Related papers: Collision Probabilities for Continuous-Time System…
Bayesian inference in the presence of an intractable likelihood function is computationally challenging. When following a Markov chain Monte Carlo (MCMC) approach to approximate the posterior distribution in this context, one typically…
The region of attraction characterizes well-behaved and safe operation of a nonlinear system and is hence sought after for verification. In this paper, a framework for probabilistic region of attraction estimation is developed that combines…
Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this…
While techniques have been developed for chance constrained stochastic optimal control using sample disturbance data that provide a probabilistic confidence bound for chance constraint satisfaction, far less is known about how to use sample…
Motion planning for autonomous driving must account for multi-modal uncertainty in both the intentions and trajectories of surrounding vehicles. Handling uncertainty in a worst-case manner guarantees robustness but often leads to excessive…
Advanced collision avoidance and driver hand-off systems can benefit from the ability to accurately predict, in real time, the probability a vehicle will be involved in a collision within an intermediate horizon of 10 to 20 seconds. The…
The capability to follow a lead-vehicle and avoid rear-end collisions is one of the most important functionalities for human drivers and various Advanced Driver Assist Systems (ADAS). Existing safety performance justification of the…
This paper introduces Chance Constrained Gaussian Process-Motion Planning (CCGP-MP), a motion planning algorithm for robotic systems under motion and state estimate uncertainties. The paper's key idea is to capture the variations in the…
A treatment of direct simulation Monte Carlo method (DSMC) as a Markov process with a master equation is given and the corresponding master equation is derived. A hierarchy of equations for the reduced probability distributions is derived…
The problem of optimising functions with intractable gradients frequently arise in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation…
This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the…
Many motion planning algorithms for automated driving require estimating the probability of collision (POC) to account for uncertainties in the measurement and estimation of the motion of road users. Common POC estimation techniques often…
This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling…
We present a model predictive control (MPC) framework for nonlinear stochastic systems that ensures safety guarantee with high probability. Unlike most existing stochastic MPC schemes, our method adopts a set-erosion that converts the…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
Real-world autonomous systems operate under uncertainty about both their pose and dynamics. Autonomous control systems must simultaneously perform estimation and control tasks to maintain robustness to changing dynamics or modeling errors.…
We consider Monte Carlo approximations to the maximum likelihood estimator in models with intractable norming constants. This paper deals with adaptive Monte Carlo algorithms, which adjust control parameters in the course of simulation. We…
In Monte Carlo simulations, proposed configurations are accepted or rejected according to an acceptance ratio, which depends on an underlying probability distribution and an a priori sampling probability. By carefully selecting the…
We present a continuous-time collision detection algorithm for quickly detecting whether certain polynomial trajectories in time intersect with convex obstacles. The algorithm is used in conjunction with an existing multicopter trajectory…
We present an analytical method to estimate the continuous-time collision probability of motion plans for autonomous agents with linear controlled Ito dynamics. Motion plans generated by planning algorithms cannot be perfectly executed by…