Merge pull request #2 from FSC-Lab/readme-update

update readme plots

Author: ChaoqinRobotics

.gitignore

@@ -17,4 +17,5 @@ build/*
 **/.csv
 
 # Python cache
-**/.pyc
+__pycache__/
+**/.pyc

README.md

@@ -1,19 +1,19 @@
 # TOGT-Planner
 
-**Time-Optimal Gate-Traversing (TOGT) Planner** is a light-weight racing trajectory generator that can accommondate a broad range of race tracks comprising gates with diverse shapes and sizes. It provides high trajectory quality in terms of dynamically feasibility by employing differential-flat nature of quadrotor systems and incorporating single-rotor thrust constriants.
+**Time-Optimal Gate-Traversing (TOGT) Planner** is a lightweight trajectory generator for racing drones that can accommodate a broad range of race tracks comprising gates with diverse shapes and sizes. It provides high trajectory quality in terms of dynamic feasibility by employing the differential-flat nature of quadrotor systems and incorporating single-rotor thrust constraints.
 
 ## Related Papers
 
-If the TOGT planner helps your academic projects, please cite our paper. Thank you!
+If the TOGT planner helps your academic projects, please cite our papers. Thank you!
 
 - **Time-Optimal Gate-Traversing Planner for Autonomous Drone Racing**, Chao Qin, Maxime SJ Michet, Jingxiang Chen, and Hugh H.-T. Liu,  IEEE International Conference on Robotics and Automation (ICRA-2024)
 
 - **Time-Optimal Planning for Quadrotors: Reaching Constant Computation Costs for Arbitrary Distance**, Chao Qin, Jingxiang Chen, Yifan Lin, Abhishek Goudar, and Hugh H.-T. Liu, (On-going)
 
 ## Updates:
 
-- **Feb. 19, 2024** - First version released
 - **May. 2, 2024** - Add three different variances of the TOGT planner and make the project public
+- **Feb. 19, 2024** - First version released
 
 ## Install on Ubuntu
 
@@ -39,17 +39,16 @@ make
 ```
 
 ## Visualize the TOGT trajectory
-The default race track `race_uzh_7g_multiprisma.yaml` contains 7 gates with different shapes. They are triangle, rectangle, pentagon, rectangle, rectangle, hexagon, and ball gates in order. The resulting lap time is `8.23` s.
+The default race track `race_uzh_7g_multiprisma.yaml` contains 7 gates with different shapes, respectively, triangle, rectangle, pentagon, rectangle, rectangle, hexagon, and ball gates in order. The resulting lap time is `8.23` s.
 ```
 cd ../scripts/plots
 python3 plot_togt_traj.py
-
 ```
 
 ![Alt Text](documents/images/togt_traj.png)
 
 ## Visualize the TOGT-Refined trajectory
-The TOGT trajectory can be refined to reach true time optimality. We take the optimal gate-traveral point as the waypiont, and use the obtained time allocation to compute a proper node number for each segment bewteen two consecutive waypoints. Then, we warm-start the multiple-shooting method with the planned TOGT trajectory. The following python script conducts the refinement for us. The resulting lap time is `7.01` s.
+The TOGT trajectory can be refined to reach true time optimality. We take the optimal gate-traversal point as the waypoint and use the obtained time allocation to compute a proper node number for each segment between two consecutive waypoints. Then, we warm-start the multiple-shooting method with the planned TOGT trajectory. The following Python script conducts the refinement for us. The resulting lap time is `7.01` s.
 ```
 cd ../scripts/togt_refine
 python3 togt_refine.py
@@ -60,7 +59,7 @@ python3 plot_togt_refined_traj.py
 
 ## Visualize the AOS trajectory for waypoint flight
 
-Another example is the Split-S track provided in [this](https://www.science.org/doi/full/10.1126/scirobotics.abh1221) paper. It consists of 19 waypoints in total with a tolerance of 0.3 m for each point. Below is our generated trajectory. The AOS stands for automatic optimal synthesis, a novel framework to address time-optimal planning problem. It is part of the result from the second reference above. It takes around 6 s to solve the minimum-time trajectory that originally requires \~50 minutes in previous methods. The resulting lap time is only 1\~2% longer than the optimal solution. We will provide in-depth analytical analysis in the paper about its distance-insensitive nature. The resulting lap time is `17.93` s while the true optimal is `17.56` s.
+Another example is the Split-S track provided in [this](https://www.science.org/doi/full/10.1126/scirobotics.abh1221) paper. It consists of 19 waypoints in total with a tolerance of 0.3 m for each point. Below is our generated trajectory. The AOS stands for Automatic Optimal Synthesis, a novel framework to address time-optimal planning problems. It is part of the result from the second reference above. It takes around 6 seconds to solve the minimum-time trajectory that originally required \~50 minutes in previous methods. The resulting lap time is only 1\~2% longer than the optimal solution. We will provide an in-depth analytical analysis in the paper about its distance-insensitive nature. The resulting lap time is `17.93` s while the true optimal is `17.56` s.
 
 
 ```
@@ -71,7 +70,7 @@ python3 plot_aos_traj.py
 
 ## Visualize the AOS-TOGT trajectory
 
-The TOGT and AOS planners can be seemly integrated, contributing to a super efficienct and accurate method to solve the time-optimal gate-traversing problem. The code below can visualize the result. The resulting lap time is `16.83` s, which is 4% faster than time-optimal waypoint flights.
+The TOGT and AOS planners can be seamlessly integrated, contributing to a highly efficient and accurate method to solve the time-optimal gate-traversing problem. The code below can visualize the result. The resulting lap time is `16.83` s, which is 4% faster than time-optimal waypoint flights.
 
 ```
 cd ../scripts/plots
@@ -82,7 +81,7 @@ python3 plot_aos_togt_traj.py
 
 ## Acknowledgements
 
-- We use [LBFGS-Lite](https://github.com/ZJU-FAST-Lab/LBFGS-Lite) as the internal solver: An Easy-to-Use Header-Only L-BFGS Solver.
+- We use [LBFGS-Lite: An Easy-to-Use Header-Only L-BFGS Solver](https://github.com/ZJU-FAST-Lab/LBFGS-Lite) as the internal solver.
 - We use [GCOPTER](https://github.com/ZJU-FAST-Lab/GCOPTER) for geometric constraint elimination.
 - We use several utility functions in [Agilicious](https://github.com/uzh-rpg/agilicious) to facilitate development.
 - We refer to [FastFly](https://github.com/BIT-KAUIS/Fast-fly) for the implementation of the multiple shooting method.