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@@ -40,6 +40,11 @@ Project: Model Predictive Control for obstacle avoidance
 Mentors: Pablo Bustos, Pedro Núñez
 
 1. [Introduction](/web/gsoc/2022/posts/kaustab_pal/1-introduction)
+2. [Community bonding period](/web/gsoc/2022/posts/kaustab_pal/2-community_bonding_period)
+3. [Phase 1](/web/gsoc/2022/posts/kaustab_pal/3-phase_1_coding_period)
+4. [Phase 2](/web/gsoc/2022/posts/kaustab_pal/4-phase_2_coding_period)
+5. [Conclusion](/web/gsoc/2022/posts/kaustab_pal/5-conclusion)
+
 
 ## Swati Dantu
 
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+# GSoC'22 RoboComp project: Model Predictive Control for obstacle avoidance 
+
+08 September 2022
+
+## Phase 2
+
+The phase 2 started from July 25th. The plans for phase 2 are:
+1. Introduce a feature where if the target is given inside an obstacle, the
+   target will automatically be moved to the nearest unoccupied cell.
+2. We discoreved a problem where the agent is unable to pass through narrow
+   corridors. This bug needs to be fixed.
+3. Re-formulating the obstacle avoidance constraints as free-balls [ [Paper] ](
+   https://arxiv.org/abs/1909.08267 ) and implement that as a constraint in the
+   MPC.
+
+## Contribution 1: Move target if it is in occupied cell
+
+During our testing in phase-1, I observed that if the target is given inside an
+occupied cell, the MPC tries to move towards it as one of the cost function of
+the MPC is to minimize the distance between the robot position and the goal
+position. This often leads to the robot crashing as it reeached near the
+obstacle. To fix this issue I first checked if the target and all it's
+neighbouring cells are unoccupied. If even one of the neighbouring 16 cells of
+the target is occupied, I consider the target to be inside a occupied cell and
+move the target to the nearest free cell available. 
+
+The following code snippet is taking care of this:
+
+```C++
+if(neighboors_16(target).size()<16){
+      std::optional<QPointF> new_target = closest_free(target_);
+      target = pointToKey(new_target->x(), new_target->y());
+      std::cout<<"OCCUPIED"<<std::endl;
+ }
+```
+In the video [ [Target in obstacle] ]( https://youtu.be/mq_63IHb0MQ ), you can
+see how the robot performs when the target is given in an obstacle. Before
+fixing this issue, the robot used to crash but now the robot no longer crashes.
+It goes near the obstacle and stops. [ [Pull Request #377] ](
+https://github.com/robocomp/robocomp/pull/377 ) 
+
+## Contribution 2: Passing through narrow corridors
+
+Another problem I found during my phase-1 testing period was that with the
+euclidean distance obstacle avoidance constraints, the robot can't pass through
+narrow corridors. The below image shows that the occupied cells in the map are
+marked overconservatively. In the image, the green lines represent the actual
+obstacle boundaries.
+
+![](assets/narrow_corridor.png)
+
+Because of this overconstrained representation of the obstacles, the MPC was
+unable to come up with a feasible trajectory that can take the robot across the
+corridors. Currently this was happening because given an occupied cell, all it's
+16 neighbouring cells were also marked as obstacles. I fixed this my marking the
+8 neighbouring cells as obstacles instead of 16. 
+
+The below code snippet does is taking care of this:
+
+```C++
+for (auto &&[k, v]: iter::filterfalse([](auto v) { return std::get<1>(v).free; }, fmap))
+{
+    v.cost = 100;
+    v.tile->setBrush(occ_brush);
+    for (auto neighs = neighboors_8(k); auto &&[kk, vv]: neighs)
+    {
+        fmap.at(kk).cost = 100;
+        fmap.at(kk).tile->setBrush(occ_brush);
+    }
+}
+```
+
+In the video [ [Passing through narrow corridors] ](
+https://youtu.be/1x6ngcrBRds ), you can see that the robot can now pass through
+the narrow corridors with the euclidean distance obstacle avoidance constraints.
+We can also observe that the obstacles are now represented in a much less
+conservative way.
+[ [Pull Rrequest #379] ]( https://github.com/robocomp/robocomp/pull/379 ) 
+
+## Contribution 3: Reformulating the obstacle avoidance constraints as freeballs
+
+Suppose we have N obstacles and we are planning for T timesteps into the
+future. Using the euclidean distance obstacle avoidance constraints, for each
+timestep we will have a constraint for each of the N obstacles such that the
+distance between the robot and the obstacle is greater than the sum of the
+radius. Therefore for T timesteps, we will have N\*T constraints. This is a lot
+of constraints and will slow down the computation time. To overcome this , we
+use the freeballs algorithm as mentioned in the paper [ [An NMPC Approach using
+Convex Inner Approximations for Online Motion Planning with Guaranteed Collision
+Avoidance] ]( https://arxiv.org/abs/1909.08267 )  to avoid obstacles. In this
+approach, we first take an initial guess for T centerpoints and and optimize for
+them using a gradient based update rule such that the center points are furthest
+away from the closest obstacle at that timestep. Now for each free ball we draw
+a circle such that it's radius is the distance to the closest obstalce. If the
+distance is above a certain threshold, we take a maximum circle radius defined
+by the user. Once we have the center points and the radius, we add a constraint
+to the MPC formualtion such that the robot always stays inside the circle. With
+this approach, we only have T constraints and because of the decrease in the
+number of constraints the computation time also decreases a lot. 
+
+However this approach is very dependent on the value of the weight variables.
+That is why to improve this, I added the feature that we will do a line search
+for the weight variables and whichever weight will lead to a trajectory that is
+furthest away from all the obstacles will be selected. In my experimentation, I
+observed that we can only search for 3 weight variables after which the
+computation time increases too much to operate safely in the environment.
+
+In the video [ [Free Balls obstacle avoidance with automatic weights tuning] ](
+https://youtu.be/BvM0eflDXGI ), the robot uses the freeballs algorith, with the
+automatic weight search to navigate in the environment with narrow corridors.
+[ [Pull Request #9] ]( https://github.com/robocomp/optimizer/pull/9 ) 
+
diff --git a/gsoc/2022/posts/kaustab_pal/5-conclusion.md b/gsoc/2022/posts/kaustab_pal/5-conclusion.md
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+# GSoC'22 RoboComp project: Model Predictive Control for obstacle avoidance 
+
+08 September 2022
+
+## Detailed report
+
+While the above contributions explain my GSoC'22 work, you can find a more
+detailed explanation along with mathematical explanations here: [ [GSoC'22
+Project Report] ]( https://kaustabpal.github.io/gsoc_22_report ) 
+
+## Future scope
+
+While the free balls algorithm works really well in complex environment, there
+are much to be explored on how we can speed up the computation time to compute
+the trajectories more efficiently. One approach would be to comne up with better
+ways to initialize the optimizer. Another approach can be to make the trajectory
+optimization formulation differentiable. Having a differentiable formulation
+will enable us to integrate the trajectory computation with the perception
+system in an end to end manner.
+
+
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