Bibhya Sharma
Bibhya Sharma (Phd) is an Associate Professor of Mathematics at the University of The South Pacific (USP). He is a member of a number of professional mathematics societies and unions and has published more than 70 articles and book chapters in the fields of mathematics education, robotics, biologically inspired processes and the TLPs of higher education. He champions adaptive works and innovations in the areas of eLearning and mLearning for higher education. More information regarding his work and achievements can be found at http://staff.usp.ac.fj/~sharma_b/
less
Interests
Uploads
Papers by Bibhya Sharma
Because of the success of Revision Guide for Form Seven, we are extremely buoyed and encouraged, knowing that our work has had an impact on our beloved country and her people. Accordingly, we have decided to establish the SV Series of books that will incorporate our style of writing and presentation. The Revision Guide for Form Seven started off a series that will be continued under the same title. Indeed, the second edition (F7 Revision Guide II) will be ready soon. Another book in the SV series will cover the area of computing (Computing for Senior Secondary), while the third will cover statistics (Statistics for Senior Secondary).
A Study Guide for the Seventh Form, which you now have in your hands is a unique book. Here we have incorporated clear and succinct summaries of all mathematical concepts covered in Form 7. These concepts are then followed with a detailed solutions of problems that appear in exam questions of previous years. We have included hints, formulas and comments by our mascot, the parrot. They are very useful in understanding what is happening. Another new feature is the addition of similar tutorial problems with which students and teachers can practice. Detailed solutions of the tutorial problems are also given. A big plus is the inclusion of mock exams, similar to form 7 final exams. An online version of the book will soon be launched as well.
We have carried fourth our writing style from our first publication, namely, we have tried to produce the simplest of numerical techniques that are available. In some cases, we have expanded the solutions to include discussions on how they must be presented in cases where the questions are quite vague and incomplete from a strict mathematical view-point. Indeed, in some places, we have offered an alternative on how a question should have been stated. Throughout, we are conscious of the difficulties of the mathematical concepts involved such as continuity. Thus, wherever possible, we have included graphs for a better understanding of the problem. We have also given new techniques.
This book utilizes some questions that were prepared by Fiji's Ministry of Education. We acknowledge this source. Our contribution is in terms of reviewing the questions and in developing further on the topics covered in the questions.
Our efforts have been supplemented with valuable inputs from the other mathematicians whose name appear as contributors in this book. We acknowledge the most useful comments by all referees for this publication. We would like to also acknowledge the very detailed comments by Ms. Sharmila Kumari, senior lecturer in mathematics at the Lautoka Teachers College; these comments helped us in our effort to produce the best guide for our students.
The introductory chapter describes the design of the Lyapunov—based control scheme and
provides its algorithmic representation. The steps constructed in the algorithm will be implemented throughout the thesis in order to generate a set of feasible navigation laws for the point masses or the mobile planar robots. In parallel, the control scheme also facilitates stability analysis of kinodynamic systems considered in this thesis by employing the Direct Method of Lyapunov.
The work carried out naturally falls into four distinctive parts.
The first part presents an overview on how the new control scheme will be applied to motion planning of point masses, carefully considering all the notations and definitions required of the research. Both the velocity controls and the acceleration controls have been successfully extracted for a point—mass system Via the control scheme. The part also designs appropriate obstacle avoidance functions, and hence the repulsive potential field functions, for the avoidance of obstacles which have been gathered into three categories. Another worthy contribution here is the unique treatment of constraints and mechanical singularities of systems, ensuring a successful merger to the control scheme.
The second and the third parts constitute the applications of this thesis. The parts address various sub—tasks involved in kinodynamic planning and control problem of the dynamic models of various mechanical systems from real—world Via the Lyapunov—based control scheme. Each chapter herein is essentially a separate project and has its own unique strengths and contributions which have been built progressively into the chapters that follow. All in all, the obstacle alignment technique, the minimum distance technique, the ghost walls/parking bays and new target attractive functions have been designed and implemented to strategically generate the desired activities of the mobile planar robots modelled from different mechanical systems. A description of the design of the blindman’s problem and the required potential fields have also been captured in one of the chapters. Formations of different degree have been considered and new techniques have been formulated to establish, maintain and translate these formations. Amongst others, the networking of minimum distance technique and ghost
walls/parking bays to obtain the prescribed final orientation of each body of the articulated robot turns out be one of the coins of realm of this thesis.
The final part is arguably the main strength of this thesis. Artificial potential fields are normally beset by difficulties arising from the existence of local minima. Notwithstanding the practical limitation, this part of the thesis has proposed a stabilizing solution within
the framework of the Lyapunov—based control scheme. The asymptotically stable point—mass system is without any local minima other than the goal configuration. As an application, the point stabilization of a planar mobile car—like robot moving in the presence of a static obstacle
has been considered.
Efficiency of the control framework and the resultant nonlinear control laws have been demonstrated with simulation results of interesting situations mimicking real—world applications of mobile planar robots throughout the thesis.
By varying these parameters in a precise way, computer simulations show that for a sufficiently large number of individuals, our proposed model generates four types of
swarming-like behaviors. They are (1) the cruise formation (linear or nonlinear) reminiscent of a cruising and leaderless school of fish, or a moving herd of land animals with a leader (leader-following), (2) random walks similar to the swarming behavior of
fruit flies Drosophila melanogaster, (3) constant arrangements requiring individuals to aggregate and stop, as in fruiting body formation by bacteria, and (4) circular motions reminiscent of the behavior of a school of fish when threatened by a predator.
response. It aims to showcase how learning/instructional material can be made more enticing and conducive for ZGeneration learners in academia. The paper looks at different tools (commercial and free) that can be utilized to create
edutainment content and facilitate more creative and effective learning. It also explores the beneficial implications of
edutainment from enhancing learner perception and engagement to learner responsiveness and knowledge retention. To
measure the effects of edutainment a test case was selected in which students of selected courses were required to
complete a weekly survey on their workload for an entire semester. An animated video objectively designed with
edutainment at mind was used to deliver instructions on the purpose and importance of completing the survey and made
available to students of a particular targeted course. Subsequently, response rate from students was by far the highest for
the targeted course who received their instructions through the animated edutainment video when compared to all the
other courses for all fourteen weeks of the survey.
amd whenever required. Mobile learning would be a great advantage in the Pacific with the possibilities of various ways
of interactions with students and instructors. Other advantages for the Pacific include the notions of just-for-me, just- enough and just-in-time. This paper presents some case studies and success stories garnered at The University of the South Pacific. It also considers the issues of adoption and adaptability of features and functionalities of mLearning tools for the Pacific region.
practical stability of the system. The effectiveness of the proposed control laws are demonstrated via computer simulations of an emergent behavior.
moves from arbitrary initial positions through a tunnel of given geometry. This paper proposes a decentralized planner that guarantees collision-free tunnel passing maneuvers of a team of nonholonomic car-like robots fixed in a prescribed formation, whilst considering all the practical limitations and constraints due to nonholonomy, tunnel geometry and the formation specifications. While solutions in literature are restricted to tunnels with linear segments, this paper includes piecewise tunnel walls with linear and curved segments. The motion planner, derived from the Lyapunov-based control scheme works
within an overarching leader-follower framework to generate either split/rejoin or expansion/contraction of the formation, as feasible solutions. Results from simulating virtual scenarios demonstrated the effectiveness of the proposed nonlinear controllers.
In this paper we are proposing that we look at the findpath problem from the point of view of having an obstacle avoidance system that is at least Lyapunov stable. We consider a simple planar obstacle avoidance system that consists of a point-mass being controlled to its destination or target whilst avoiding a fixed object in two-dimensional space. The proposed Lyapunov
function for the system produces artificial potential fields both for obstacle avoidance and for target attraction. After establishing Lyapunov stability, we then show that it is possible to identify a region of asymptotic stability in which the target is the only minimum point.
The background of our method lies in the application of the Lyapunov method to qualitative differential games that involve dynamical systems subject to control by one or more players ([2], [1]). Using these differential games concepts, a simple method to solve the findpath problem was proposed in [3]. The methods therein are used in this paper.