Instant Basketball Defensive Trajectory Generation

Tactic learning in virtual reality (VR) has been proven to be effective for basketball training. Endowed with the ability of generating virtual defenders in real time according to the movement of virtual offenders controlled by the user, a VR basketball training system can bring more immersive and realistic experiences for the trainee. In this article, an autoregressive generative model for instantly producing basketball defensive trajectory is introduced. We further focus on the issue of preserving the diversity of the generated trajectories. A differentiable sampling mechanism is adopted to learn the continuous Gaussian distribution of player position. Moreover, several heuristic loss functions based on the domain knowledge of basketball are designed to make the generated trajectories assemble real situations in basketball games. We compare the proposed method with the state-of-the-art works in terms of both objective and subjective manners. The objective manner compares the average position, velocity, and acceleration of the generated defensive trajectories with the real ones to evaluate the fidelity of the results. In addition, more high-level aspects such as the empty space for offender and the defensive pressure of the generated trajectory are also considered in the objective evaluation. As for the subjective manner, visual comparison questionnaires on the proposed and other methods are thoroughly conducted. The experimental results show that the proposed method can achieve better performance than previous basketball defensive trajectory generation works in terms of different evaluation metrics.

A Lagrangian Backward Air Parcel Trajectories Clustering Framework

Many studies concerning atmosphere moisture paths use Lagrangian backward air parcel trajectories to determine the humidity sources for specific locations. Automatically grouping trajectories according to their geographical position simplifies and speeds up their analysis. In this paper, we propose a framework for clustering Lagrangian backward air parcel trajectories, from trajectory generation to cluster accuracy evaluation. We employ a novel clustering algorithm, called DenLAC, to cluster troposphere air currents trajectories. Our main contribution is representing trajectories as a one-dimensional array consisting of each trajectory’s points position vector directions. We empirically test our pipeline by employing it on several Lagrangian backward trajectories initiated from Břeclav District, Czech Republic.

Cartesian Constrained Stochastic Trajectory Optimization for Motion Planning

This paper presents novel extensions of the Stochastic Optimization Motion Planning (STOMP), which considers cartesian path constraints. It potentially has high usage in many autonomous applications with robotic arms, where preservation or minimization of tool-point rotation is required. The original STOMP algorithm is unable to use the cartesian path constraints in a trajectory generation because it works only in robot joint space. Therefore, the designed solution, described in this paper, extends the most important parts of the algorithm to take into account cartesian constraints. The new sampling noise generator generates trajectory samples in cartesian space, while the new cost function evaluates them and minimizes traversed distance and rotation change of the tool-point in the resulting trajectory. These improvements are verified with simple experiments and the solution is compared with the original STOMP. Results of the experiments show that the implementation satisfies the cartesian constraints requirements.