Related papers: GPU Accelerated Convex Approximations for Fast Mul…
The convex hull is a fundamental geometrical structure for many applications where groups of points must be enclosed or represented by a convex polygon. Although efficient sequential convex hull algorithms exist, and are constantly being…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…
One of the keys to flying quadrotors is to optimize their trajectories within the set of collision-free corridors. These corridors impose nonconvex constraints on the trajectories, making real-time trajectory optimization challenging. We…
In this paper, we present a learning-based framework that accelerates time- and energy-optimal trajectory planning for connected and automated vehicles (CAVs) using graph neural networks (GNNs). We formulate the multi-agent coordination…
While Model Predictive Control (MPC) delivers strong performance across robotics applications, solving the underlying (batches of) nonlinear trajectory optimization (TO) problems online remains computationally demanding. Existing…
This paper presents a modeling and optimization framework to compute the minimum-lap-time spatial trajectory and powertrain operation of racing cars in a computationally efficient fashion. Specifically, we first derive a quasi-steady-state…
The alternating direction method of multipliers (ADMM) is a powerful operator splitting technique for solving structured convex optimization problems. Due to its relatively low per-iteration computational cost and ability to exploit…
This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
We implement a quantum optimal control algorithm based on automatic differentiation and harness the acceleration afforded by graphics processing units (GPUs). Automatic differentiation allows us to specify advanced optimization criteria and…
The computation of time-optimal velocity profiles along prescribed paths, subject to generic acceleration constraints, is a crucial problem in robot trajectory planning, with particular relevance to autonomous racing. However, the existing…
The Convex Hull algorithm is one of the most important algorithms in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is…
We propose a GPU-based distributed optimization algorithm, aimed at controlling optimal power flow in multi-phase and unbalanced distribution systems. Typically, conventional distributed optimization algorithms employed in such scenarios…
Conflict-Based Search is one of the most popular methods for multi-agent path finding. Though it is complete and optimal, it does not scale well. Recent works have been proposed to accelerate it by introducing various heuristics. However,…
Matrix factorization (MF) is employed by many popular algorithms, e.g., collaborative filtering. The emerging GPU technology, with massively multicore and high intra-chip memory bandwidth but limited memory capacity, presents an opportunity…
We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
In this work, we leverage GPUs to construct probabilistically collision-free convex sets in robot configuration space on the fly. This extends the use of modern motion planning algorithms that leverage such representations to changing…
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…