# Mechanical Design and Gait Optimization of Hydraulic Hexapod Robot Based on Energy Conservation
## 2 Modeling and Design Process  
As shown in Figure 1, the HHR is designed according to the mammalian structure with a body and six legs. Hexapod robots can walk with different gaits to overcome various terrains and have a higher load-bearing capacity and stability than bipedal and quadrupedal robots [33]. The legs of HHRs adopt the same mechanism, which are designed as a 3 DOF (degree of freedom) structure to meet the hexapod gaits requirements. The area of the middle leg cylinders is twice as much as the others. The driving hydraulic cylinders for the hip joint and knee joint are fixed on the thigh, and the root joint cylinder is set on the pelvis, as shown in Figure 1.  
In this paper, an integrated modeling-optimizing robot design process is proposed where the modeling steps are combined with the optimal structural design process, as shown in Figure 2. The optimization stage formulates the problem based on the modeling stage, and the robot structure is regulated according to the optimal solution.  
Figure 1: Hydraulic hexapod robot.  
Figure 2: Robot modeling and design process.  
The modeling stage starts with geometric modeling, which illustrates the leg structure of the HHR and the relationship between the cylinder and joint angle. The kinematic model is established to find the relation between the foot position and joint angles based on the Denavit-Hartenberg (D-H) homogenous matrix representation. Inverse kinematics and Jacobian matrix of the single leg is derived. By statics modeling, the joint output force and walking stability margin are obtained. Foot trajectory planning is analyzed based on the HHR motion requirement, and the length and velocity of the cylinders are achieved with the geometric and kinematic model. Combined with the above results, the model of the hydraulic driving system is established to calculate the flow rate and pressure for each cylinder as well as the overall energy consumption for the HHR.  
The optimization stage is a process that consists of optimization problem formulation, optimal design solutions, and design sensitivity analysis. In the optimization problem formulation step, flow rate, maximum pressure, and stability margin are defined as objective functions with appropriate constraints. In order to improve computing efficiency, the archive-based micro genetic algorithm (AMGA) is applied to find the optimal design solutions in the next step. Design sensitivity analysis is used to determine the changes needed to regulate the mechanical structure and gait parameter for installation and manufacture requirements. The virtual prototype is employed to prove the optimization result is reasonable and reliable.  
Before modeling the robot, the following preconditions are made:  
1. The robot is walking on a flat surface with triangle gait, and the height change of the robot body's center of mass (COM) is ignored.
2. The payload of the HHR is far more than the leg mass, so gravity and inertial force of the leg components are ignored.
3. When the HHR moves at a constant speed, the ground friction force can be ignored, and the contact force on the foot can be supposed as vertical upward.
4. The pressure of the cylinder chamber is lower than the system pressure and greater than zero.