Related papers: A Hamilton-Jacobi Formulation for Time-Optimal Pat…
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The…
For multi-vehicle complex traffic scenarios in shared spaces such as intelligent intersections, safe coordination and trajectory planning is challenging due to computational complexity. To meet this challenge, we introduce a computationally…
In this paper a search algorithm is proposed to find a sub optimal path for a non-holonomic system. For this purpose the algorithm starts sampling the front part of the vehicle and moves towards the destination with a cost function. The…
Autonomous robots commonly aim to complete a nominal behavior while minimizing a cost; this leaves them vulnerable to failure or unplanned scenarios, where a backup or contingency plan to a safe set is needed to avoid a total mission…
Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the…
A new framework for formulating reachability problems with competing inputs, nonlinear dynamics and state constraints as optimal control problems is developed. Such reach-avoid problems arise in, among others, the study of safety problems…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
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…
In this paper the computational challenges of time-optimal path following are addressed. The standard approach is to minimize the travel time, which inevitably leads to singularities at zero path speed, when reformulating the optimization…
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on…
Path planning is a key component in motion planning for autonomous vehicles. A path specifies the geometrical shape that the vehicle will travel, thus, it is critical to safe and comfortable vehicle motions. For urban driving scenarios,…
We present a fast planning architecture called Hamilton-Jacobi-based bidirectional A* (HJBA*) to solve general tight parking scenarios. The algorithm is a two-layer composed of a high-level HJ-based reachability analysis and a lower-level…
We consider viscosity solutions of Hamilton-Jacobi equations with oscillatory spatial dependence and rough time dependence. The time dependence is in the form of the derivative of a continuous path that converges to a possibly…
The optimal visiting problem is the optimization of a trajectory that has to touch or pass as close as possible to a collection of target points. The problem does not verify the dynamic programming principle, and it needs a specific…
This paper addresses planning and control of robot motion under uncertainty that is formulated as a continuous-time, continuous-space stochastic optimal control problem, by developing a topology-guided path integral control method. The path…
Ensuring safety in autonomous vehicles necessitates advanced path planning and obstacle avoidance capabilities, particularly in dynamic environments. This paper introduces a bi-level control framework that efficiently augments road…
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dimensionality nature of HJD by proposing a generalized Hopf…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…