Optimal Navigation Functions for Nonlinear Stochastic Systems

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential equation. This approach allows for optimality criteria to be incorporated into the navigation function, and generalizes several existing results in navigation functions. It is shown that the HJB and that existing navigation functions in the literature sit on ends of a spectrum of optimization problems, upon which tradeoffs may be made in problem complexity. In particular, it is shown that under certain criteria the optimal navigation function is related to Laplace's equation, previously used in the literature, through an exponential transform. Further, analytical solutions to the HJB are available in simplified domains, yielding guidance towards optimality for approximation schemes. Examples are used to illustrate the role that noise, and optimality can potentially play in navigation system design.Comment: Accepted to IROS 2014. 8 Page

A Hybrid Controller for Obstacle Avoidance in an n-dimensional Euclidean Space

For a vehicle moving in an $n$-dimensional Euclidean space, we present a construction of a hybrid feedback that guarantees both global asymptotic stabilization of a reference position and avoidance of an obstacle corresponding to a bounded spherical region. The proposed hybrid control algorithm switches between two modes of operation: stabilization (motion-to-goal) and avoidance (boundary-following). The geometric construction of the flow and jump sets of the hybrid controller, exploiting a hysteresis region, guarantees robust switching (chattering-free) between the stabilization and avoidance modes. Simulation results illustrate the performance of the proposed hybrid control approach for a 3-dimensional scenario.Comment: 8 pages, 3 figures, conferenc

HCTNav: A path planning algorithm for low-cost autonomous robot navigation in indoor environments

© 2013 by MDPI (http://www.mdpi.org). Reproduction is permitted for noncommercial purposes.Low-cost robots are characterized by low computational resources and limited energy supply. Path planning algorithms aim to find the optimal path between two points so the robot consumes as little energy as possible. However, these algorithms were not developed considering computational limitations (i.e., processing and memory capacity). This paper presents the HCTNav path-planning algorithm (HCTLab research group’s navigation algorithm). This algorithm was designed to be run in low-cost robots for indoor navigation. The results of the comparison between HCTNav and the Dijkstra’s algorithms show that HCTNav’s memory peak is nine times lower than Dijkstra’s in maps with more than 150,000 cells.This work has been partially supported by the Spanish “Ministerio de Ciencia e Innovación”, under project TEC2009-09871

Trim State Discovery for an Adaptive Flight Planner

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83601/1/AIAA-2010-416-783.pd

Obstacle Avoidance for Mobile Robots

As a part of the RUNES project a robot has been developed and it has as a part of this theses been improved with an obstacle avoidance component. Work has also been done to make room for additional components on the Tmote sky (one of the micro controllers mounted on the robot) such as a power control component developed at KTH. Attempts has also been made to try to enhance the performance of the robot. Finally a program has been created so that an operator can control the robot from a PC