In this paper a closing lemma for C1 nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C1 equivariant perturbation.

In this first paper, we consider how to putt a golf ball on an uneven green so that it arrives at the cup with minimal speed.

We present a framework for bi-level trajectory optimization in which system’s dynamics are encoded as the solution to constrained problem and smooth gradients of this lower-level passed an upper-level optimizer. This optimization-based representation enables constraint handling, additional variables, non-smooth behavior be abstracted away from optimizer, allows classical unconstrained optimizer...

Continuously moving objects are prevalent in many domains. Although there have been attempts to combine both spatial and temporal relationships from a reasoning, a database, as well as from a logical perspective, the question remains how to describe motion adequately within a qualitative calculus. In this paper, a Qualitative Trajectory Calculus (QTC) for representing and reasoning about moving...

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

Symbolic Trajectory Evaluation (STE) is a formal verification technique for hardware. The current STE semantics is not faithful to the proving power of existing STE tools, which obscures the STE theory unnecessarily. In this paper, we present a new closure semantics for STE which does match the proving power of STE model-checkers, and makes STE easier to understand.

In this paper we explore trajectory clustering as a means for representing the normal behavior of vessels in a coastal surveillance scenario. Trajectory clustering however suffers from some drawbacks in this type of setting and we therefore propose a new approach, spline-based clustering, with a potential for solving the task of representing the normal course of events.