trajectories generally used to describe the space and time required to perform a desired motion task for a mobile robot or manipulator system. in this paper, we considered a cubic polynomial trajectory for the problem of moving a mobile robot from its initial position to a goal position in over a continuous set of time. along the path, the robot requires to observe a certain acceleration profil...

In this paper, we propose an approach to effectively accelerating the computation of continuous normalizing flow (CNF), which has been proven be a powerful tool for tasks such as variational inference and density estimation. The training time cost CNF can extremely high because required number function evaluations (NFE) solving corresponding ordinary differential equations (ODE) is very large. ...

This paper presents a technique to efficiently index and retrieve video clips in terms of motion-trajectory-based similarity. We describe the motion trajectory in three representations: the horizontal and vertical movements of the trajectory, and the motion trail that indicates shape of the trajectory. Each representation is approximated by a polynomial function. We index the polynomial coeffic...

This paper summarises works carried out for defining tool trajectory formats well adapted to High Speed Machining (HSM). Advantages in using native polynomial formats, calculated directly from the CAD model, are highlighted. In particular, polynomial surface formats are presented as a generic format for tool trajectory. Illustrations show that surface formats represent a good compromise between...

For the inverse synthetic aperture radar (ISAR) imaging of a target at a long range, range alignment using the existing polynomial method brings about poor results because the flight trajectory changes depending on the initial position, and the motion parameters, meaning the polynomial cannot fit the trajectory. This paper proposes an improved range alignment method that models the trajectory u...

We explore the challenges of planning trajectories through complex environments for quadrotors. We use the RRT* algorithm to generate an initial route through a 3D environment and then construct a trajectory consisting of a sequence of polynomial spline segments to follow that route. We present a method of jointly optimizing polynomial path segments that is numerically stable for high-order pol...

Building trajectories for biped robot walking is a complex task considering all degrees of freedom (DOFs) commonly bound within the mechanical structure. A typical problem for such robots is the instability produced by violent transitions between walking phases in particular when a swinging leg impacts the surface. Although extensive research on novel efficient walking algorithms has been condu...

We present an extensible-link kinematic model for characterizing the motion trajectory of an arbitrary planar compliant mechanism. This is accomplished by creating an analogous kinematic model consisting of links that change length over the course of actuation to represent elastic deformation of the compliant mechanism. Within the model, the motion trajectory is represented as an analytical fun...

In air traffic management, conflict detection algorithms are used to determine whether or not aircraft are predicted to lose horizontal and vertical separation minima within a time interval assuming a trajectory model. In the case of linear trajectories, conflict detection algorithms have been proposed that are both complete, i.e., they detect all conflicts, and sound, i.e., they do not present...