Predicting shot locations in tennis using spatiotemporal data

Over the past decade, vision-based tracking systems have been successfully deployed in professional sports such as tennis and cricket for enhanced broadcast visualizations as well as aiding umpiring decisions. Despite the high-level of accuracy of the tracking systems and the sheer volume of spatiotemporal data they generate, the use of this high quality data for quantitative player performance and prediction has been lacking. In this paper, we present a method which predicts the location of a future shot based on the spatiotemporal parameters of the incoming shots (i.e. shot speed, location, angle and feet location) from such a vision system. Having the ability to accurately predict future short-term events has enormous implications in the area of automatic sports broadcasting in addition to coaching and commentary domains. Using Hawk-Eye data from the 2012 Australian Open Men's draw, we utilize a Dynamic Bayesian Network to model player behaviors and use an online model adaptation method to match the player's behavior to enhance shot predictability. To show the utility of our approach, we analyze the shot predictability of the top 3 players seeds in the tournament (Djokovic, Federer and Nadal) as they played the most amounts of games.

Analyzing and predicting events in soccer and tennis using spatiotemporal data

In this paper, we summarize our recent work in analyz- ing and predicting behaviors in sports using spatiotemporal data. We specifically focus on two recent works: 1) Predicting the location of shot in tennis using Hawk-Eye tennis data, and 2) Clustering spatiotemporal plays in soccer to discover the methods in which they get a shot on goal from a professional league.

Space Station Design Report 2007

Design Proposal for the Blue Lunar Support Hub The conceptual design of a space station is one of the most challenging tasks in aerospace engineering. The history of the space station Mir and the assembly of the International Space Station demonstrate that even within the assembly phase quick solutions have to be found to cope with budget and technical problems or changing objectives. This report is the outcome of the conceptual design of the Space Station Design Workshop (SSDW) 2007, which took place as an international design project from the 16th to the 21st of July 2007 at the Australian Centre for Field Robotics (ACFR), University of Sydney, Australia. The participants were tasked to design a human-tended space station in low lunar orbit (LLO) focusing on supporting future missions to the moon in a programmatic context of space exploration beyond low Earth orbit (LEO). The design included incorporating elements from systems engineering to interior architecture. The customised, intuitive, rapid-turnaround software tools enabled the team to successfully tackle the complex problem of conceptual design of crewed space systems. A strong emphasis was put on improving the integration of the human crew, as it is the major contributor to mission success, while always respecting the boundary conditions imposed by the challenging environment of space. This report documents the methodology, tools and outcomes of the Space Station Design Workshop during the SSDW 2007. The design results produced by Team Blue are presented.

Verification and Operation of Adaptive Materials in Space

Piezoelectric polymers based on polyvinylidene fluoride (PVDF) are of interest as smart materials for novel space-based telescope applications. Dimensional adjustments of adaptive thin polymer films are achieved via controlled charge deposition. Predicting their long-term performance requires a detailed understanding of the piezoelectric property changes that develop during space environmental exposure. The overall materials performance is governed by a combination of chemical and physical degradation processes occurring in low Earth orbit as established by our past laboratory-based materials performance experiments (see report SAND 2005-6846). Molecular changes are primarily induced via radiative damage, and physical damage from temperature and atomic oxygen exposure is evident as depoling, loss of orientation and surface erosion. The current project extension has allowed us to design and fabricate small experimental units to be exposed to low Earth orbit environments as part of the Materials International Space Station Experiments program. The space exposure of these piezoelectric polymers will verify the observed trends and their degradation pathways, and provide feedback on using piezoelectric polymer films in space. This will be the first time that PVDF-based adaptive polymer films will be operated and exposed to combined atomic oxygen, solar UV and temperature variations in an actual space environment. The experiments are designed to be fully autonomous, involving cyclic application of excitation voltages, sensitive film position sensors and remote data logging. This mission will provide critically needed feedback on the long-term performance and degradation of such materials, and ultimately the feasibility of large adaptive and low weight optical systems utilizing these polymers in space.

Model Predictive Static Programming: A Computationally Efficient Technique For Suboptimal Control Design

Combining the philosophies of nonlinear model predictive control and approximate dynamic programming, a new suboptimal control design technique is presented in this paper, named as model predictive static programming (MPSP), which is applicable for finite-horizon nonlinear problems with terminal constraints. This technique is computationally efficient, and hence, can possibly be implemented online. The effectiveness of the proposed method is demonstrated by designing an ascent phase guidance scheme for a ballistic missile propelled by solid motors. A comparison study with a conventional gradient method shows that the MPSP solution is quite close to the optimal solution.

Models of reserve manpower

Absenteeism is one of the major problems of Indian industries. It necessitates the employment of more manpower than the jobs require, resulting in the increase of manpower costs, and lowers the efficiency of plant operation through lowered performance and higher rejects. It also causes machine idleness, if extra manpower is not hired, resulting in disrupted work schedules and assignments. Several studies have investigated the causes of absenteeism (Vaid 1967) for example and their remedy and relationship between absenteeism and turnover with a suggested model for diagnosis and treatment (Hawk 1976) However, the production foremen and supervisor will face the operating task of determining how many extra operatives are to be hired in order to stave off the adverse effects of absenteeism on the man-machine system. This paper deals with a class of reserve manpower models based on the reject allowance model familiar in quality control literature. The present study considers, in addition to absenteeism, machine failures and the graded nature of manpower met within production systems and seeks to find optimal reserve manpower through computer simulation.

An Online Implementable Differential Evolution Tuned Optimal Guidance Law

This paper proposes a novel application of differential evolution to solve a difficult dynamic optimisation or optimal control problem. The miss distance in a missile-target engagement is minimised using differential evolution. The difficulty of solving it by existing conventional techniques in optimal control theory is caused by the nonlinearity of the dynamic constraint equation, inequality constraint on the control input and inequality constraint on another parameter that enters problem indirectly. The optimal control problem of finding the minimum miss distance has an analytical solution subject to several simplifying assumptions. In the approach proposed in this paper, the initial population is generated around the seed value given by this analytical solution. Thereafter, the algorithm progresses to an acceptable final solution within a few generations, satisfying the constraints at every iteration. Since this solution or the control input has to be obtained in real time to be of any use in practice, the feasibility of online implementation is also illustrated.

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three- dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.

Capturability analysis of a geometric guidance law in relative velocity space

In this paper, a relative velocity approach is used to analyze the capturability of a geometric guidance law. Point mass models are assumed for both the missile and the target. The speeds of the missile and target are assumed to remain constant throughout the engagement. Lateral acceleration, obtained from the guidance law, is applied to change the path of the missile. The kinematic equations for engagements in the horizontal plane are derived in the relative velocity space. Some analytical results for the capture region are obtained for non-maneuvering and maneuvering targets. For non-maneuvering targets it is enough for the navigation gain to be a constant to intercept the target, while for maneuvering targets a time varying navigation gain is needed for interception. These results are then verified through numerical simulations.

Effect Of Electroslag Refining On Microstructure And Mechanical-Properties Of Is-7670 Alloy

The electroslag refining technique is one of the modern tools which is capable of imparting superior mechanical and chemical properties to metals and alloys. Refining usually results in the elimination of a number of casting or solidification defects, such as shrinkage porosity, gas porosity, pipe, micro- and macro segregation. Remelting also imparts a directional grain structure apart from refining the size of the inclusions, grains and precipitates. This technique has over the years been used widely and successfully to improve the mechanical and chemical properties of steels and alloy steels which are used in the nuclear, missile, aerospace and marine industries for certain critical applications. But the application of ESR to aluminium and its alloys is only recent. This paper investigates the response of an aluminium alloy (corresponding to the Indian Specification IS: 7670) to ESR. Based on theoretical considerations and microstructural evidence it elucidates how ESR of aluminium alloys differs from that of ferrous alloys. The improvement achieved in mechanical properties of the alloy is correlated with the microstructure.

A Study of The Fatigue, Impact and fracture-Toughness Characteristics of Electroslag Refined IS-7670 Alloy

The nuclear, aerospace, naval and missile industries place emphasis on materials with high structural integrity and reliable performance so as to meet certain stringent requirements in service. Strength is not the only criterion for selection. Properties such as fatigue resistance. impact toughness and fracture toughness are equally important. Electroslag refining (ESR) has been used widely and successfully over the years for improving the fatigue resistance, creep resistance, impact strength and fracture toughness of steels and alloy steels. But application of ESR to aluminium alloys is only a recent endeavour. A high-strength aircraft aluminium alloy IS: 7670 was therefore chosen for studies on the fatigue strength and the impact and fracture toughness. The results indicate that the fatigue resistance is considerably improved after refining and that the impact strength and fracture toughness of the refined alloy are comparable with that of the unrefined alloy.

Capturability of realistic generalized true proportional navigation

The capturability of a realistic generalized true proportional navigation (RGTPN) guidance law, against a nonmaneuvering target, is analyzed. The RGTPN law is obtained by relaxing the somewhat unrealistic assumption of constant closing velocity, made in all earlier studies on generalized true proportional navigation (GTPN), and incorporating the actual time-varying value in the guidance law. Closed-form solutions for the complete capture region of RGTPN is obtained in terms of both zero and acceptable non-zero miss distances. It is shown that the capture region of RGTPN in the initial relative velocity space is significantly smaller than that of GTPN, for reasonable values of navigation constant (N) and angular direction (eta) of the missile commanded latax. However, for certain values of N and eta, capturability of RGTPN is found to be better. It is also shown that if in one of the versions of GTPN, which uses constant values of both the closing velocity and the line-of-sight (LOS) angular velocity in the guidance law, the corresponding realistic time-varying quantities are used, the capture region actually expands to cover the whole of the initial relative velocity space. A number of examples are given to compare the capture performance of RGTPN with other versions of the GTPN guidance laws.

Suboptimal Midcourse Guidance of Interceptors for High-Speed Targets with Alignment Angle Constraint

Using the recently developed computationally efficient model predictive static programming and a closely related model predictive spread control concept, two nonlinear suboptimal midcourse guidance laws are presented in this paper for interceptors engaging against incoming high-speed ballistic missiles. The guidance laws are primarily based on nonlinear optimal control theory, and hence imbed effective trajectory optimization concepts into the guidance laws. Apart from being energy efficient by minimizing the control usage throughout the trajectory (minimum control usage leads to minimum turning, and hence leads to minimum induced drag), both of these laws enforce desired alignment constraints in both elevation and azimuth in a hard-constraint sense. This good alignment during midcourse is expected to enhance the effectiveness of the terminal guidance substantially. Both point mass as well as six-degree-of-freedom simulation results (with a realistic inner-loop autopilot based on dynamic inversion) are presented in this paper, which clearly shows the effectiveness of the proposed guidance laws. It has also been observed that, even with different perturbations of missile parameters, the performance of guidance is satisfactory. A comparison study, with the vector explicit guidance scheme proposed earlier in the literature, also shows that the newly proposed model-predictive-static-programming-based and model-predictive-spread-control-based guidance schemes lead to lesser lateral acceleration demand and lesser velocity loss during engagement.

Nonlinear Model Predictive Spread Acceleration Guidance with Impact Angle Constraint for Stationary Targets

A new technique named as model predictive spread acceleration guidance (MPSAG) is proposed in this paper. It combines nonlinear model predictive control and spread acceleration guidance philosophies. This technique is then used to design a nonlinear suboptimal guidance law for a constant speed missile against stationary target with impact angle constraint. MPSAG technique can be applied to a class of nonlinear problems, which leads to a closed form solution of the lateral acceleration (latax) history update. Guidance command assumed is the lateral acceleration (latax), applied normal to the velocity vector. The new guidance law is validated by considering the nonlinear kinematics with both lag-free as well as first order autopilot delay. The simulation results show that the proposed technique is quite promising to come up with a nonlinear guidance law that leads to both very small miss distance as well as the desired impact angle.

Nonlinear Model Predictive Spread Acceleration Guidance with Impact Angle Constraint for Slow-moving Targets

A new technique named as model predictive spread acceleration guidance (MPSAG) is proposed in this paper. It combines nonlinear model predictive control and spread acceleration guidance philosophies. This technique is then used to design a nonlinear suboptimal guidance law for a constant speed missile against stationary target with impact angle constraint. MPSAG technique can be applied to a class of nonlinear problems, which leads to a closed form solution of the lateral acceleration (latax) history update. Guidance command assumed is the lateral acceleration (latax), applied normal to the velocity vector. The new guidance law is validated by considering the nonlinear kinematics with both lag-free as well as first order autopilot delay. The simulation results show that the proposed technique is quite promising to come up with a nonlinear guidance law that leads to both very small miss distance as well as the desired impact angle.