Related papers: A Hamilton-Jacobi Formulation for Time-Optimal Pat…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
Presented is a new method for calculating the time-optimal guidance control for a multiple vehicle pursuit-evasion system. A joint differential game of k pursuing vehicles relative to the evader is constructed, and a Hamilton-Jacobi-Isaacs…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
This paper studies path synthesis for nonholonomic mobile robots moving in two-dimensional space. We first address the problem of interpolating paths expressed as sequences of straight line segments, such as those produced by some planning…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
The purpose of this paper is to describe the numerical solution of the Hamilton-Jacobi-Bellman (HJB) for an optimal control problem for quantum spin systems. This HJB equation is a first order nonlinear partial differential equation defined…
We present a complete framework for fast motion planning of non-holonomic autonomous mobile robots in highly complex but structured environments. Conventional grid-based planners struggle with scalability, while many kinematically-feasible…
In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) at different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its…
We consider the time-convex hull problem in the presence of two orthogonal highways H. In this problem, the travelling speed on the highway is faster than off the highway, and the time-convex hull of a point set P is the closure of P with…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
In order to describe the impact of different geometric structures and constraints for the dynamics of a Hamiltonian system, in this paper, for a magnetic Hamiltonian system defined by a magnetic symplectic form, we first drive precisely the…
Path planning is an important component in any highly automated vehicle system. In this report, the general problem of path planning is considered first in partially known static environments where only static obstacles are present but the…
In this work, an efficient method for constructing a complete integral of the geodesic Hamilton-Jacobi equation on pseudo-Riemannian manifolds with simply transitive groups of motions is suggested. The method is based on using a special…
In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly,…
We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…
We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths…
In this paper, we look into the minimum obstacle displacement (MOD) planning problem from a mobile robot motion planning perspective. This problem finds an optimal path to goal by displacing movable obstacles when no path exists due to…
Vehicle trajectory planning is a key component for an autonomous driving system. A practical system not only requires the component to compute a feasible trajectory, but also a comfortable one given certain comfort metrics. Nevertheless,…
This paper is concerned with the axiomatic foundation and explicit construction of a general class of optimality criteria that can be used for investment problems with multiple time horizons, or when the time horizon is not known in…
We study driver's optimal trajectory planning under uncertainty in the duration of a traffic light's green phase. We interpret this as an optimal control problem with an objective of minimizing the expected cost based on the fuel use,…