Related papers: Differentiable Collision-Free Parametric Corridors
Connected and autonomous vehicles (CAVs), unlike conventional cars, will utilise the whole space of intersections and cross in a lane-free order. This paper formulates such a lane-free crossing of intersections as a multi-objective optimal…
We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…
In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…
We propose in this paper a minimal speed-based pedestrian model for which particle dynamics are intrinsically collision-free. The speed model is an optimal velocity function depending on the agent length (i.e.\ particle diameter), maximum…
We present a unified framework for solving trajectory optimization problems in a derivative-free manner through the use of sequential convex programming. Traditionally, nonconvex optimization problems are solved by forming and solving a…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
This paper presents a new collision avoidance procedure for unmanned aerial vehicles in the presence of static and moving obstacles. The proposed procedure is based on a new form of local parametrized guidance vector fields, called…
We study the problem of planning collision-free paths for a group of homogeneous robots. We propose a novel approach for turning the paths that were planned egocentrically by the robots, e.g. without taking other robots' moves into account,…
In this paper, we consider the minimization of a $C^2-$smooth and strongly convex objective depending on a given parameter, which is usually found in many practical applications. We suppose that we desire to solve the problem with some…
We present a novel approach to perform probabilistic collision detection between a high-DOF robot and high-DOF obstacles in dynamic, uncertain environments. In dynamic environments with a high-DOF robot and moving obstacles, our approach…
A significant challenge in autonomous racing is to generate overtaking maneuvers. Racing agents must execute these maneuvers on complex racetracks with little room for error. Optimization techniques and graph-based methods have been…
This paper addresses the problem of motion planning for differential drive micro-mobility platforms. This class of vehicle is designed to perform small-distance transportation of passengers and goods in structured environments. Our approach…
To reduce complexity and achieve scalable performance in high-dimensional black-box settings, we propose a distributed method for nonconvex derivative-free optimization of continuous variables with an additively separable objective, subject…
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…
We combine concepts from multilevel solvers for partial differential equations (PDEs) with neural network based deep learning and propose a new methodology for the efficient numerical solution of high-dimensional parametric PDEs. An…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of…
The detection of previously unseen, unexpected obstacles on the road is a major challenge for automated driving systems. Different from the detection of ordinary objects with pre-definable classes, detecting unexpected obstacles on the road…
For simulating incompressible flows by projection methods. it is generally accepted that the pressure-correction stage is the most time-consuming part of the flow solver. The objective of the present work is to develop a fast hybrid…
In this paper, we introduce a generalized continuous collision detection (CCD) framework for the mobile robot along the polynomial trajectory in cluttered environments including various static obstacle models. Specifically, we find that the…