# A Path Motion Planning For Humanoid Climbing Robot

The paper presents an algorithm for motion planning for humanoid robots in order to climb vertical surfaces. It focuses on developing an autonomous humanoid climbing robot whereas previous research focused mainly on adhesion methods and locomotion of climbing robots. Autonomous means in this context that the robot is able to search for the best climbing route, identify and analyze the holds, and climb up the wall along the selected route (a hold means a point that can be grabbed on the wall). The main application of these humanoid climbing robots would be to help rescue humans in disaster areas. The project is separated into three technical parts: vision part, planning part, and motion part. In the paper, the focus lies on the second part in the form of a motion planning algorithm. The goal of the developed algorithm is to find the best route to climb up walls at each instant hold coordinate. The presented algorithm is a kind of graph algorithm on clustering, and it can analyze whether target holds are useful or not. The algorithm takes into account the specific abilities of the robot, and it is labeled “Right Hand Search Algorithm” (RHSA). Given a robot’s location in known environment, this algorithm can be used to construct a trajectory that connects the start point to the goal point. Then, the robot can follow the trajectory safely. The basic idea of RHSA is to consider only holds that can be reached by the robot’s right hand while the robot keeps balance. When the robot’s right hand hooks into a “Right Hand Reachable Hold” (RHRH), the robot can find at least one hold located in the left hand reachable area, and also find one hold for each legs reachable area. The RHSA algorithm works as follows:

First the whole wall is scanned from each position for RHRHs, taking into account the abilities of the robot in the form of reachable areas for each of its limbs. RHRH is the hold existing in the reachable space of the right hand, and simultaneously at least a group consists of three holds in the reachable spaces for left hand, right foot, and left foot. We call this group the “family hold group”. We note that one RHRH may have many “family hold groups”. A set V is defined as a set of all the right hand reachable holds. Every entry in this set represents a RHRH and can have several elements, each constituting of the 4 positions of the hands and feet. These elements are thus the family hold groups. Two additional sets of RHRHs are defined, the set of all start holds (denoted by St) and the set of all target holds (denoted by Tg).

Second, cost evaluations are made between the RHRHs and a graph of RHRHs is build based on the costs. A RHRH[i] is called “adjacent hold” of RHRH[j] if RHRH[i] and RHRH[j] have at least one similar family hold group. The cost between two RHRHs is the numbers of similar “family hold groups”. Two family hold groups are similar if the positions of the left hand and two feets are equal. Obviously, climbing robots can only move between two RHRHs having one or more similar ”family hold groups” and the more similar family hold groups, the easier it is to go from on RHRH to another. All RHRHs are compared pairwise with each other to determine the number of similar family hold groups and thus the costs between the two members of the pair. From this information, a graph of the RHRHs is created with the RHRHs as nodes. The costs for going from a node to another node is indicated for each line connecting a pair of nodes. The robot can now query this graph to find the easiest way to get from a start hold to a target hold. The easiest way is in this case the path through the graph with the highest cost, since the higher the cost between to RHRHs the easier it is to get from one to the other.