# A Random Sampling-Based Method via Gaussian Process for Motion Planning in Dynamic Environments
## 3 Experiments
### Robot Experiments  
We provide the robot simulations and experiments on a 6-DOF manipulator to evaluate the performance of the DGLP by comparing it with the sampling-based algorithms, i.e., RRT and FMT*. All algorithms are run on the Open Motion Planning Library (OMPL) [27], the Robot Operating System (ROS), the MoveIt, and a computer with a 2.3-GHz Intel Core i7-3610 QE CPU and 8 GB RAM. The position precision and orientation precision are set to  
Figure 5: The DGLP re-plans the local paths online in a dynamic environment. **(a)** The dynamic obstacle is moving from left to right in the environment. **(b)** The dynamic obstacle invalidates a part of the global path and the DGLP provides a local re-planning path online. **(c)** As the movement of the obstacle, the previous local path collides with the obstacle, and a new feasible local path is quickly generated by the DGLP. **(d)** The DGLP samples 100 alternate local paths to select a high-quality collision-free local path. **(e)** The local re-planning path from the DGPL is smooth and its ends all satisfy orientation constraints to merge into the global path smoothly. **(f)** The dynamic obstacle no longer collides with the global path, and thus the global path returns to the original state. 0.001 m and 0.001 rad, respectively. The default OMPL settings are employed for RRT and FMT* in the OMPL. The DGLP parameters \(n_{p}\), \(n_{s}\), and \(v_{a}\) are 1000, 10, and 0.9, respectively. All algorithms run 10 times for the local motion re-planning of the manipulator in the robot simulations and experiments. At the beginning of movement of the manipulator, the obstacle is placed about 10 cm in front of the elbow joint of the initial position of the manipulator as soon as possible. We provide the same global path for all algorithms respectively in the simulations and experiments. After the manipulator starts to move, we add an obstacle in the environment to invalidate part of the global path. Every algorithm has to re-plan a local path as soon as possible to guide the manipulator clear of the obstacle in the dynamic environment. The robot simulation and experiment are shown in Figures 6 and 7, respectively. Table 2 shows the results of the robot simulations and experiments, where Avg. time is the average time of local re-planning and Avg. path cost is the average path length of the manipulator end effector. In terms of local re-planning efficiency, the DGLP is more  
Figure 6: The DGLP provides local re-planning path during the robot simulation. (**a**) The global path of the manipulator. (**b**) The partial invalid path because of the environmental change. (**c**) The local path is planned by the DGLP and merged into the global path. Figure 7: Based on the DGLP method, the manipulator avoids dynamic obstacle online in the robot experiment. outstanding than RRT and FMT*. The average local planning time of the DGLP in the simulation is 0.03 s, which is 97.12% and 93.02% faster than RRT and FMT*, respectively. In the experiment, the average time of the DGLP is 95.56% and 92.31% faster than RRT and FMT*, respectively. By directly sampling local re-planning paths with sparse nodes via the GRPS method, instead of building large-scale random trees, such as RRT and FMT*, the DGLP can rapidly provide feasible local paths, in addition, the lazy collision detection technique further improves the efficiency of local path re-planning. For local re-planning quality, both in the simulation and experiment, the average path costs of FMT* are minimal since FMT* is an asymptotically optimal method that is good at finding high-quality paths, even the optimal paths. The average path costs of the DGLP in the simulation and experiment are 6.89% and 4.85% higher than FMT*, which means that the DGLP has the ability to plan high-quality local paths. The DGLP based on the random sampling paths is able to conveniently sort sampling path candidates by path cost, so as to quickly select the feasible local path with the highest quality from the candidates.