# Results From Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

Results video:

## (Modified) KUKA iiwa Results

This is a link to the meshcat recording of the mug organization demo.

## PR2 Results

Below are interactive meshcat recordings of all PR2 plans from the paper Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets, submitted to RSS. This replicates Table I of the paper, with each cell linking to its corresponding meshcat recording. Struckthrough cells indicate that collision(s) are present in the trajectory, and the time stamps corresponding to the collision(s) are included. Both GCS workarounds include their best and worst case results (linked to separate meshcat recordings).

 Experiment GGCS-Planner Drake-Trajopt PRM PRM + Drake-Trajopt GCS-Planner (Joint Limits) GCS-Planner (No Joint Limits) 1T to 1B 1.827 1.803 4.359 1.808 1.828 1.839 1CL to 1CR 2.255 2.204 9.219 2.182 2.239 2.247 1M to 4M 3.875 6.938Left arm t=0.275 Right arm t=5.272 14.554 5.874Right arm t=0.714 Left arm t=4.381 6.482/10.478 3.990/12.589 1CL to 2CR 4.473 5.409Right arm t=2.155 12.110 4.108Right arm t=0.49 4.441/13.815 4.640/13.233 1CL to 3CR 8.182 10.263 15.250 7.166Right arm t=0.7 Right arm t=1.87 Left arm t=2.02 Right arm t=2.77 7.820/12.125 8.501/12.125 1Cl to 4CR 4.382 7.583 17.459 6.088Right arm t=0.27 Left arm t=0.555 Right arm t=4.39 4.728/9.961 4.559/12.418 1T to 4B 4.538 8.781 12.351 5.949Left arm t=0.34 Right arm t=0.68 5.320/14.928 5.473/14.160

## How to Interact with Meshcat Trajectory Recordings

Click and drag the screen to rotate the camera. Holding shift will instead pan the camera. Scroll to zoom in or out.

To adjust playback of the trajectory, click the "Open Controls" button in the top right corner. You will see an image similar to below:

The controls for playback are under the "Animations" menu. "play" and "pause" start and stop the playback from the current timestamp, and "reset" sets the time to 0. "time" indicates the current time of the pose within the trajectory, and "timeScale" controls the playback speed (e.g. 0.5 is half speed). The values for "time" and "timeScale" are text fields, and can be edited directly.