We propose an unsupervised neural network model to learn and recall complex robot trajectories. Two cases are considered: (1) A single trajectory in which a particular arm configuration may occur more than once, and (2) trajectories sharing states with other ones – they are said to contain a shared state. Hence, ambiguities occur in both cases during recall of such trajectories. The proposed mo...

This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane. Previous work has used Pontryagin’s Principle to find strong necessary conditions on time-optimal trajectories of the rigid body; trajectories satisfying these conditions are called extremal trajectories. The main contribution of this paper is a met...

In this paper, we propose parameter estimation techniques for mixture density polynomial segment models (MDPSMs) where their trajectories are specified with an arbitrary regression order. MDPSM parameters can be trained in one of three different ways: (1) segment clustering; (2) expectation maximization (EM) training of mean trajectories; and (3) EM training of mean and variance trajectories. T...

Abstract Relativistic particles in the Kepler and Coulomb potentials may have trajectories that are qualitatively different from the trajectories found in nonrelativistic mechanics. Spiral scattering trajectories were pointed out by C. G. Darwin in 1913 in connection with the relativistic Rutherford scattering of classical charged particles. Relativistic trajectories are of current interest in ...

This paper applies Pontryagin’s Maximum Principle to the time optimal control of differential drive mobile robots with velocity bounds. The Maximum Principle gives necessary conditions for time optimality. Extremal trajectories are those which satisfy these conditions, and are thus a superset of the time optimal trajectories. This paper derives a compact geometrical structure for extremal traje...

The Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semi-classical) radiation. The transition between the 1s ground state and the 2p0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R. The...

This paper presents a trajectory planning algorithm for multi-axis systems. It generates smooth trajectories of any order subject to general initial and final conditions, and constant state and control constraints. The algorithm is recursive, as it constructs a high order trajectory using lower order trajectories. Multi-axis trajectories are computed by synchronizing independent single-axis tra...

The aim of this study was to identify subgroups of early and mid-adolescents with different drinking trajectories. In addition, we examined whether gender, parental, and peer factors predicted adolescents' membership of these drinking trajectories. We used longitudinal data of 428 families (fathers, mothers, mid-adolescents, and their younger siblings). Latent Class Growth Analyses were perform...

We show, contrary to expectation, that the trajectory predicted by general-relativistic mechanics for a low-speed weak-gravity system is not always well-approximated by the trajectories predicted by special-relativistic and newtonian mechanics for the same parameters and initial conditions. If the system is dissipative, the breakdown of agreement occurs for chaotic trajectories only. If the sys...

Recently, the study of near- and below- threshold regime harmonics as a potential source of intense coherent vacuum-ultraviolet radiation has received considerable attention. However, the dynamical origin of these lower harmonics, particularly for the molecular systems, is less understood and largely unexplored. Here we perform the first fully ab initio and high precision 3D quantum study of th...