Related papers: Path integral derivations of novel complex traject…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Movement Primitives (MPs) are a well-known concept to represent and generate modular trajectories. MPs can be broadly categorized into two types: (a) dynamics-based approaches that generate smooth trajectories from any initial state, e. g.,…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrodinger equation for certain spin…
In this paper, we propose a novel trajectory optimization algorithm for mobile manipulators under end-effector path, collision avoidance and various kinematic constraints. Our key contribution lies in showing how this highly non-linear and…
A semiclassical formula for the coherent-state propagator requires the determination of specific classical paths inhabiting a complex phase-space through a Hamiltonian flux. Such trajectories are constrained to special boundary conditions…
The quantum trajectories in the de Broglie-Bohm formulation of quantum mechanics depend on an additional quantum potential derived from the full wave solution of Schr\"odinger's equation. The task of supplying collectively all the correct…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
In the regime of weak bath coupling and low temperature we demonstrate numerically for the spin-boson dynamics the equivalence between two widely used but seemingly different roads of approximation, namely the path integral approach and the…
Semiclassical methods are extremely important in the subjects of wave packet and coherent state dynamics. Unfortunately, these essentially saddle point approximations are considered nearly impossible to carry out in detail for systems with…
This paper presents a tutorial overview of path integral (PI) control approaches for stochastic optimal control and trajectory optimization. We concisely summarize the theoretical development of path integral control to compute a solution…
We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation…
The path integral approach to quantum mechanics requires a substantial generalisation to describe the dynamics of systems confined to bounded domains. Non-local boundary conditions can be introduced in Feynman's approach by means of…
Feynman's path integral approach is studied in the framework of the Wigner-Dunkl deformation of quantum mechanics. We start with reviewing some basics from Dunkl theory and investigate the time evolution of a Gaussian wave packet, which…
Feynman's path integral approach is to sum over all possible spatio-temporal paths to reproduce the quantum wave function and the corresponding time evolution, which has enormous potential to reveal quantum processes in classical view.…
Path integral control solves a class of stochastic optimal control problems with a Monte Carlo (MC) method for an associated Hamilton-Jacobi-Bellman (HJB) equation. The MC approach avoids the need for a global grid of the domain of the HJB…
The path integral formulation of constrained systems leads to obtain the equations of motion as total differential equations in many variables. If these equations are integrable then one can constuct a valid and a canonical phase space…
Path integration is a navigation strategy widely observed in nature where an animal maintains a running estimate of its location during an excursion. Evidence suggests it is both ancient and ubiquitous in nature. Over the past century or…
Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of…