Pramod Abichandani

Mathematical programming for Multi-Vehicle Motion Planning problems

Real world Multi-Vehicle Motion Planning (MVMP) problems require the optimization of suitable performance measures under an array of complex and challenging constraints involving kinematics, dynamics, communication connectivity, target tracking, and collision avoidance. The general MVMP problem can thus be formulated as a mathematical program (MP). In this paper we present a mathematical programming (MP) framework that captures the salient features of the general MVMP problem. To demonstrate the use of this framework for the formulation and solution of MVMP problems, we examine in detail four representative works and summarize several other related works. As MP solution algorithms and associated numerical solvers continue to develop, we anticipate that MP solution techniques will be applied to an increasing number of MVMP problems and that the framework and formulations presented in this paper may serve as a guide for future MVMP research.

Multi-vehicle path coordination under communication constraints

We generate time-optimal velocity profiles for a group of path-constrained vehicles with fixed and known initial and goal locations. Each vehicle robot must follow a fixed path, arrive at its goal as quickly as possible (or at least not increase the time for the last robot to arrive at its goal) and stay in communication with other robots in the arena throughout its journey. We seek to solve this multi-objective optimization problem by generating optimal velocities along the paths. The problem is formulated as a nonlinear programming problem (NLP) with constraints on the kinematics, dynamics, collision avoidance and communication. Solutions demonstrate the trade off between the arrival time, the required transmission power and the communication connectivity requirements. Typically the optimization improved connectivity at no appreciable cost in journey time (as measured by the time of arrival of the last-arriving robot).

Multi-vehicle path coordination in support of communication

This paper presents a framework for generating time-optimal velocity profiles for a group of path-constrained vehicle robots that have fixed and known initial and goal locations and are required to maintain communication connectivity. Each robot must follow a fixed and known path, arrive at its goal as quickly as possible (or at least not increase the time for the last robot to arrive at its goal) and stay in communication with other robots in the arena throughout its journey. The main contribution of this paper is the formulation of the problem as a discrete time nonlinear programming problem (NLP) with constraints on robot kinematics, dynamics, collision avoidance, and communication connectivity. We develop Partition Elimination constraints that assist in ensuring that the communication network is fully connected (no network partitions). These constraints are enforced only when network partitions would otherwise occur, an approach which significantly reduces the problem size and the required computational effort. In addition, we introduce path-constrained jammer robots with known paths and velocity profiles into the scenario. These jammer robots have an effective jamming range and disrupt all communications within this range. Except for the jammers, all robots must remain outside this jamming range at all times. We investigate the scalability of the proposed approach by testing scenarios involving up to fifty (50) robots. Solutions demonstrate (i) the trade off between the arrival time and the communication connectivity requirements in scenarios with and without jamming; and (ii) the dependence of computation time on the number of robots.

Decentralized multi-vehicle path coordination under communication constraints

We present a mathematical programming based decentralized framework to generate time optimal velocity profiles for a group of path constrained mobile vehicle robots subject to communication connectivity constraints. Each vehicle robot starts from a fixed start point and moves towards a goal point along a fixed path so as to avoid collisions with other robots, and remain in communication connectivity with other robots. The main contribution of this paper is the discrete time decentralized Receding Horizon Mixed Integer Nonlinear Programming (RH-MINLP) formulation of the multi-vehicle path coordination problem with constraints on kinematics, dynamics, collision avoidance, and communication connectivity, and the application of state-of-the-art MINLP solution techniques. We test scenarios involving up to ten (10) robots to demonstrate (i) the effect of communication connectivity requirements on robot velocity profiles; and (ii) the dependence of the solution computation time on communication connectivity requirements.

Experimental Multi-Vehicle Path Coordination under Communication Connectivity Constraints

The main contribution of this paper is the experimental validation of a decentralized Receding Horizon Mixed Integer Nonlinear Programming (RH-MINLP) framework that can be used to solve the Multi-Vehicle Path Coordination (MVPC) problem. The MVPC problem features path-constrained vehicles that begin their transit from a fixed starting point and move towards a goal point along fixed paths so as to avoid collisions with other robots and static obstacles. This framework allows to solve for time optimal velocity profiles for such robots in the presence of constraints on kinematics, dynamics, collision avoidance, and inter-robot communication connectivity. Experiments involving up to five (5) robots operating in a reasonably complex workspace are reported. Results demonstrate the effect of communication connectivity requirements on robot velocity profiles and the effect of sensing and actuation noise on the path-following performance of the robots. Typically, the optimization improved connectivity at no appreciable cost in journey time, as measured by the time of arrival of the last-arriving robot.

An initial comparison of the learning propensities of 10 through 12 students for data analytics education

The main focus of this ongoing effort is to compare the learning propensities of 10 through 12 students for data analytics education. Towards this end, a Microsoft Excel based university-level environmental engineering module was taught in a high school classroom with students in grades 10 through 12. The module focused on understanding the current trends and challenges in environmental pollution management and policy. Students were required to procure, analyze, and visualize data in order to propose an environmental policy that was aimed at reducing pollution. Initial data collected from the assessment of the student work alludes to the fact that despite being taught the same material by the same professor and teaching assistant, the success of the students, as measured by their final grades, varies substantially with their academic year. The underclassmen in high school did not display the academic maturity and comprehension that was displayed by the high school seniors. On the other hand, seniors demonstrated a strong propensity to learn and perform well.

Simulation Detection in Handwritten Documents by Forensic Document Examiners

This study documents the results of a controlled experiment designed to quantify the abilities of forensic document examiners (FDEs) and laypersons to detect simulations in handwritten documents. Nineteen professional FDEs and 26 laypersons (typical of a jury pool) were asked to inspect test packages that contained six (6) known handwritten documents written by the same person and two (2) questioned handwritten documents. Each questioned document was either written by the person who wrote the known documents, or written by a different person who tried to simulate the writing of the person who wrote the known document. The error rates of the FDEs were smaller than those of the laypersons when detecting simulations in the questioned documents. Among other findings, the FDEs never labeled a questioned document that was written by the same person who wrote the known documents as “simulation.” There was a significant statistical difference between the responses of the FDEs and layperson for documents without simulations.

Should the first course in computational problem solving and programming be student-centered or teacher-centered?

Computational problem solving and programming are foundational skills for engineers. The first undergraduate level course that covers these topics is critical to laying these foundations. As instructors strive to incorporate the spirit of inquiry in their courses, an important question that comes forth is whether the teaching methodology should be student-centered or teacher-centered. This paper adds helpful information in the ongoing debate on this question. The paper reports on the student performance results obtained by teaching two sections (cohorts) of an introductory Computation Lab course sequence. This course sequence aims to teach new engineering students MATLAB scripting and programming in the context of technical problem-solving using mathematical models. Cohort A was taught using a traditional teacher-centered approach, while Cohort B employed an open-ended student-centered approach. Our results indicate that the teacher-centered approach has the potential of creating polarized grade distributions with relatively more A grades in the class compared to the student centered approach. On the other hand, the student-centered approach provided a smoother grade distribution, indicating that a higher number of students demonstrate noticeable progress as compared to the teacher-centered approach.

Mathematical Programming Approaches for Multi-Vehicle Motion Planning: Linear, Nonlinear, and Mixed Integer Programming

Mathematical Programming Approaches for Multi-Vehicle Motion Planning: Linear, Nonlinear, and Mixed Integer Programming

Symbolic Scientific Software Skills for Engineering Students

The emergence of powerful numeric and symbolic scientific software applications, including MATLAB, Maple, and Mathematica, has revolutionized engineering design. These applications have allowed users to perform computations and calculations at levels of sophistication and depth that were not available to practitioners even one generation ago. They have also given educators the ability to convey advanced mathematical and engineering concepts in new ways and spend more time on analysis of engineering systems and less time on remedial mathematics. This new capability, which has become a fundamental tool for sophisticated designers in industry, is still not fully embraced in many engineering curricula. To exemplify the potential of scientific software in the engineering classroom, we describe a laboratory exercise conducted by second-year engineering students at Drexel University. It introduces a geosynchronous satellite orbital entry problem, and demonstrates how scientific software can help students understand the behavior of an interesting physical system in a way that would have required much more effort using traditional methods. We believe that early introduction to symbolic computation tools and scientific software would be very valuable to engineering students. Such tools should become standard instruments in the arsenal of present-day engineers. Moreover, their use should be adopted across the curriculum (not only in introductory mathematics classes) and become part of the design experience in all engineering disciplines.