Related papers: Computation of avoidance regions for driver assist…
We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a control variable, we can determine the optimal control by…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
Autonomous coverage of a specified area by robots operating in close proximity with each other has many potential applications such as real-time monitoring of rapidly changing environments, and search and rescue; however, coordination and…
Presented is a method to compute certain classes of Hamilton-Jacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the…
As safety-critical autonomous vehicles (AVs) will soon become pervasive in our society, a number of safety concepts for trusted AV deployment have recently been proposed throughout industry and academia. Yet, achieving consensus on an…
Time-optimal obstacle avoidance is a prevalent problem encountered in various fields, including robotics and autonomous vehicles, where the task involves determining a path for a moving vehicle to reach its goal while navigating around…
This article proposes a Novel Nonlinear Model Predictive Control (NMPC) for navigation and obstacle avoidance of an Unmanned Aerial Vehicle (UAV). The proposed NMPC formulation allows for a fully parametric obstacle trajectory, while in…
We propose a method to efficiently compute the forward stochastic reach (FSR) set and its probability measure for nonlinear systems with an affine disturbance input, that is stochastic and bounded. This method is applicable to systems with…
Provably safe and scalable multi-vehicle trajectory planning is an important and urgent problem. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing such safety-critical systems and has been successfully applied to several…
Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…
Avoiding collisions between obstacles and vehicles such as cars, robots or aircraft is essential to the development of automation and autonomy. To simplify the problem, many collision avoidance algorithms and proofs consider vehicles to be…
Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and…
We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
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…
We present a method for optimal coordination of multiple vehicle teams when multiple endpoint configurations are equally desirable, such as seen in the autonomous assembly of formation flight. The individual vehicles' positions in the…
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case.…
Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…
We study the optimal control of path-dependent piecewise deterministic processes. An appropriate dynamic programming principle is established. We prove that the associated value function is the unique minimax solution of the corresponding…
In this paper, a novel closed-loop control framework for autonomous obstacle avoidance on a curve road is presented. The proposed framework provides two main functionalities; (i) collision free trajectory planning using MPC and (ii) a…