
Package Summary
Tags  No category tags. 
Version  0.3.0 
License  BSD 
Build type  CATKIN 
Use  RECOMMENDED 
Repository Summary
Checkout URI  https://github.com/locusrobotics/robot_navigation.git 
VCS Type  git 
VCS Version  noetic 
Last Updated  20220627 
Dev Status  DEVELOPED 
CI status 

Released  RELEASED 
Tags  No category tags. 
Contributing 
Help Wanted (0)
Good First Issues (0) Pull Requests to Review (0) 
Package Description
Additional Links
Maintainers
 David V. Lu!!
Authors
dlux_global_planner
This package implements a pluginbased global wavefront planner that conforms to the nav_core2
interface. The two
major components that you can plugin are
1. PotentialCalculator
 A function that calculates a numerical score (which we call potential) for some subset
of the cells in the costmap. The potential should be zero at the goal and grow higher from there.
2. Traceback
 A function that uses the potential to trace a path from the start position back to the goal position.
These are loaded via pluginlib
to allow for maximal customizability. This package contains the wrapper code, whereas
the dlux_plugins
package provides a handful of implementations of the plugins.
History
This package is a refactoring for nav_core2
of the global_planner
package
which in turn was a refactoring of the navfn
package. Much of the core implementation
is based on design decisions of the authors of navfn
, for better or for worse.
Weighing the Costmap
There is a fundamental tradeoff in planning between the length of the path and the costs contained within the costmap. This requires two variables. * The first is the neutral cost which is a penalty for moving from one cell to an adjacent cell (a.k.a. the cost for moving a distance equivalent to the grid resolution) * The second is the cost within the cell itself, which may be scaled up or down. Changing how these costs are used will result in possibly different paths. For example, low neutral costs will result in longer paths that avoid high costs. Higher neutral costs will sometimes result in paths that go through high costs if the path is much shorter.
The other key consideration in interpreting the costmap is whether to allow the planner to venture into cells marked
as unknown in the costmap. There are three interpretations possible here.
* LETHAL
 Unknown cells are treated as lethal obstacles and cannot be passed through.
* EXPENSIVE
 Unknown cells are valid, but assigned a high cost.
* FREE
 Unknown cells are valid and given the same weight as free cells.
For convenience, the interpretation of all these costs is contained within the CostInterpreter
class.
Potential Calculation
As mentioned above, the PotentialCalculator
calculates a numerical score called potential for the cells in the costmap.
This is stored in the PotentialGrid
which is defined as a nav_grid
.
using PotentialGrid = nav_grid::VectorNavGrid<float>;
The interface that must be implemented consists of up to two methods.
virtual void initialize(ros::NodeHandle& private_nh, nav_core2::Costmap::Ptr costmap,
CostInterpreter::Ptr cost_interpreter);
virtual void updatePotentials(PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal);
The first provides access to the Costmap
/CostInterpreter
. The second is where potentials are actually calculated.
How the potentials are calculated is left to the pluginwriter, but in general, the potential should be zero at the goal
and grow higher from there.
Traceback.
The Traceback
uses the calculated potential to create a path from the start position back to the goal position.
The interface to be implemented has two methods.
virtual void initialize(ros::NodeHandle& private_nh, CostInterpreter::Ptr cost_interpreter);
virtual nav_2d_msgs::Path2D getPath(const PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal,
double& path_cost);
The main thing to note is that the getPath
method returns a Path2D
and also calculates a path_cost
, which is
used when performing path caching.
Path Caching
Sometimes you don't want the global path to change if it doesn't have to. This global planner can cache its most
recently returned plan (assuming the goal stays the same). Whether the old plan or new plan gets returned depends on a
number of different factors.
* If the old plan becomes invalid (navigates through an obstacle), the new plan should be used.
* The relative path_cost
of each of the plans. Generally, if the old plan is still valid, you should never get
a new plan with a higher cost, but its possible depending on the exact plugin configuration.
There are four different configurations with regard to path caching, and when to use the cached path.
 Don't ever use the cached path. This is the standard
nav_core
behavior and is enabled withpath_caching=false
.  Always use the cached plan if it is valid. It doesn't matter how much the new plan might improve the path, stay with
the old path if it is valid.
path_caching=true
andimprovement_threshold<0
 Use the new plan if it is better than the cached plan. This will definitely rerun the planning algorithm each
iteration, and use the new plan if its score according to the traceback is better at all than the old plan.
path_caching=true
andimprovement_threshold=0
. This is very close to configuration #1 but doesn't use new plans if their path cost is equal to or greater than the cached path cost.  Use the new plan if it is significantly better. Require the improvement to be greater than
improvement_threshold
to ensure plans that are minorly better aren't used.path_caching=true
andimprovement_threshold>=0
Base Parameters

potential_calculator
 default:dlux_plugins::AStar

traceback
 default:dlux_plugins::GradientPath

publish_potential
 default: false  Whether to publish the calculated potentials as an OccupancyGrid 
print_statistics
 default: false  If true, will print the number of cells expanded, and the length and number of poses in the path. 
neutral_cost
 default: 50  see above section on weighing costmap 
scale
 default: 3  likewise 
unknown_interpretation
 default:"expensive"
 legal values:["lethal", "expensive", "free"]

path_caching
 default:false

improvement_threshold
 default1.0
The Kernel
One frequent operation that will be performed is to calculate the potential of a particular cell given the value of its neighboring cells. The most straightforward approach is to assign the potential as the minimum possible sum of a neighboring cell's potential and the cost of moving to that cell (i.e. the neutral cost plus the cost in the costmap). However, this approach does not take advantage of the twodimensional structure of the grid. If there are two neighbors with previously calculated potentials, then we may want to combine them for a better potential.
This package provides the kernel_function
class for combining neighboring potentials, which comes from navfn
which in turn comes from
A Light Formulation of the E Interpolated Path Replanner by Philippsen, Roland.
Below, we provide a "brief" mathematical derivation of the calculation.
 For calculating the potential $P$ for a cell $X$ (a.k.a. $P(X)$) we will look at the four neighbors of the cell $X$, which we'll call $A$, $B$, $C$ and $D$, where $A$ and $B$ are on the same axis (i.e. above and below $X$) and $C$ and $D$ are on the other axis.
 The cost of moving to a cell is the cost from the costmap, which we'll call $h$ (to match the paper's notation)
 We assume, without loss of generality that
 $P(A) <= P(B)$
 $P(C) <= P(D)$
 $P(A) <= P(C)$
 If $P(C)$ is infinite, that is, not initialized yet, the new potential calculation is straightforwardly $P(X) = P(A) + h$.
 Otherwise, we want to find a value of $P(X)$ that satisfies the equation $\Big(P(X)  P(A)\Big)^2 + \Big(P(X)  P(C)\Big)^2 = h^2$
 It's possible there are no real values that satisfy the equation if $P(C)  P(A) \geq h$ in which case the straightforward update is used.
 Otherwise, through clever manipulation of the quadratic formula, we can solve the equation with the following:
 $P(X) = \frac{\beta + \sqrt{\beta^2  4 \gamma}}{2}$
 $\beta = \Big(P(A)+P(C)\Big)$
 $\gamma = \frac{P(A)^2 + P(C)^2  h^2}{2}$
 That all looks complicated, and computationally inefficient due to the square root operation. Hence, we reformulate the equation in terms of a new variable $\delta$ and calculate a seconddegree Taylor series approximation as
 $\delta = \frac{P(C)  P(A)}{h}$
 $P(X) = P(A) + \frac{h}{2} (\delta + \sqrt{2\delta^2})$
 $P(X) \approx P(A) + h (c_2 \delta^2 + c_1\delta + c_0)$
 If you're really interested, you can look into the full derivation
 You can compare these equations on this plot
It is this final approximation that we use in our potential calculation. Although this method has been used since the origins of the nav stack, this is likely the first time the meaning of the constants has ever been documented.
Planner Node
This package also provides a standalone planner node, which will load a costmap from the global_costmap
namespace,
then listen on the /initialpose
and /move_base_simple/goal
topics for the start and goal poses respectively, and
then publish the plan between the two poses as a Path and as Markers.
Wiki Tutorials
Source Tutorials
Dependant Packages
Launch files
Messages
Services
Plugins
Recent questions tagged dlux_global_planner at Robotics Stack Exchange

Package Summary
Tags  No category tags. 
Version  0.2.5 
License  BSD 
Build type  CATKIN 
Use  RECOMMENDED 
Repository Summary
Checkout URI  https://github.com/locusrobotics/robot_navigation.git 
VCS Type  git 
VCS Version  master 
Last Updated  20200703 
Dev Status  DEVELOPED 
CI status  Continuous Integration 
Released  RELEASED 
Tags  No category tags. 
Contributing 
Help Wanted (0)
Good First Issues (0) Pull Requests to Review (0) 
Package Description
Additional Links
Maintainers
 David V. Lu!!
Authors
dlux_global_planner
This package implements a pluginbased global wavefront planner that conforms to the nav_core2
interface. The two
major components that you can plugin are
1. PotentialCalculator
 A function that calculates a numerical score (which we call potential) for some subset
of the cells in the costmap. The potential should be zero at the goal and grow higher from there.
2. Traceback
 A function that uses the potential to trace a path from the start position back to the goal position.
These are loaded via pluginlib
to allow for maximal customizability. This package contains the wrapper code, whereas
the dlux_plugins
package provides a handful of implementations of the plugins.
History
This package is a refactoring for nav_core2
of the global_planner
package
which in turn was a refactoring of the navfn
package. Much of the core implementation
is based on design decisions of the authors of navfn
, for better or for worse.
Weighing the Costmap
There is a fundamental tradeoff in planning between the length of the path and the costs contained within the costmap. This requires two variables. * The first is the neutral cost which is a penalty for moving from one cell to an adjacent cell (a.k.a. the cost for moving a distance equivalent to the grid resolution) * The second is the cost within the cell itself, which may be scaled up or down. Changing how these costs are used will result in possibly different paths. For example, low neutral costs will result in longer paths that avoid high costs. Higher neutral costs will sometimes result in paths that go through high costs if the path is much shorter.
The other key consideration in interpreting the costmap is whether to allow the planner to venture into cells marked
as unknown in the costmap. There are three interpretations possible here.
* LETHAL
 Unknown cells are treated as lethal obstacles and cannot be passed through.
* EXPENSIVE
 Unknown cells are valid, but assigned a high cost.
* FREE
 Unknown cells are valid and given the same weight as free cells.
For convenience, the interpretation of all these costs is contained within the CostInterpreter
class.
Potential Calculation
As mentioned above, the PotentialCalculator
calculates a numerical score called potential for the cells in the costmap.
This is stored in the PotentialGrid
which is defined as a nav_grid
.
using PotentialGrid = nav_grid::VectorNavGrid<float>;
The interface that must be implemented consists of up to two methods.
virtual void initialize(ros::NodeHandle& private_nh, nav_core2::Costmap::Ptr costmap,
CostInterpreter::Ptr cost_interpreter);
virtual void updatePotentials(PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal);
The first provides access to the Costmap
/CostInterpreter
. The second is where potentials are actually calculated.
How the potentials are calculated is left to the pluginwriter, but in general, the potential should be zero at the goal
and grow higher from there.
Traceback.
The Traceback
uses the calculated potential to create a path from the start position back to the goal position.
The interface to be implemented has two methods.
virtual void initialize(ros::NodeHandle& private_nh, CostInterpreter::Ptr cost_interpreter);
virtual nav_2d_msgs::Path2D getPath(const PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal,
double& path_cost);
The main thing to note is that the getPath
method returns a Path2D
and also calculates a path_cost
, which is
used when performing path caching.
Path Caching
Sometimes you don't want the global path to change if it doesn't have to. This global planner can cache its most
recently returned plan (assuming the goal stays the same). Whether the old plan or new plan gets returned depends on a
number of different factors.
* If the old plan becomes invalid (navigates through an obstacle), the new plan should be used.
* The relative path_cost
of each of the plans. Generally, if the old plan is still valid, you should never get
a new plan with a higher cost, but its possible depending on the exact plugin configuration.
There are four different configurations with regard to path caching, and when to use the cached path.
 Don't ever use the cached path. This is the standard
nav_core
behavior and is enabled withpath_caching=false
.  Always use the cached plan if it is valid. It doesn't matter how much the new plan might improve the path, stay with
the old path if it is valid.
path_caching=true
andimprovement_threshold<0
 Use the new plan if it is better than the cached plan. This will definitely rerun the planning algorithm each
iteration, and use the new plan if its score according to the traceback is better at all than the old plan.
path_caching=true
andimprovement_threshold=0
. This is very close to configuration #1 but doesn't use new plans if their path cost is equal to or greater than the cached path cost.  Use the new plan if it is significantly better. Require the improvement to be greater than
improvement_threshold
to ensure plans that are minorly better aren't used.path_caching=true
andimprovement_threshold>=0
Base Parameters

potential_calculator
 default:dlux_plugins::AStar

traceback
 default:dlux_plugins::GradientPath

publish_potential
 default: false  Whether to publish the calculated potentials as an OccupancyGrid 
print_statistics
 default: false  If true, will print the number of cells expanded, and the length and number of poses in the path. 
neutral_cost
 default: 50  see above section on weighing costmap 
scale
 default: 3  likewise 
unknown_interpretation
 default:"expensive"
 legal values:["lethal", "expensive", "free"]

path_caching
 default:false

improvement_threshold
 default1.0
The Kernel
One frequent operation that will be performed is to calculate the potential of a particular cell given the value of its neighboring cells. The most straightforward approach is to assign the potential as the minimum possible sum of a neighboring cell's potential and the cost of moving to that cell (i.e. the neutral cost plus the cost in the costmap). However, this approach does not take advantage of the twodimensional structure of the grid. If there are two neighbors with previously calculated potentials, then we may want to combine them for a better potential.
This package provides the kernel_function
class for combining neighboring potentials, which comes from navfn
which in turn comes from
A Light Formulation of the E Interpolated Path Replanner by Philippsen, Roland.
Below, we provide a "brief" mathematical derivation of the calculation.
 For calculating the potential
P
for a cellX
(a.k.a.P(X)
) we will look at the four neighbors of the cellX
, which we'll callA
,B
,C
andD
, whereA
andB
are on the same axis (i.e. above and belowX
) andC
andD
are on the other axis.  The cost of moving to a cell is the cost from the costmap, which we'll call
h
(to match the paper's notation)  We assume, without loss of generality that
 If is infinite, that is, not initialized yet, the new potential calculation is straightforwardly .
 Otherwise, we want to find a value of
P(X)
that satisfies the equation  It's possible there are no real values that satisfy the equation if in which case the straightforward update is used.
 Otherwise, through clever manipulation of the quadratic formula, we can solve the equation with the following:
 That all looks complicated, and computationally inefficient due to the square root operation. Hence, we reformulate the equation in terms of a new variable and calculate a seconddegree Taylor series approximation as
 If you're really interested, you can look into the full derivation
 You can compare these equations on this plot
It is this final approximation that we use in our potential calculation. Although this method has been used since the origins of the nav stack, this is likely the first time the meaning of the constants has ever been documented.
Planner Node
This package also provides a standalone planner node, which will load a costmap from the global_costmap
namespace,
then listen on the /initialpose
and /move_base_simple/goal
topics for the start and goal poses respectively, and
then publish the plan between the two poses as a Path and as Markers.
Wiki Tutorials
Source Tutorials
Dependant Packages
Launch files
Messages
Services
Plugins
Recent questions tagged dlux_global_planner at Robotics Stack Exchange

Package Summary
Tags  No category tags. 
Version  0.2.5 
License  BSD 
Build type  CATKIN 
Use  RECOMMENDED 
Repository Summary
Checkout URI  https://github.com/locusrobotics/robot_navigation.git 
VCS Type  git 
VCS Version  master 
Last Updated  20200703 
Dev Status  DEVELOPED 
CI status  Continuous Integration 
Released  RELEASED 
Tags  No category tags. 
Contributing 
Help Wanted (0)
Good First Issues (0) Pull Requests to Review (0) 
Package Description
Additional Links
Maintainers
 David V. Lu!!
Authors
dlux_global_planner
This package implements a pluginbased global wavefront planner that conforms to the nav_core2
interface. The two
major components that you can plugin are
1. PotentialCalculator
 A function that calculates a numerical score (which we call potential) for some subset
of the cells in the costmap. The potential should be zero at the goal and grow higher from there.
2. Traceback
 A function that uses the potential to trace a path from the start position back to the goal position.
These are loaded via pluginlib
to allow for maximal customizability. This package contains the wrapper code, whereas
the dlux_plugins
package provides a handful of implementations of the plugins.
History
This package is a refactoring for nav_core2
of the global_planner
package
which in turn was a refactoring of the navfn
package. Much of the core implementation
is based on design decisions of the authors of navfn
, for better or for worse.
Weighing the Costmap
There is a fundamental tradeoff in planning between the length of the path and the costs contained within the costmap. This requires two variables. * The first is the neutral cost which is a penalty for moving from one cell to an adjacent cell (a.k.a. the cost for moving a distance equivalent to the grid resolution) * The second is the cost within the cell itself, which may be scaled up or down. Changing how these costs are used will result in possibly different paths. For example, low neutral costs will result in longer paths that avoid high costs. Higher neutral costs will sometimes result in paths that go through high costs if the path is much shorter.
The other key consideration in interpreting the costmap is whether to allow the planner to venture into cells marked
as unknown in the costmap. There are three interpretations possible here.
* LETHAL
 Unknown cells are treated as lethal obstacles and cannot be passed through.
* EXPENSIVE
 Unknown cells are valid, but assigned a high cost.
* FREE
 Unknown cells are valid and given the same weight as free cells.
For convenience, the interpretation of all these costs is contained within the CostInterpreter
class.
Potential Calculation
As mentioned above, the PotentialCalculator
calculates a numerical score called potential for the cells in the costmap.
This is stored in the PotentialGrid
which is defined as a nav_grid
.
using PotentialGrid = nav_grid::VectorNavGrid<float>;
The interface that must be implemented consists of up to two methods.
virtual void initialize(ros::NodeHandle& private_nh, nav_core2::Costmap::Ptr costmap,
CostInterpreter::Ptr cost_interpreter);
virtual void updatePotentials(PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal);
The first provides access to the Costmap
/CostInterpreter
. The second is where potentials are actually calculated.
How the potentials are calculated is left to the pluginwriter, but in general, the potential should be zero at the goal
and grow higher from there.
Traceback.
The Traceback
uses the calculated potential to create a path from the start position back to the goal position.
The interface to be implemented has two methods.
virtual void initialize(ros::NodeHandle& private_nh, CostInterpreter::Ptr cost_interpreter);
virtual nav_2d_msgs::Path2D getPath(const PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal,
double& path_cost);
The main thing to note is that the getPath
method returns a Path2D
and also calculates a path_cost
, which is
used when performing path caching.
Path Caching
Sometimes you don't want the global path to change if it doesn't have to. This global planner can cache its most
recently returned plan (assuming the goal stays the same). Whether the old plan or new plan gets returned depends on a
number of different factors.
* If the old plan becomes invalid (navigates through an obstacle), the new plan should be used.
* The relative path_cost
of each of the plans. Generally, if the old plan is still valid, you should never get
a new plan with a higher cost, but its possible depending on the exact plugin configuration.
There are four different configurations with regard to path caching, and when to use the cached path.
 Don't ever use the cached path. This is the standard
nav_core
behavior and is enabled withpath_caching=false
.  Always use the cached plan if it is valid. It doesn't matter how much the new plan might improve the path, stay with
the old path if it is valid.
path_caching=true
andimprovement_threshold<0
 Use the new plan if it is better than the cached plan. This will definitely rerun the planning algorithm each
iteration, and use the new plan if its score according to the traceback is better at all than the old plan.
path_caching=true
andimprovement_threshold=0
. This is very close to configuration #1 but doesn't use new plans if their path cost is equal to or greater than the cached path cost.  Use the new plan if it is significantly better. Require the improvement to be greater than
improvement_threshold
to ensure plans that are minorly better aren't used.path_caching=true
andimprovement_threshold>=0
Base Parameters

potential_calculator
 default:dlux_plugins::AStar

traceback
 default:dlux_plugins::GradientPath

publish_potential
 default: false  Whether to publish the calculated potentials as an OccupancyGrid 
print_statistics
 default: false  If true, will print the number of cells expanded, and the length and number of poses in the path. 
neutral_cost
 default: 50  see above section on weighing costmap 
scale
 default: 3  likewise 
unknown_interpretation
 default:"expensive"
 legal values:["lethal", "expensive", "free"]

path_caching
 default:false

improvement_threshold
 default1.0
The Kernel
One frequent operation that will be performed is to calculate the potential of a particular cell given the value of its neighboring cells. The most straightforward approach is to assign the potential as the minimum possible sum of a neighboring cell's potential and the cost of moving to that cell (i.e. the neutral cost plus the cost in the costmap). However, this approach does not take advantage of the twodimensional structure of the grid. If there are two neighbors with previously calculated potentials, then we may want to combine them for a better potential.
This package provides the kernel_function
class for combining neighboring potentials, which comes from navfn
which in turn comes from
A Light Formulation of the E Interpolated Path Replanner by Philippsen, Roland.
Below, we provide a "brief" mathematical derivation of the calculation.
 For calculating the potential
P
for a cellX
(a.k.a.P(X)
) we will look at the four neighbors of the cellX
, which we'll callA
,B
,C
andD
, whereA
andB
are on the same axis (i.e. above and belowX
) andC
andD
are on the other axis.  The cost of moving to a cell is the cost from the costmap, which we'll call
h
(to match the paper's notation)  We assume, without loss of generality that
 If is infinite, that is, not initialized yet, the new potential calculation is straightforwardly .
 Otherwise, we want to find a value of
P(X)
that satisfies the equation  It's possible there are no real values that satisfy the equation if in which case the straightforward update is used.
 Otherwise, through clever manipulation of the quadratic formula, we can solve the equation with the following:
 That all looks complicated, and computationally inefficient due to the square root operation. Hence, we reformulate the equation in terms of a new variable and calculate a seconddegree Taylor series approximation as
 If you're really interested, you can look into the full derivation
 You can compare these equations on this plot
It is this final approximation that we use in our potential calculation. Although this method has been used since the origins of the nav stack, this is likely the first time the meaning of the constants has ever been documented.
Planner Node
This package also provides a standalone planner node, which will load a costmap from the global_costmap
namespace,
then listen on the /initialpose
and /move_base_simple/goal
topics for the start and goal poses respectively, and
then publish the plan between the two poses as a Path and as Markers.
Wiki Tutorials
Source Tutorials
Dependant Packages
Launch files
Messages
Services
Plugins
Recent questions tagged dlux_global_planner at Robotics Stack Exchange

Package Summary
Tags  No category tags. 
Version  0.3.0 
License  BSD 
Build type  CATKIN 
Use  RECOMMENDED 
Repository Summary
Checkout URI  https://github.com/locusrobotics/robot_navigation.git 
VCS Type  git 
VCS Version  kinetic 
Last Updated  20210108 
Dev Status  DEVELOPED 
CI status  Continuous Integration 
Released  RELEASED 
Tags  No category tags. 
Contributing 
Help Wanted (0)
Good First Issues (0) Pull Requests to Review (0) 
Package Description
Additional Links
Maintainers
 David V. Lu!!
Authors
dlux_global_planner
This package implements a pluginbased global wavefront planner that conforms to the nav_core2
interface. The two
major components that you can plugin are
1. PotentialCalculator
 A function that calculates a numerical score (which we call potential) for some subset
of the cells in the costmap. The potential should be zero at the goal and grow higher from there.
2. Traceback
 A function that uses the potential to trace a path from the start position back to the goal position.
These are loaded via pluginlib
to allow for maximal customizability. This package contains the wrapper code, whereas
the dlux_plugins
package provides a handful of implementations of the plugins.
History
This package is a refactoring for nav_core2
of the global_planner
package
which in turn was a refactoring of the navfn
package. Much of the core implementation
is based on design decisions of the authors of navfn
, for better or for worse.
Weighing the Costmap
There is a fundamental tradeoff in planning between the length of the path and the costs contained within the costmap. This requires two variables. * The first is the neutral cost which is a penalty for moving from one cell to an adjacent cell (a.k.a. the cost for moving a distance equivalent to the grid resolution) * The second is the cost within the cell itself, which may be scaled up or down. Changing how these costs are used will result in possibly different paths. For example, low neutral costs will result in longer paths that avoid high costs. Higher neutral costs will sometimes result in paths that go through high costs if the path is much shorter.
The other key consideration in interpreting the costmap is whether to allow the planner to venture into cells marked
as unknown in the costmap. There are three interpretations possible here.
* LETHAL
 Unknown cells are treated as lethal obstacles and cannot be passed through.
* EXPENSIVE
 Unknown cells are valid, but assigned a high cost.
* FREE
 Unknown cells are valid and given the same weight as free cells.
For convenience, the interpretation of all these costs is contained within the CostInterpreter
class.
Potential Calculation
As mentioned above, the PotentialCalculator
calculates a numerical score called potential for the cells in the costmap.
This is stored in the PotentialGrid
which is defined as a nav_grid
.
using PotentialGrid = nav_grid::VectorNavGrid<float>;
The interface that must be implemented consists of up to two methods.
virtual void initialize(ros::NodeHandle& private_nh, nav_core2::Costmap::Ptr costmap,
CostInterpreter::Ptr cost_interpreter);
virtual void updatePotentials(PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal);
The first provides access to the Costmap
/CostInterpreter
. The second is where potentials are actually calculated.
How the potentials are calculated is left to the pluginwriter, but in general, the potential should be zero at the goal
and grow higher from there.
Traceback.
The Traceback
uses the calculated potential to create a path from the start position back to the goal position.
The interface to be implemented has two methods.
virtual void initialize(ros::NodeHandle& private_nh, CostInterpreter::Ptr cost_interpreter);
virtual nav_2d_msgs::Path2D getPath(const PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal,
double& path_cost);
The main thing to note is that the getPath
method returns a Path2D
and also calculates a path_cost
, which is
used when performing path caching.
Path Caching
Sometimes you don't want the global path to change if it doesn't have to. This global planner can cache its most
recently returned plan (assuming the goal stays the same). Whether the old plan or new plan gets returned depends on a
number of different factors.
* If the old plan becomes invalid (navigates through an obstacle), the new plan should be used.
* The relative path_cost
of each of the plans. Generally, if the old plan is still valid, you should never get
a new plan with a higher cost, but its possible depending on the exact plugin configuration.
There are four different configurations with regard to path caching, and when to use the cached path.
 Don't ever use the cached path. This is the standard
nav_core
behavior and is enabled withpath_caching=false
.  Always use the cached plan if it is valid. It doesn't matter how much the new plan might improve the path, stay with
the old path if it is valid.
path_caching=true
andimprovement_threshold<0
 Use the new plan if it is better than the cached plan. This will definitely rerun the planning algorithm each
iteration, and use the new plan if its score according to the traceback is better at all than the old plan.
path_caching=true
andimprovement_threshold=0
. This is very close to configuration #1 but doesn't use new plans if their path cost is equal to or greater than the cached path cost.  Use the new plan if it is significantly better. Require the improvement to be greater than
improvement_threshold
to ensure plans that are minorly better aren't used.path_caching=true
andimprovement_threshold>=0
Base Parameters

potential_calculator
 default:dlux_plugins::AStar

traceback
 default:dlux_plugins::GradientPath

publish_potential
 default: false  Whether to publish the calculated potentials as an OccupancyGrid 
print_statistics
 default: false  If true, will print the number of cells expanded, and the length and number of poses in the path. 
neutral_cost
 default: 50  see above section on weighing costmap 
scale
 default: 3  likewise 
unknown_interpretation
 default:"expensive"
 legal values:["lethal", "expensive", "free"]

path_caching
 default:false

improvement_threshold
 default1.0
The Kernel
One frequent operation that will be performed is to calculate the potential of a particular cell given the value of its neighboring cells. The most straightforward approach is to assign the potential as the minimum possible sum of a neighboring cell's potential and the cost of moving to that cell (i.e. the neutral cost plus the cost in the costmap). However, this approach does not take advantage of the twodimensional structure of the grid. If there are two neighbors with previously calculated potentials, then we may want to combine them for a better potential.
This package provides the kernel_function
class for combining neighboring potentials, which comes from navfn
which in turn comes from
A Light Formulation of the E Interpolated Path Replanner by Philippsen, Roland.
Below, we provide a "brief" mathematical derivation of the calculation.
 For calculating the potential
P
for a cellX
(a.k.a.P(X)
) we will look at the four neighbors of the cellX
, which we'll callA
,B
,C
andD
, whereA
andB
are on the same axis (i.e. above and belowX
) andC
andD
are on the other axis.  The cost of moving to a cell is the cost from the costmap, which we'll call
h
(to match the paper's notation)  We assume, without loss of generality that
 If is infinite, that is, not initialized yet, the new potential calculation is straightforwardly .
 Otherwise, we want to find a value of
P(X)
that satisfies the equation  It's possible there are no real values that satisfy the equation if in which case the straightforward update is used.
 Otherwise, through clever manipulation of the quadratic formula, we can solve the equation with the following:
 That all looks complicated, and computationally inefficient due to the square root operation. Hence, we reformulate the equation in terms of a new variable and calculate a seconddegree Taylor series approximation as
 If you're really interested, you can look into the full derivation
 You can compare these equations on this plot
It is this final approximation that we use in our potential calculation. Although this method has been used since the origins of the nav stack, this is likely the first time the meaning of the constants has ever been documented.
Planner Node
This package also provides a standalone planner node, which will load a costmap from the global_costmap
namespace,
then listen on the /initialpose
and /move_base_simple/goal
topics for the start and goal poses respectively, and
then publish the plan between the two poses as a Path and as Markers.
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Package Summary
Tags  No category tags. 
Version  0.3.0 
License  BSD 
Build type  CATKIN 
Use  RECOMMENDED 
Repository Summary
Checkout URI  https://github.com/locusrobotics/robot_navigation.git 
VCS Type  git 
VCS Version  melodic 
Last Updated  20210730 
Dev Status  DEVELOPED 
CI status 

Released  RELEASED 
Tags  No category tags. 
Contributing 
Help Wanted (0)
Good First Issues (0) Pull Requests to Review (0) 
Package Description
Additional Links
Maintainers
 David V. Lu!!
Authors
dlux_global_planner
This package implements a pluginbased global wavefront planner that conforms to the nav_core2
interface. The two
major components that you can plugin are
1. PotentialCalculator
 A function that calculates a numerical score (which we call potential) for some subset
of the cells in the costmap. The potential should be zero at the goal and grow higher from there.
2. Traceback
 A function that uses the potential to trace a path from the start position back to the goal position.
These are loaded via pluginlib
to allow for maximal customizability. This package contains the wrapper code, whereas
the dlux_plugins
package provides a handful of implementations of the plugins.
History
This package is a refactoring for nav_core2
of the global_planner
package
which in turn was a refactoring of the navfn
package. Much of the core implementation
is based on design decisions of the authors of navfn
, for better or for worse.
Weighing the Costmap
There is a fundamental tradeoff in planning between the length of the path and the costs contained within the costmap. This requires two variables. * The first is the neutral cost which is a penalty for moving from one cell to an adjacent cell (a.k.a. the cost for moving a distance equivalent to the grid resolution) * The second is the cost within the cell itself, which may be scaled up or down. Changing how these costs are used will result in possibly different paths. For example, low neutral costs will result in longer paths that avoid high costs. Higher neutral costs will sometimes result in paths that go through high costs if the path is much shorter.
The other key consideration in interpreting the costmap is whether to allow the planner to venture into cells marked
as unknown in the costmap. There are three interpretations possible here.
* LETHAL
 Unknown cells are treated as lethal obstacles and cannot be passed through.
* EXPENSIVE
 Unknown cells are valid, but assigned a high cost.
* FREE
 Unknown cells are valid and given the same weight as free cells.
For convenience, the interpretation of all these costs is contained within the CostInterpreter
class.
Potential Calculation
As mentioned above, the PotentialCalculator
calculates a numerical score called potential for the cells in the costmap.
This is stored in the PotentialGrid
which is defined as a nav_grid
.
using PotentialGrid = nav_grid::VectorNavGrid<float>;
The interface that must be implemented consists of up to two methods.
virtual void initialize(ros::NodeHandle& private_nh, nav_core2::Costmap::Ptr costmap,
CostInterpreter::Ptr cost_interpreter);
virtual void updatePotentials(PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal);
The first provides access to the Costmap
/CostInterpreter
. The second is where potentials are actually calculated.
How the potentials are calculated is left to the pluginwriter, but in general, the potential should be zero at the goal
and grow higher from there.
Traceback.
The Traceback
uses the calculated potential to create a path from the start position back to the goal position.
The interface to be implemented has two methods.
virtual void initialize(ros::NodeHandle& private_nh, CostInterpreter::Ptr cost_interpreter);
virtual nav_2d_msgs::Path2D getPath(const PotentialGrid& potential_grid,
const geometry_msgs::Pose2D& start, const geometry_msgs::Pose2D& goal,
double& path_cost);
The main thing to note is that the getPath
method returns a Path2D
and also calculates a path_cost
, which is
used when performing path caching.
Path Caching
Sometimes you don't want the global path to change if it doesn't have to. This global planner can cache its most
recently returned plan (assuming the goal stays the same). Whether the old plan or new plan gets returned depends on a
number of different factors.
* If the old plan becomes invalid (navigates through an obstacle), the new plan should be used.
* The relative path_cost
of each of the plans. Generally, if the old plan is still valid, you should never get
a new plan with a higher cost, but its possible depending on the exact plugin configuration.
There are four different configurations with regard to path caching, and when to use the cached path.
 Don't ever use the cached path. This is the standard
nav_core
behavior and is enabled withpath_caching=false
.  Always use the cached plan if it is valid. It doesn't matter how much the new plan might improve the path, stay with
the old path if it is valid.
path_caching=true
andimprovement_threshold<0
 Use the new plan if it is better than the cached plan. This will definitely rerun the planning algorithm each
iteration, and use the new plan if its score according to the traceback is better at all than the old plan.
path_caching=true
andimprovement_threshold=0
. This is very close to configuration #1 but doesn't use new plans if their path cost is equal to or greater than the cached path cost.  Use the new plan if it is significantly better. Require the improvement to be greater than
improvement_threshold
to ensure plans that are minorly better aren't used.path_caching=true
andimprovement_threshold>=0
Base Parameters

potential_calculator
 default:dlux_plugins::AStar

traceback
 default:dlux_plugins::GradientPath

publish_potential
 default: false  Whether to publish the calculated potentials as an OccupancyGrid 
print_statistics
 default: false  If true, will print the number of cells expanded, and the length and number of poses in the path. 
neutral_cost
 default: 50  see above section on weighing costmap 
scale
 default: 3  likewise 
unknown_interpretation
 default:"expensive"
 legal values:["lethal", "expensive", "free"]

path_caching
 default:false

improvement_threshold
 default1.0
The Kernel
One frequent operation that will be performed is to calculate the potential of a particular cell given the value of its neighboring cells. The most straightforward approach is to assign the potential as the minimum possible sum of a neighboring cell's potential and the cost of moving to that cell (i.e. the neutral cost plus the cost in the costmap). However, this approach does not take advantage of the twodimensional structure of the grid. If there are two neighbors with previously calculated potentials, then we may want to combine them for a better potential.
This package provides the kernel_function
class for combining neighboring potentials, which comes from navfn
which in turn comes from
A Light Formulation of the E Interpolated Path Replanner by Philippsen, Roland.
Below, we provide a "brief" mathematical derivation of the calculation.
 For calculating the potential
P
for a cellX
(a.k.a.P(X)
) we will look at the four neighbors of the cellX
, which we'll callA
,B
,C
andD
, whereA
andB
are on the same axis (i.e. above and belowX
) andC
andD
are on the other axis.  The cost of moving to a cell is the cost from the costmap, which we'll call
h
(to match the paper's notation)  We assume, without loss of generality that
 If is infinite, that is, not initialized yet, the new potential calculation is straightforwardly .
 Otherwise, we want to find a value of
P(X)
that satisfies the equation  It's possible there are no real values that satisfy the equation if in which case the straightforward update is used.
 Otherwise, through clever manipulation of the quadratic formula, we can solve the equation with the following:
 That all looks complicated, and computationally inefficient due to the square root operation. Hence, we reformulate the equation in terms of a new variable and calculate a seconddegree Taylor series approximation as
 If you're really interested, you can look into the full derivation
 You can compare these equations on this plot
It is this final approximation that we use in our potential calculation. Although this method has been used since the origins of the nav stack, this is likely the first time the meaning of the constants has ever been documented.
Planner Node
This package also provides a standalone planner node, which will load a costmap from the global_costmap
namespace,
then listen on the /initialpose
and /move_base_simple/goal
topics for the start and goal poses respectively, and
then publish the plan between the two poses as a Path and as Markers.