# Optimal Collision-Free Grip Planning for Biped Climbing Robots in Complex Truss Environment
## 1 Introduction  
Spatial trusses consisting of members are widely used in the construction of roofs, towers, bridges, and the like. However, so far truss-associated routine tasks such as construction, painting, inspection, maintenance, and so on rely highly on manual labor. These routine tasks are usually high-rise and high-intensity, signifying a great risk to workers' safety. Thus, a kind of biped climbing robot has been designed as an ideal assistant or substitute for human workers carrying out these tasks. Typical representatives of BiCRs include SM2 [1], ROMA [2], Shady3D [3], 3 DCLIMBER [4; 5], PoleClimbingRobot [6] and Treebot [7]. These BiCRs generally comprise of an arm-like serial body for locomotion and grippers at both ends for attachment. Thanks to their biped climbing patterns, BiCRs can agilely move in complex 3D truss environments. Motivated by these characteristics, we also developed a biped climbing robot [8], named Climbot as shown in Figure 1. For the system implementation details and the climbing performance of Climbot, refer to [9]. To complete a given task, for example inspecting the connection reliability of truss joints, BiCRs must be capable of motion planning. Basically, the motion planning of BiCRs consists of grip planning and single-step motion planning [10]. In the grip planning procedure, a list of discrete grip locations, following which robots can navigate from the starting point to the destination, is determined. While in the single-step motion planning procedure, the shifting motion between adjacent grips is generated. It should be noted that not only the grips but also the single-step shifting motion must be free ofcollision. In this paper, we focus on the study of collision-free grip planning, assuming the truss environment is known or captured with integrated sensors such as in [11]. Figure out the grip sequences in a 3D truss environment is challenging for BiCRs. Besides the demand for collision avoidance, grips must satisfy the robot kinematic constraints for continuous cycles of climbing from the point of view of reachability. Furthermore, grips should contribute to the formation of a reasonable combination of various gaits with corresponding step lengths, to save the climbing time and energy. The grip sequences to BiCRs are like the footprint sequences to humanoid robots. Therefore, we can learn from the foot placement problem of humanoid robots that has been addressed in the literature. There are two families of approaches for solving the humanoid robot foot placement problem, which is based on discrete search and continuous optimization, respectively. The discrete search methods normally require a pre-generated set of potential footprints before planning. Then classical methods, such as \(A^{*}\) and RRT, are commonly used for searching. Based on the terrain map and a discrete set of footstep placement positions, [PERSON] [12; 13] presented a global dynamic programming approach using greedy heuristics to plan safe navigation strategies for biped robots moving in obstacle-cluttered environments. [PERSON] et al. [14; 15] used an \(A^{*}\) search algorithm to generate a sequence of collision-free footstep locations to reach a given goal state. A tiered planning strategy was introduced in [16] that split the planner into three layers to traverse different terrain types. [PERSON] et al. [17; 18] presented a global reactive footstep planning strategy based upon a humanistic approach, in which a heuristic cost based on the complexity of stepping motion was used to assign foot placements and an exhaustive search was employed to identify the best path. These approaches can easily handle obstacle avoidance but introduce the trade-off between computational efficiency and solution precision. The continuous optimization approaches operate directly on the poses of the footsteps as continuous decision variables. Thus, it can make up for the precision deficiency of the discrete search methods.