Optimal Gait Planning and Thruster Force Allocation for Rough Terrain Climbing of an Underwater Hexapod Robot

The underwater hexapod robot, driven by eight thrusters and six C-shaped legs, can perform complex locomotion tasks such as climbing rough terrain. Unlike conventional point-contact legs, the C-shaped leg rolls on the terrain. The rolling fashion brings significantly complex loop-closure kinematic constraints and complicates the finding of feasible gaits. In addition, when C-shaped legs roll on rough terrain, their contact condition will change in real-time, leading to time-varying contact force, which may result in the leg slipping or even the robot falling. To address the two issues, we propose gait planning and thruster force allocating methods for rough terrain climbing. First, we propose a sampling-based gait planner that extends random trees in task space and finds feasible gaits to fulfill the loop-closure kinematic constraints, which avoids designing the complex sampling and steering procedures in an implicitly-defined manifold. Second, by designing a gait interval-based cost function, we propose an optimal sampling-based planner to find smooth climbing gaits. Third, by establishing a simplified single rigid body (SRB) model, we formulate an optimization problem to allocate thruster forces to guarantee that contact forces cannot lead to the leg slipping. Finally, the effectiveness and practicality of the proposed methods are validated via extensive Gazebo simulations as well as hardware experiments. Note to Practitioners—The motivation for this paper stems from the need to develop a practical rough terrain climbing algorithm for a thruster-assisted underwater hexapod robot that can walk the underwater structure with any dip angles to perform some meticulous small-range operations such as hull cleaning, fracture detection, and damage restoration. However, existing climbing algorithms mainly focus on finding legs’ torques or footsteps for point-contact legged robots. They may fail to be directly used in the underwater robot simultaneously driven by thrusters and C-shaped rolling-contact legs. Then, we propose an optimal gait planning method to find C-shaped legs’ smooth desired rotation angles and an optimal thruster force allocation method to regulate each support leg’s contact force to avoid slipping. Finally, the gait planning method can also be applied to other rolling-contact legged robots, and the thruster force allocation method can help other thruster-assisted legged robots perform complex locomotion tasks.