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--- tutorials:intermediate:costmaps [2019/03/07 11:51] – [Visualization of costmaps] gkazhoya
+++ tutorials:intermediate:costmaps [2019/06/13 11:01] – Added section about height and orientation generators amar
@@ Line 3: / Line 3: @@
 This tutorial demonstrates the location costmap library of CRAM, including its API, examples of existing costmaps and how to write your own new costmaps.
+===== Introduction =====
+If you recall, the resolution of a location designator is divided into two steps - a generation step and a verification step. The generators yield sequences of solution candidates in the form of lazy lists and verification functions accept or reject solutions. The constraints specified with designators normally restrict the solution space but still leave many potentially valid solutions. The process of resolving location designator properties and generating poses in space is split up into three parts in order to deal with the computational complexity of the six-dimensional space of poses and to make a sampling-based approach feasible. Informally, the generation of a pose can be resolved as follows:
+  - Generate a two-dimensional grid based on location designator constraints with values greater than zero for all potentially valid solutions. It is a map representing the solution density of a specific cell where greater values represent more solutions for a specific constraint.
+  - Use the grid as a probability density function to generate random samples.
+  - Use Heuristics to resolve the orientation and Z coordinate of the generated pose.
+  - Use the physics-based reasoning system to prove that the solution is valid.
+As can be seen, the first three steps generate a solution candidate while the last step verifies it.
+Costmaps are density maps of two-dimensional matrices of positive real numbers which allow for representing spacial constraints such as ''on'' or ''in'' but also represent locations from which objects can be reached to a certain extent. Additionally, they can be merged easily and they can be converted to valid probability density functions to be used for sampling. Each entry corresponds to a grid cell in the x-y-plane of the robot's environment. Values of zero indicate that the corresponding grid cell cannot be a solution for the designator to be resolved and values greater than zero indicate potential solution candidates.
+For further reading, refer to section 4 of [[https://mediatum.ub.tum.de/doc/1239461/1239461.pdf|Lorenz Mösenlechner Ph.D. Thesis]].
 ===== Setup =====
@@ Line 92: / Line 103: @@
                      (abs (/ (cl-transforms:x point) vector-length))
 .0d0)))))
-</code>
+</code> To summarize this, we can see that the individual value in the costmap generator is set to the normalized x value of the sampling point if it lies behind the reference point (when x is negative compared to the reference). Else it's set to 0.
   * define order for your costmap function and give it a name:
@@ Line 98: / Line 109: @@
 <code lisp>
 (defmethod location-costmap:costmap-generator-name->score ((name (eql 'behind-cost-function))) 10)
-</code>
+</code> The name of our costmap function would be ''behind-cost-function'' and it's order is 10
   * define the prolog rule for generating costmaps:
@@ Line 114: / Line 125: @@
               (make-behind-cost-function ?ref-x ?ref-y)
               ?costmap)))
-</code>
+</code> In short, the reference x and y is obtained from the pose we have to calculate the ''behind'' relation to. These are then passed on to our previously defined costmap generator, which in turn will generate the costmap we require.
   * resolve a designator with your new awesome costmap:
@@ Line 174: / Line 185: @@
 </code>
+===== Using your own Z coordinate function =====
+So far the costmaps that you have generated/used is set on the 2D XY plane and the Z is taken to be 0 by default. Height generators can also be defined along with the cost functions which determines the z coordinate of the sampled pose from the costmap. There are a couple of ways you can define a height generator for your costmap:
+==== Consistent Height ====
+With this, you can fix the z coordinate to one constant value for all the poses generated. CRAM provides you the method to do this easily. Let's take the example we used above and modify it a little bit.
+<code lisp>
+(prolog:def-fact-group tutorial-rules (location-costmap:desig-costmap)
+  (prolog:<- (location-costmap:desig-costmap ?designator ?costmap)
+    (desig:desig-prop ?designator (:behind ?pose))
+    (location-costmap:costmap ?costmap)
+    (location-costmap:costmap-add-function
+     behind-cost-function
+     (location-costmap:make-range-cost-function ?pose 1.0)
+     ?costmap)
+    (costmap:costmap-add-cached-height-generator
+     (costmap:make-constant-height-function 1.0)
+     ?costmap)))
+</code>
+Notice that the only thing that we added is this particular line:
+<code lisp>
+(costmap:costmap-add-height-generator
+  (costmap:make-constant-height-function 1.0)
+  ?costmap)
+</code>
+The end result is that all the poses generated will now have a z-coordinate of 1.0 units.
+==== Configuring height according to conditions ====
+In a real scenario, not all the z coordinate would be constant, due to terrain differences, obstacles, etc. CRAM allows you to model this similar to how you created your own custom costmap. For this, let's define our own height-generator, as shown below:
+<code lisp>
+(defun positive-y-height-generator ()
+  (lambda (x y)
+    (if (> y 0.0)
+        '(1.0) '(0.0))))
+</code>
+As before, the lambda function will get both x and y as inputs but this time we are expected to return a list of possible heights and a random value out of the satisfied condition list is taken.
+In this example, if y is greater than 0, then the height generator returns 1, else 0 otherwise.
+To use it in our designator, we redefine our fact group again:
+<code lisp>
+(prolog:def-fact-group tutorial-rules (location-costmap:desig-costmap)
+  (prolog:<- (location-costmap:desig-costmap ?designator ?costmap)
+    (desig:desig-prop ?designator (:behind ?pose))
+    (location-costmap:costmap ?costmap)
+    (location-costmap:costmap-add-function
+     behind-cost-function
+     (location-costmap:make-range-cost-function ?pose 1.0)
+     ?costmap)
+    (costmap:costmap-add-height-generator
+     (positive-y-height-generator)
+     ?costmap)))
+</code>
+Note that we only replaced the constant height generator with our own function.
+===== Using your own Orientation Generator =====
+As mentioned in the introduction, the resolution of the designator can also involve resolving an orientation in addition to resolving height and the pose from the costmap. In this section, we will see how we can employ orientation generators to give various poses when resolving a location costmap. This works similar to how we defined and used the height generator, with some minor changes. By default, if no custom orientation generators are used, the system will use it's own identity orientation generator where all the poses will have identity rotation aligned to the reference axis.
+Let's jump into defining and using our own version of an orientation generator:
+<code lisp>
+(defun make-4-orientations-generator ()
+  (lambda (x y previous-orientations)
+    (declare (ignore x y previous-orientations))
+    (mapcar
+     (lambda (angle)
+       (cl-transforms:axis-angle->quaternion
+        (cl-transforms:make-3d-vector 0 0 1)
+        angle))
+     `(0.0 ,(/ pi 2) ,pi ,(- (/ pi 2))))))
+</code>
+Note: Here we will receive a parameter called previous-orientations in addition to x and y, and this parameter can be used to incrementally modify the orientation that are generated. In this particular example, we are not using these parameters, but just creating 4 possible orientations (0, pi/2, pi and -pi/2) regardless of the previous orientation or the current position. The user can make use of these parameters according to their own use-case.
+And finally adding it to the fact-group
+<code lisp>
+(prolog:def-fact-group tutorial-rules (location-costmap:desig-costmap)
+  (prolog:<- (location-costmap:desig-costmap ?designator ?costmap)
+    (desig:desig-prop ?designator (:behind ?pose))
+    (location-costmap:costmap ?costmap)
+    (location-costmap:costmap-add-function
+     behind-cost-function
+     (location-costmap:make-range-cost-function ?pose 1.0)
+     ?costmap)
+    (costmap:costmap-add-height-generator
+     (positive-y-height-generator)
+     ?costmap)
+    (costmap:costmap-add-orientation-generator
+     (make-4-orientations-generator)
+     ?costmap)))
+</code>