A geometrical analysis of trajectory design for underwater vehicles

Designing trajectories for a submerged rigid body motivates this paper. Two approaches are addressed: the time optimal approach and the motion planning ap- proach using concatenation of kinematic motions. We focus on the structure of singular extremals and their relation to the existence of rank-one kinematic reduc- tions; thereby linking the optimization problem to the inherent geometric frame- work. Using these kinematic reductions, we provide a solution to the motion plan- ning problem in the under-actuated scenario, or equivalently, in the case of actuator failures. We finish the paper comparing a time optimal trajectory to one formed by concatenation of pure motions.

Robust tracking control of autonomous underwater vehicles in the presence of disturbance inputs

An autonomous underwater vehicle (AUV) is expected to operate in an ocean in the presence of poorly known disturbance forces and moments. The uncertainties of the environment makes it difficult to apply open-loop control scheme for the motion planning of the vehicle. The objective of this paper is to develop a robust feedback trajectory tracking control scheme for an AUV that can track a prescribed trajectory amidst such disturbances. We solve a general problem of feedback trajectory tracking of an AUV in SE(3). The feedback control scheme is derived using Lyapunov-type analysis. The results obtained from numerical simulations confirm the asymptotic tracking properties of the feedback control law. We apply the feedback control scheme to different mission scenarios, with the disturbances being initial errors in the state of the AUV.

A geometrical approach to the motion planning problem for a submerged rigid body

The main focus of this paper is the motion planning problem for a deeply submerged rigid body. The equations of motion are formulated and presented by use of the framework of differential geometry and these equations incorporate external dissipative and restoring forces. We consider a kinematic reduction of the affine connection control system for the rigid body submerged in an ideal fluid, and present an extension of this reduction to the forced affine connection control system for the rigid body submerged in a viscous fluid. The motion planning strategy is based on kinematic motions; the integral curves of rank one kinematic reductions. This method is of particular interest to autonomous underwater vehicles which can not directly control all six degrees of freedom (such as torpedo shaped AUVs) or in case of actuator failure (i.e., under-actuated scenario). A practical example is included to illustrate our technique.

The development of fast bowling experts in Australian cricket

In this paper, we highlight key concepts from dynamical systems theory and complexity sciences to exemplify constraints on talent development in a sample of elite cricketers. Eleven international fast bowlers who cumulatively had taken more than 2,400 test wickets in over 600 international test matches were interviewed using an in-depth, open-ended, and semi-structured approach. Qualitative data were analysed to identify key components in fast bowling expertise development. Results revealed that, contrary to traditional perspectives, the athletes progressed through unique, nonlinear trajectories of development, which appears to be a commonality in the experts' developmental pathways. During development, individual experts encountered unique constraints on the acquisition of expertise in cricket fast bowling, resulting in unique performance adaptations. Specifically, data illustrated experts' ability to continually adapt behaviours under multifaceted ecological constraints.

An introduction to the constraints-led approach to learning in outdoor education

Participation in outdoor education is underpinned by a learner's ability to acquire skills in activities such as canoeing, bushwalking and skiing and consequently the outdoor leader is often required to facilitate skill acquisition and motor learning. As such, outdoor leaders might benefit from an appropriate and tested model on how the learner acquires skills in order to design appropriate learning contexts. This paper introduces an approach to skill acquisition based on ecological psychology and dynamical systems theory called the constraints-led approach to skills acquisition. We propose that this student-centred approach is an ideal perspective for the outdoor leader to design effective learning settings. Furthermore, this open style of facilitation is also congruent with learning models that focus on other concepts such as teamwork and leadership.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

Building the foundations : skill acquisition in children

Introduction: Why we need to base childrens’ sport and physical education on the principles of dynamical systems theory and ecological psychology As the childhood years are crucial for developing many physical skills as well as establishing the groundwork leading to lifelong participation in sport and physical activities, (Orlick & Botterill, 1977, p. 11) it is essential to examine current practice to make sure it is meeting the needs of children. In recent papers (e.g. Renshaw, Davids, Chow & Shuttleworth, in press; Renshaw, Davids, Chow & Hammond, in review; Chow et al., 2009) we have highlighted that a guiding theoretical framework is needed to provide a principled approach to teaching and coaching and that the approach must be evidence- based and focused on mechanism and not just on operational issues such as practice, competition and programme management (Lyle, 2002). There is a need to demonstrate how nonlinear pedagogy underpins teaching and coaching practice for children given that some of the current approaches underpinning children’s sport and P.E. may not be leading to optimal results. For example, little time is spent undertaking physical activities (Tinning, 2006) and much of this practice is not representative of the competition demands of the performance environment (Kirk & McPhail, 2002; Renshaw et al., 2008). Proponents of a non- linear pedagogy advocate the design of practice by applying key concepts such as the mutuality of the performer and environment, the tight coupling of perception and action, and the emergence of movement solutions due to self organisation under constraints (see Renshaw, et al., in press). As skills are shaped by the unique interacting individual, task and environmental constraints in these learning environments, small changes to individual structural (e.g. factors such as height or limb length) or functional constraints (e.g. factors such as motivation, perceptual skills, strength that can be acquired), task rules, equipment, or environmental constraints can lead to dramatic changes in movement patterns adopted by learners to solve performance problems. The aim of this chapter is to provide real life examples for teachers and coaches who wish to adopt the ideas of non- linear pedagogy in their practice. Specifically, I will provide examples related to specific issues related to individual constraints in children and in particular the unique challenges facing coaches when individual constraints are changing due to growth and development. Part two focuses on understanding how cultural environmental constraints impact on children’s sport. This is an area that has received very little attention but plays a very important part in the long- term development of sporting expertise. Finally, I will look at how coaches can manipulate task constraints to create effective learning environments for young children.

Manipulating task constraints to improve tactical knowledge and collective decision-making in rugby union

In team sports such as rugby union, a myriad of decisions and actions occur within the boundaries that compose the performance perceptual- motor workspace. The way that these performance boundaries constrain decision making and action has recently interested researchers and has involved developing an understanding of the concept of constraints. Considering team sports as complex dynamical systems, signifies that they are composed of multiple, independent agents (i.e. individual players) whose interactions are highly integrated. This level of complexity is characterized by the multiple ways that players in a rugby field can interact. It affords the emergence of rich patterns of behaviour, such as rucks, mauls, and collective tactical actions that emerge due to players’ adjustments to dynamically varying competition environments. During performance, the decisions and actions of each player are constrained by multiple causes (e.g. technical and tactical skills, emotional states, plans, thoughts, etc.) that generate multiple effects (e.g. to run or pass, to move forward to tackle or maintain position and drive the opponent to the line), a prime feature in a complex systems approach to team games performance (Bar- Yam, 2004). To establish a bridge between the complexity sciences and learning design in team sports like rugby union, the aim of practice sessions is to prepare players to pick up and explore the information available in the multiple constraints (i.e. the causes) that influence performance. Therefore, learning design in training sessions should be soundly based on the interactions amongst players (i.e.teammates and opponents) that will occur in rugby matches. To improve individual and collective decision making in rugby union, Passos and colleagues proposed in previous work a performer- environment interaction- based approach rather than a traditional performer- based approach (Passos, Araújo, Davids & Shuttleworth, 2008).