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This work introduces progressive spatio-temporal filtering, an efficient method to build all-frequency approximations to the light transport distribution into a scene by filtering individual samples produced by an underlying path sampler,…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
With the pervasiveness of Stochastic Shortest-Path (SSP) problems in high-risk industries, such as last-mile autonomous delivery and supply chain management, robust planning algorithms are crucial for ensuring successful task completion…
Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…
The urban environment is amongst the most difficult domains for autonomous vehicles. The vehicle must be able to plan a safe route on challenging road layouts, in the presence of various dynamic traffic participants such as vehicles,…
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…
Sampling rare events in metastable dynamical systems is often a computationally expensive task and one needs to resort to enhanced sampling methods such as importance sampling. Since we can formulate the problem of finding optimal…
Motion planning is a key element of robotics since it empowers a robot to navigate autonomously. Particle Swarm Optimization is a simple, yet a very powerful optimization technique which has been effectively used in many complex…
This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the…
In this work, we analyze an efficient sampling-based algorithm for general-purpose reachability analysis, which remains a notoriously challenging problem with applications ranging from neural network verification to safety analysis of…
The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…
Cardinality estimation algorithms receive a stream of elements whose order might be arbitrary, with possible repetitions, and return the number of distinct elements. Such algorithms usually seek to minimize the required storage and…
In this paper, we propose a stochastic optimization method that adaptively controls the sample size used in the computation of gradient approximations. Unlike other variance reduction techniques that either require additional storage or the…
Sampling-based motion planning is a well-established approach in autonomous driving, valued for its modularity and analytical tractability. In complex urban scenarios, however, uniform or heuristic sampling often produces many infeasible or…
This paper proposes an optimization-based approach to predict trajectories of autonomous race cars. We assume that the observed trajectory is the result of an optimization problem that trades off path progress against acceleration and jerk…
We present an evaluation of several representative sampling-based and optimization-based motion planners, and then introduce an integrated motion planning system which incorporates recent advances in trajectory optimization into a sparse…
In this paper, we present a new algorithm that extends RRT* and RT-RRT* for online path planning in complex, dynamic environments. Sampling-based approaches often perform poorly in environments with narrow passages, a feature common to many…
Motion planning can be cast as a trajectory optimisation problem where a cost is minimised as a function of the trajectory being generated. In complex environments with several obstacles and complicated geometry, this optimisation problem…
Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for…