial optimisation, used to determine the maximum flow from a source node to a sink node in a flow network. It finds applications in diverse domains, including computer networks,…
Safe path planning is a crucial component in autonomous robotics. The many approaches to find a collision free path can be categorically divided into trajectory optimisers and sampling-based methods. When planning using occupancy maps, the…
Finding a suitable layout represents a crucial task for diverse applications in graphic design. Motivated by simpler and smoother sampling trajectories, we explore the use of Flow Matching as an alternative to current diffusion-based layout…
We cast motion planning under uncertainty as a stochastic optimal control problem, where the optimal posterior distribution has an explicit form. To approximate this posterior, this work frames an optimization problem in the space of…
We propose a framework for active mapping and exploration that leverages Gaussian splatting for constructing dense maps. Further, we develop a GPU-accelerated motion planning algorithm that can exploit the Gaussian map for real-time…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
We propose a new architecture for optimization modeling frameworks in which solvers are expressed as computation graphs in a framework like TensorFlow rather than as standalone programs built on a low-level linear algebra interface. Our new…
Centralized trajectory optimization in the joint space of multiple robots allows access to a larger feasible space that can result in smoother trajectories, especially while planning in tight spaces. Unfortunately, it is often…
We propose a GPU accelerated proximal message passing algorithm for solving contingency-constrained DC optimal power flow problems (OPF). We consider a highly general formulation of OPF that uses a sparse device-node model and supports a…
In this paper, we discuss our approach and algorithmic framework for solving large-scale security constrained optimal power flow (SCOPF) problems. SCOPF is a mixed integer non-convex optimization problem that aims to obtain the minimum…
Cartograms are maps that rescale geographic regions (e.g., countries, districts) such that their areas are proportional to quantitative demographic data (e.g., population size, gross domestic product). Unlike conventional bar or pie charts,…
We propose an efficient motion planning method designed to efficiently find collision-free trajectories for multiple manipulators. While multi-manipulator systems offer significant advantages, coordinating their motions is computationally…
Existing Global Path Planning (GPP) algorithms predominantly presume planning in static environments. This assumption immensely limits their applications to Unmanned Surface Vehicles (USVs) that typically navigate in dynamic environments.…