07/20/2018 at 01:13 •
This post deals with the Octomaps library which deals with creation of an efficient way of storing, querying and include uncertainty in measurements. Octomaps are data structures t represent 3d space. There are many approaches for modelling 3D space in the robotics domain by creating voxels.
Octomaps differ from them as it does not suffer from space constraints and the problems such as inability to model unknown and free space. Octomaps can model uncertainty in obstacles in the occupancy grid by incorporating probabilistic updates of the occupancy maps. Octomaps can be used to represent voxels at different resolutions. The datastructure used for their implementation are octrees.
Every Octree has eight children. Basically the root of the tree is the area that you are modelling. This region can be unknown initially as the restriction here is the size that you want your octree to be. If the size of the Octree should be small then a dynamically exploring a bigger area would yield leaves with coarser resolutions and vice versa. To include free space in the modelling Octrees explicitly include two types of node: Occupied and Free. Unknown nodes are not generated. Each root is a volume in real world. The children are obtained by dividing the root volume into eight equal parts (voxels) something similar to the four quadrants that we normally use in 2 dimensions. The occupancy values are updated using some distance measurement sensor. The voxels containing the endpoints of the sensor readings are marked as occupied in a discrete map and updated according to some predefined formula in a probabilistic occupancy grid. The region on the ray between the sensor and the endpoint is marked as free and the octree is updated accordingly.
Currently I am looking at ways to represent the Lidar scans that would be acquired using Octomaps and get a 3D map for the environment. Octomaps are purely for generation of maps. Octomaps are however flexible as they are available as a opensource C++ library which can be included in any C++ project. I am also looking to study the Hector-SLAM package for ROS which is restricted to ROS from what I know. Hector-SLAM though includes mapping, localization which is highly desirable if you want to get started with your planning projects. Currently I am looking to study both of them and try to implement some examples
07/11/2018 at 12:29 •
Currently I am working with simulating the project in ArduPilot and then taking it to hardware. ArduPilot SITL is one way to simulate the flight and the sensors. I am pretty sure that the SITL does have a Laser scanner simulator but am not sure what is its field of view. The process to download and run SITL on a Ubuntu 16.04 is as follows:
- Open Terminal and clone the git repository.
git clone git://github.com/ArduPilot/ardupilot.git cd ardupilot git submodule update --init --recursive
- The next step depends on the operating system that you are using. Go to the installation instructions for your OS on Ardupilot website for more details. For Ubuntu 16.04 you just need to run a script:
- Add the following to the end of your bashrc file and source it.
export PATH=$PATH:$HOME/ardupilot/Tools/autotest export PATH=/usr/lib/ccache:$PATH
- Start the simulator.
cd ardupilot/ArduCopter sim_vehicle.py -w #to load the default parameters
sim_vehicle.py --console --map
The copter can be run in several modes:
1. Guided: To run in Guided mode do the following.
mode guided arm throttle takeoff 40
For more detailed commands and information goto:
2. Auto: For navigating the copter in Auto mode do the following:
wp load ..\Tools\autotest\copter_mission.txt arm throttle mode auto rc 3 1500
07/11/2018 at 12:14 •
I am planning to use ROS to interface the Lidar with the copter. The LIDAR messages are published using the message format defined in the sensor_msgs/laserscan message type in ROS. The message consists of :
The angles are in radians. angle_min is the start angle from which the LIDAR starts taking observations in one scan. It then takes observations by incrementing the angle with steps equal to angle_increment until it reaches the angle_max when the scan completes. The time between two scan is equal to time_increment. Scan_time is the time to complete one scan in the FOV defined for the LIDAR. Range_min and range_max are the minimum and maximum values that the LIDAR can detect. Ranges give you the distance observation that has been calculated by the LIDAR.
03/24/2018 at 03:39 •
I had explained Kalman filter in the last post. What happens when the motion model and observation model is not linear. In robotics, the linear case occurs rarely. So algorithms that can handle non-linear models can be used to localize. The Extended Kalman filter is one such algorithm.
The observation and motion model for non-linear case can be represented by:
03/23/2018 at 23:25 •
Kalman filters can be intrepreted as Bayes filter with the gaussian linear case. There application range from economics to weather forecasting to satellite navigation. If models are not linear the beliefs do not remain gaussian and we can not work with a simple kalman filter.
A multivariate Gaussians can be described:Let v be a multivariate gaussian distribution:
03/16/2018 at 03:14 •
Simultaneous Localization and Mapping (SLAM):
SLAM is a probabilistic technique to construct and update maps for navigation while localizing the object pose in the map. The problem appears to be a chicken and egg problem as to localize the vehicle we need a map and to update the map we need to know the pose of the vehicle. This problem can be solved through multiple approximate techniques such as Extended kalman filters and Particle filters.
The problem can be formulated mathematically as finding:
Input: robot's controls inputs u and observations z.
Output: Map of the environment m and the pose of the robot x
This can be done using bayes filter. Bayes filter is a two step process: Prediction and Correction.
Predicton step predicts the state of the vehicle using the motion model, control inputs and previous belief while the correction step reduces the uncertainty using the observation model. The motion model describes the distribution of the current state of the system given the control inputs for this time step and the previous belief of the pose of the vehicle. This can be represented mathematically as:The predicted state of the system is :
The Sensor model or the Observation model is responsible for reducing the uncertainty that is introduced by the random nature of the problem. The predicted state is:This belief value is the current pose of the system.
There are multiple ways to implement the Bayes filter:
- Kalman Filters which deals with gaussian distributions and linear models
- Particle Filters which deal with non-parametric arbitrary models
Kalman filters deal with the linear gaussian case. By linear we mean a linear model and by gaussian we mean gaussian noise is associated with the pose and observations.