Conformal Navigation Transformations with Application to Robot Navigation in Complex Workspaces

Navigation functions provide both path and motion planning, which can be used to ensure obstacle avoidance and convergence in the sphere world. When dealing with complex and realistic scenarios, constructing a transformation to the sphere world is essential and, at the same time, challenging. This work proposes a novel transformation termed the conformal navigation transformation to achieve collision-free navigation of a robot in a workspace populated with obstacles of arbitrary shapes. The properties of the conformal navigation transformation, including uniqueness, invariance of navigation properties, and no angular deformation, are investigated, which contribute to the solution of the robot navigation problem in complex environments. Based on navigation functions and the proposed transformation, feedback controllers are derived for the automatic guidance and motion control of kinematic and dynamic mobile robots. Moreover, an iterative method is proposed to construct the conformal navigation transformation in a multiply-connected workspace, which transforms the multiply-connected problem into multiple simply-connected problems to achieve fast convergence. In addition to the analytic guarantees, simulation studies verify the effectiveness of the proposed methodology in workspaces with non-trivial obstacles

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

Autonomous navigation system

An inertial navigation system utilizing a servo-controlled two degree of freedom pendulum to obtain specific force components in the locally level coordinate system is described. The pendulum includes a leveling gyroscope and an azimuth gyroscope supported on a two gimbal system. The specific force components in the locally level coordinate system are converted to components in the geographical coordinate system by means of a single Euler transformation. The standard navigation equations are solved to determine longitudinal and lateral velocities. Finally, vehicle position is determined by a further integration

Accurate and automatic NOAA-AVHRR image navigation using a global contour matching approach

The problem of precise and automatic AVHRR image navigation is tractable in theory, but has proved to be somewhat difficult in practice. The authors' work has been motivated by the need for a fully automatic and operational navigation system capable of geo-referencing NOAA-AVHRR images with high accuracy and without operator supervision. The proposed method is based on the simultaneous use of an orbital model and a contour matching approach. This last process, relying on an affine transformation model, is used to correct the errors caused by inaccuracies in orbit modeling, nonzero value for the spacecraft's roll, pitch and yaw, errors due to inaccuracies in the satellite positioning and failures in the satellite internal clock. The automatic global contour matching process is summarized as follows: i) Estimation of the gradient energy map (edges) in the sensed image and detection of the cloudless (reliable) areas in this map. ii) Initialization of the affine model parameters by minimizing the Euclidean distance between the reference and sensed images objects. iii) Simultaneous optimization of all reference image contours on the sensed image by energy minimization in the domain of the global transformation parameters. The process is iterated in a hierarchical way, reducing the parameter searching space at each iteration. The proposed image navigation algorithm has proved to be capable of geo-referencing a satellite image within 1 pixel.Peer ReviewedPostprint (published version

The Datums Transformation for GPS Navigation Measurements Correction

The GPS navigation measurements become more widely used in many civilian and scientific application. All GPS navigation data holds many errors, the main error sources arise from the geodetic Datum variation when user apply the GPS measurements with the map. Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth surface. In this paper, the Datum transformation was evaluated in two mathematical methods to overcome the errors due to the difference between the WGS-84 and our country Datum Clarck-1880. The results was evaluated and investigated using Carmin GPS device for GCPs comparison, topographic map for Hilla city, mid Iraq 1:100000 scale, and two georefrencing ETM+ & TM satellite images. The spatial transformation error was less than 10 meter for UTM projection & less than 1 sec for (?, ?) projection, which can considered as suitable results in transformation calculation All results were overcome using two written program for each method with the help of Matlab facility. GPS: Global Positioning System, GCPs: Ground Control Point

Cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging

The implementation challenges of cooperative localization by dual foot-mounted inertial sensors and inter-agent ranging are discussed and work on the subject is reviewed. System architecture and sensor fusion are identified as key challenges. A partially decentralized system architecture based on step-wise inertial navigation and step-wise dead reckoning is presented. This architecture is argued to reduce the computational cost and required communication bandwidth by around two orders of magnitude while only giving negligible information loss in comparison with a naive centralized implementation. This makes a joint global state estimation feasible for up to a platoon-sized group of agents. Furthermore, robust and low-cost sensor fusion for the considered setup, based on state space transformation and marginalization, is presented. The transformation and marginalization are used to give the necessary flexibility for presented sampling based updates for the inter-agent ranging and ranging free fusion of the two feet of an individual agent. Finally, characteristics of the suggested implementation are demonstrated with simulations and a real-time system implementation.Comment: 14 page