Related papers: An Interior Point Method Solving Motion Planning P…

Atmospheric powered descent guidance can be solved by successive convexification; however, its onboard application is impeded by the sharp increase in computation caused by nonlinear aerodynamic forces. The problem has to be converted into…

Trajectory planning for mobile robots in cluttered environments remains a major challenge due to narrow passages, where conventional methods often fail or generate suboptimal paths. To address this issue, we propose the adaptive trajectory…

Sampling-based motion planning methods, while effective in high-dimensional spaces, often suffer from inefficiencies due to irregular sampling distributions, leading to suboptimal exploration of the configuration space. In this paper, we…

This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…

This paper presents a framework for fast and robust motion planning designed to facilitate automated driving. The framework allows for real-time computation even for horizons of several hundred meters and thus enabling automated driving in…

We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…

In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…

Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…

Rotation Averaging is a non-convex optimization problem that determines orientations of a collection of cameras from their images of a 3D scene. The problem has been studied using a variety of distances and robustifiers. The intrinsic (or…

In this paper, we propose a learning algorithm that speeds up the search in task and motion planning problems. Our algorithm proposes solutions to three different challenges that arise in learning to improve planning efficiency: what to…

This paper addresses the path planning problems for recommending parking spaces, given the difficulties of identifying the most optimal route to vacant parking spaces and the shortest time to leave the parking space. Our optimization…

Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…

This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving…

Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path on the constraint manifolds between a given start and goal configuration. These planning…

We introduce a new algorithm to construct travel time distances between a point in the interior of a Riemannian manifold and points on the boundary of the manifold, and describe a numerical implementation of the algorithm. It is known that…

Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…

Conic optimization plays a crucial role in many machine learning (ML) problems. However, practical algorithms for conic constrained ML problems with large datasets are often limited to specific use cases, as stochastic algorithms for…

Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…

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…

Many real-world applications need path planning algorithms to solve tasks in different areas, such as social applications, autonomous cars, and tracking activities. And most importantly motion planning. Although the use of path planning is…