Autonomous outdoor navigation requires reliable multisensory fusion strategies. Desert ants travel widely every day, showing unrivaled navigation performance using only a few thousand neurons. In the desert, pheromones are instantly destroyed by the extreme heat. To navigate safely in this hostile environment, desert ants assess their heading from the polarized pattern of skylight and judge the distance traveled based on both a stride-counting method and the optic flow, i.e., the rate at which the ground moves across the eye. This process is called path integration (PI). Although many methods of endowing mobile robots with outdoor localization have been developed recently, most of them are still prone to considerable drift and uncertainty. We tested several ant-inspired solutions to outdoor homing navigation problems on a legged robot using two optical sensors equipped with just 14 pixels, two of which were dedicated to an insect-inspired compass sensitive to ultraviolet light. When combined with two rotating polarized filters, this compass was equivalent to two costly arrays composed of 374 photosensors, each of which was tuned to a specific polarization angle. The other 12 pixels were dedicated to optic flow measurements. Results show that our ant-inspired methods of navigation give precise performances. The mean homing error recorded during the overall trajectory was as small as 0.67% under lighting conditions similar to those encountered by ants. These findings show that ant-inspired PI strategies can be used to complement classical techniques with a high level of robustness and efficiency.

/pdf/antbot-a-six-legged-walking-robot-able-to-home-like-desert-25c175i5om.pdf

AntBot: A six-legged walking robot able to home like desert ants in outdoor environments.

In logistics operation, delivery times are often uncertain for customers, and accommodating this uncertainty poses operation challenges as well as extra cost for logistics service providers. The delivery time uncertainty is particularly an issue if there are multiple service providers in a logistics network. To address this issue, we formulate and solve a collaborative multi-depot vehicle routing problem with time window assignment (CMDVRPTWA) to effectively reduce the impact of changing time windows on operating costs. This paper establishes a bi-objective programming model that optimize the total operating cost and the total number of delivery vehicles. A hybrid heuristic algorithm consisting of K-means clustering, Clarke–Wright (CW) saving algorithm and an Extended Non-dominated Sorting Genetic Algorithm-II (E-NSGA-II) is presented to efficiently solve CMDVRPTWA. The clustering and CW saving algorithm are employed to increase the likelihood of finding the optimal vehicle routes by identifying a feasible initial solution. The E-NSGA-II procedure combines partial-mapped crossover (PMC), relocation, 2-opt* exchange and swap mutation operations to find the optimal solution with pre-defined iteration and termination rules. Profit allocation schemes are then analyzed using the Game Quadratic Programming (GQP) method, and the optimal sequences of joining coalitions are obtained based on the principle that coalition participants’ benefits should be non-decreasing when a new participant joins the coalition. We conduct three empirical studies on a small-scale example, on several benchmark datasets and on a large-scale logistics network in Chongqing city, China. Further comparative analysis indicates that E-NSGA-II outperforms most other algorithms in solving CMDVRPTWA. This novel approach identifies profit allocation strategies that ensure the stability and reliability of the collaborative coalitions in the context of flexible customer service time windows, and can be utilized to improve the efficiency of urban logistics and intelligent transportation networks.

Collaborative multi-depot logistics network design with time window assignment

The polarization states of a skylight can be used for navigation by a lot of insects as well as by human beings. However, the polarization patterns of skylight are greatly influenced by the atmospheric conditions. This paper studied the polarization patterns of skylight under different sky conditions by polarized imaging measurements, in which the AOT (Aerosol Optical Thickness) and clouds were taken into account. The results showed that both the aerosol and cloud disturbed the polarization patterns of the skylight, but the patterns of AOP (Angle of Polarization) showed great robustness. The symmetry of the AOP images was found to be quite steady under most of the sky conditions. We proposed a navigation method by finding out the solar meridian according to the symmetry of an AOP map. The results showed that the solar meridian can be identified accurately under different situations. The calculation errors slightly fluctuated along with the aerosol and cloud.

Polarization patterns under different sky conditions and a navigation method based on the symmetry of the AOP map of skylight.

This paper aims to develop a novel attitude determination system aided by polarization sensor. An improved heading angle function is derived using the perpendicular relationship between directions of E-vector of linearly polarized light and solar vector in the atmospheric polarization distribution model. The Extended Kalman filter (EKF) with quaternion differential equation as a dynamic model is applied to fuse the data from sensors. The covariance functions of filter process and measurement noises are deduced in detail. The indoor and outdoor tests are conducted to verify the validity and feasibility of proposed attitude determination system. The test results showed that polarization sensor is not affected by magnetic field, thus the proposed system can work properly in environments containing the magnetic interference. The results also showed that proposed system has higher measurement accuracy than common attitude determination system and can provide precise parameters for Unmanned Aerial Vehicle (UAV) flight control. The main contribution of this paper is implementation of the EKF for incorporating the self-developed polarization sensor into the conventional attitude determination system. The real-world experiment with the quad-rotor proved that proposed system can work in a magnetic interference environment and provide sufficient accuracy in attitude determination for autonomous navigation of vehicle.

https://www.mdpi.com/1424-8220/18/1/158/pdf

A Novel Attitude Determination System Aided by Polarization Sensor.

How to self-determine the attitude and heading of users is a challenging issue in unknown, global navigation satellite system (GNSS) denied, or magnetic disturbance environments. In this article, a bioinspired polarization-based attitude and heading reference system (PAHRS) aided by inertial sensors is presented. As compared with the existing studies, a polarization compass, which consists of three photoelectric-based polarization sensors is designed to cope with the three-dimensional polarization heading determination and distinguish issue. Hence, the real heading orientation can be determined without GNSS correction. To address the triaxis attitude and heading determination issue of PAHRS, the system measurement model tightly coupled the attitude and heading accumulate errors of inertial navigation system. Finally, the experimental platform is built and the results illustrate that the PAHRS is able to achieve satisfactory performance without the aid by GNSS and magnetic compass system.

Method and Implementation of a Bioinspired Polarization-Based Attitude and Heading Reference System by Integration of Polarization Compass and Inertial Sensors

Navigation plays a vital role in our daily life. As traditional and commonly used navigation technologies, Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) can provide accurate location information, but suffer from the accumulative error of inertial sensors and cannot be used in a satellite denied environment. The remarkable navigation ability of animals shows that the pattern of the polarization sky can be used for navigation. A bio-inspired POLarization Navigation Sensor (POLNS) is constructed to detect the polarization of skylight. Contrary to the previous approach, we utilize all the outputs of POLNS to compute input polarization angle, based on Least Squares, which provides optimal angle estimation. In addition, a new sensor calibration algorithm is presented, in which the installation angle errors and sensor biases are taken into consideration. Derivation and implementation of our calibration algorithm are discussed in detail. To evaluate the performance of our algorithms, simulation and real data test are done to compare our algorithms with several exiting algorithms. Comparison results indicate that our algorithms are superior to the others and are more feasible and effective in practice.

https://www.mdpi.com/1424-8220/14/9/17068/pdf

A Novel Angle Computation and Calibration Algorithm of Bio-Inspired Sky-Light Polarization Navigation Sensor

Skylight polarization provides a significant navigation cue for certain polarization-sensitive animals. However, the precision of the angle of polarization (AOP) of skylight for vehicle orientation is not clear. An evaluation of AOP must be performed before it is utilized. This paper reports an evaluation of AOP of skylight by measuring the skylight polarization patterns of clear and cloudy skies using a full-sky imaging polarimetry system. AOP measurements of skylight are compared with the pattern calculated by the single-scattering Rayleigh model and these differences are quantified. The relationship between the degree of polarization (DOP) and the deviation of AOP of skylight is thoroughly studied. Based on these, a solar meridian extracted method is presented. The results of experiments reveal that the DOP is a key parameter to indicate the accuracy of AOP measurements, and all the output solar meridian orientations extracted by our method in both clear and cloudy skies can achieve a high accuracy for vehicle orientation.

https://www.mdpi.com/1424-8220/15/3/5895/pdf

An Evaluation of Skylight Polarization Patterns for Navigation

Sky polarization patterns can be used both as indicators of atmospheric turbidity and as a sun compass for navigation. The objective of this study is to improve the precision of sky light polarization measurements by optimal design of the device used. The central part of the system is composed of a Charge Coupled Device (CCD) camera; a fish-eye lens and a linear polarizer. Algorithms for estimating parameters of the polarized light based on three images are derived and the optimal alignments of the polarizer are analyzed. The least-squares estimation is introduced for sky light polarization pattern measurement. The polarization patterns of sky light are obtained using the designed system and they follow almost the same patterns of the single-scattering Rayleigh model. Deviations of polarization angles between observation and the theory are analyzed. The largest deviations occur near the sun and anti-sun directions. Ninety percent of the deviations are less than 5° and 40% percent of them are less than 1°. The deviations decrease evidently as the degree of polarization increases. It also shows that the polarization pattern of the cloudy sky is almost identical as in the blue sky.

https://www.mdpi.com/1424-8220/14/8/14916/pdf

Design of a Device for Sky Light Polarization Measurements

Calibration of a polarization navigation sensor using the NSGA-II algorithm

In this paper, a polarization navigation sensor is designed based on the polarization sensitivity mechanisms of insects. A new calibration model by taking full advantage of both reference angle of polarization and constant degree of polarization is presented to determine calibration parameters. Unlike existing calibration algorithms, the proposed algorithm makes the calibration problem well-posed. The results of simulations and experiments show that the proposed algorithm is more stable than the compared methods for the calibration applications of polarization navigation sensors.

Tao Ma

Papers

A Novel Angle Computation and Calibration Algorithm of Bio-Inspired Sky-Light Polarization Navigation Sensor

An Evaluation of Skylight Polarization Patterns for Navigation

Design of a Device for Sky Light Polarization Measurements

Calibration of a polarization navigation sensor using the NSGA-II algorithm

A Novel Calibration Model of Polarization Navigation Sensor