# Optimal Collision-Free Grip Planning for Biped Climbing Robots in Complex Truss Environment
## 5 Gait Interpreter
All the simulations are launched on a desktop with Intel Core i7-7700K CPU and 16 GB RAM, running with the 64-bit operating system Windows 10 Pro. In the simulations, the starting point and the destination are specified manually but arbitrarily, and are highlighted with a green and red sphere, respectively. ### The Result of Operational Region of Negotiating Obstacle

This part of simulations is to verify the effectiveness and efficiency of the computation of operational regions for negotiating obstacles. In the first scene, Climbot is assumed to move on a member, while another member acts as an obstacle. The pose of the obstacle member is randomly generated. Four snapshots of results are shown in Figure 10. In the figure, the segments highlighted in green are the operational regions obtained for surmounting the obstacle member. A collision-free obstacle-negotiating configuration is provided as an illustration of the effectiveness. We changed the pose of the obstacle member 588 times, 305 of which got operational region. The average time consumed in the computation procedure is 0.13 s, and the maximum one is 0.44 s.

We conduct another simulation with a scene consisting of multiple obstacles, to test the applicability of our model to multi-obstacle cases. The simulation result is shown in Figure 11. In this scene, the robot is requested to move from the left end to the right end on _Member 8_, overcoming three groups of obstacles successively. In most cases, a group of obstacles, for example {_Member 1_, \(2\), _3_} or {_Member 4_, _5_} in the figure, should be considered at one shot. Because these obstacles must be overcome once and for all. In other cases, for instance, the robot overcome _Member 6_ and _Member 7_ with two adjacent steps, the operational region can be simply obtained by an intersection operation of the results for negotiating each individual obstacle. However, how to group the obstacle members reasonably is pending for further study. ### The Result of Good Manipulability

This part of simulation is conducted to verify the necessity of considering the manipulability of transition grips. In the simple scenario in Figure 12, three members comprise the climbing environment. The robot is requested to start from _Member 1_, pass _Member 2_ and finally reach _Member 3_. The operational regions for transitions, obtained in the global path planning procedure, are highlighted in green. Figure 11: The results of computing operational regions for negotiating multiple obstacles. Figure 10: The results of computing operational regions for negotiating an obstacle in various pose. The grip planning results with and without consideration of the grip manipulability are shown in the figure, illustrated with transition configurations. The two slightly transparent configurations, corresponding grips on the boundaries of operational regions, are the results without consideration of the grip manipulability. They are very close to the robot's singularity (the \(T_{2}\) joint is close to \(0^{\circ}\)). Further in the gripping procedure, it will affect the ability of the robot to adjust its gripper to align with the target member. As a comparison, the other two configurations represent the results considering the grip manipulability but keeping the number of climbing steps the same. From the figure, we can see that the grips are close to the midpoints of the operational regions. ### The Results of Collision-Free Grip Planning

The simulations in this part are conducted to verify the proposed overall grip planning algorithm. The two scenes used in our previous work, consisting of 9 and 25 members, respectively, are again deployed for simulations. Figures 13 and 14 show us the results. Figure 12: The comparison of determination of transition grips with and without consideration of the grip manipulability. Figure 13: Comparison of results of grip planning with and without consideration of collision avoidance in a scene of 9 members.