# Mohiqab Hayat

 MHEQUB HAYAT LUMS School of Science and Engineering, Department of Computer Science

# Bio

Mhequb Hayat is pursuing Masters in Computer Engineering at LUMS School of Science and Engineering (LUMS-SSE). He is a member of Laboratory for Cyber Physical Networks and Systems (CyPhyNets) headed by Dr. Abubakr Muhammad. He is working on Motion Planning Project.

Prior, he received his BS (2009) from National University of Sciences and Technology (NUST), College of Electrical and Mechanical Engineering (CE&ME) in Mechatronics Engineering. He worked on Automated Highway Driving System in supervision of Dr. Kunwar Faraz. His Project was declared best in Automation/Control Category in 8th All Pakistan Inter College/University Software Exhibition and Competition (comppec 2009).

# Education

Lahore University of Management Sciences, Lahore, Pakistan (LUMS) Sep 2009 - To date

School of Science and Engineering (SSE)
Masters of Science in Computer Engineering, Department of Computer Science (CS)
Specialization: AI, Robotics

National University of Sciences & Technology, Rawalpindi, Pakistan (NUST) Sep 2005 - Oct 2009

NUST College of Electrical & Mechanical Engineering (CEME)
Bachelors of Engineering in Mechatronics
Specialization: Control, Robotics

# Research

### Spectral Analysis and Enhancement of Probabilistic Roadmap Method (PRM)

Fig. 1 Motion Planning Problem (Example)

Probabilistic Roadmap Method (PRM) $\scriptstyle[1]$ is an extremely effective motion planning construct in robotics that captures the connectivity of a high dimensional configuration space $\scriptstyle\mathcal{C}_{space}$ cluttered with obstacles and narrow passages. In PRM, random (samples) configurations ($\scriptstyle[0\ 1]^d$) are taken and tested whether they are in free space $\scriptstyle\mathcal{C}_{free},\ \scriptstyle[Fig.\ 2]$. These collision-free configurations (nodes) are further checked for feasible paths (edges) between them. Space between all combinations of two nodes are checked for collision. These nodes and edges form a graph representing collision-free configurations and paths between them in $\scriptstyle\mathcal{C}_{free}$. This graph can easily be traversed for finding path between start and goal configuration.

Spectral Analysis of PRM Graph
The graph $\scriptstyle (G)$can be represented as $\scriptstyle G=(V,E)$, where $\scriptstyle V$ and $\scriptstyle E$ refers to vertices (nodes) and Edges, respectively. The Laplacian matrix of Graph is $\textstyle L:=(a_{i,j})_{n\times n}$ is defined as:

$\textstyle a_{i,j} := \Bigg\{ \begin{array}{ll} deg(v_{i}) & : i=j\\ -1 & :i\neq j\ \textrm{and}\ v_{i}, v_{j}\ \textrm{are\ adjacent}\\ 0 & : \textrm{otherwise} \end{array}$

Laplacian matrix gives important information about graph. The eigen-vector decomposition of laplacian matrix can be used to find algebraic connectivity of a graph. This is also called spectrum of graph $\scriptstyle[Fig.\ 3]$. Every PRM graph has different spectrum, from where we get spectral properties. These properties can be used to detect narrow passages in $\scriptstyle\mathcal{C}_{space}$, $\scriptstyle[2,\ 3]$ (work of CyPhyNets). This process of analyzing and exploration of different properties about graph is spectral analysis.

Project Abstract
We intend to explore the spectral properties of the PRM graph and subsequently find the connection between spectral geometry of configuration spaces and the topological and geometrical obstructions encountered by motion planning algorithms. This can lead to new motion planning algorithms in robotics or perhaps a way of characterizing configuration spaces from a spectral perspective.

Fig. 2 Random Sampling Example (50 Samples)
Fig. 3 Spectrum Plot (Values: Red (+ve), Blue (-ve) and Black (0)) (400 Samples)

References
[1] L.E. Kavraki, P. Svestka, J.C. Latombe and M. H. Overmars, "Probabilistic roadmaps for path planning in high-dimensional configuration spaces", IEEE Transactions on Robotics and Automation, 12 (4): 566–580, 1996.

[2] Hassan Mohy-ud-Din and Abubakr Muhammad, Detecting Narrow Passages in Configuration Spaces Via Spectra of Probabilistic Roadmaps, SAC’10, March 22-26, 2010, Sierre, Switzerland.

[3] Abubakr Muhammad and Mhequb Hayat, Spectral Properties of Probabilistic Roadmaps. (Submitted)

# Awards and Honors

• Final Year Project declared best and won 1st prize in Control/Automated Systems Category in comppec 2009 (Project Exhibition and Competition organized by NUST)
• 1st runner up Final Year Project Poster Competition, organized by Mechatronics Department
• Winner Speed Wiring Competition in All Pakistan Electrical Engineering Conference 2008, Ghulam Ishaq Khan Institute of Technology, Topi, Pakistan
• Commandants plaque of excellence on winning speed wiring competition
• Runner up nescon 2009 in Line Tracking Robot Competition (in National University of Computer & Emerging Sciences, FAST Pakistan)
• Merit Scholarship in 7th , 3rd semester of Bachelors
• Qualified in semi-finals of Pakistan Tobacco Company Battle of Minds 2009 and token of appreciation is received
• Participated in National Engineering Robotic Contest 2007 and 2008 (National University of Sciences and Technology)
• Remained in Top 5 students in College in HSSC examination
• Top position in School in SSC examination
• Top position in Wah Cantt Board in 8th standard

# Experience

Research Assistant Nov 2009-Present Laboratory for Cyber Physical Networks and Systems (CyPhyNets) School of Science and Engineering, Department of Electrical Engineering, Lahore, Pakistan

Teaching Assistant Aug 2010-Dec 2010 EE 241 Introductory Electronics Laboratory Instructors: Dr. Abubakr Muhammad, Syed Abdullah Nauroze School of Science and Engineering, Department of Electrical Engineering, Lahore, Pakistan

# Contact

Mob# +92 345 5614698