Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Force Control Compensation Method with Variable Load Stiffness and Damping of the Hydraulic Drive Unit Force Control System

Each joint of hydraulic drive quadruped robot is driven by the hydraulic drive unit（HDU）, and the contacting between the robot foot end and the ground is complex and variable, which increases the difficulty of force control inevitably. In the recent years, although many scholars researched some control methods such as disturbance rejection control, parameter self-adaptive control, impedance control and so on, to improve the force control performance of HDU, the robustness of the force control still needs improving. Therefore, how to simulate the complex and variable load characteristics of the environment structure and how to ensure HDU having excellent force control performance with the complex and variable load characteristics are key issues to be solved in this paper. The force control system mathematic model of HDU is established by the mechanism modeling method, and the theoretical models of a novel force control compensation method and a load characteristics simulation method under different environment structures are derived, considering the dynamic characteristics of the load stiffness and the load damping under different environment structures. Then, simulation effects of the variable load stiffness and load damping under the step and sinusoidal load force are analyzed experimentally on the HDU force control performance test platform, which provides the foundation for the force control compensation experiment research. In addition, the optimized PID control parameters are designed to make the HDU have better force control performance with suitable load stiffness and load damping, under which the force control compensation method is introduced, and the robustness of the force control system with several constant load characteristics and the variable load characteristics respectively are comparatively analyzed by experiment. The research results indicate that if the load characteristics are known, the force control compensation method presented in this paper has positive compensation effects on the load characteristics variation, i.e., this method decreases the effects of the load characteristics variation on the force control performance and enhances the force control system robustness with the constant PID parameters, thereby, the online PID parameters tuning control method which is complex needs not be adopted. All the above research provides theoretical and experimental foundation for the force control method of the quadruped robot joints with high robustness.

Biomimetic Lightweight Design of Legged Robot Hydraulic Drive Unit Shell Inspired by Geometric Shape of Fish Bone Rib Structure

The lightweight design of hydraulic quadruped robots,especially the lightweight design of the leg joint Hydraulic Drive Unit(HDU),can improve the robot's response speed,motion speed,endurance,and load capacity.However,the lightweight design of HDU is a huge challenge due to the need for structural strength.This paper is inspired by the geometric shape of fish bones and biomimetic reinforcing ribs on the surface of the HDU shell are designed to increase its strength and reduce its weight.First,a HDU shell with biomimetic fish bone reinforcing ribs structure is proposed.Then,the MATLAB toolbox and ANSYS finite element analysis module are used to optimize the parameters of the biomimetic reinforcing ribs structure and the overall layout of the shell.Finally,the HDU shell is manufactured using additive manufacturing technology,and a performance testing platform is built to conduct dynamic and static performance tests on the designed HDU.The experimental results show that the HDU with biomimetic fish bone reinforcing ribs has excellent dynamic performance and better static performance than the prototype model,and the weight of the shell is reduced by 20%compared to the prototype model.This work has broad application prospects in the lightweight and high-strength design of closed-pressure vessel components.

Force-controlled Compensation Scheme for P-Q Valve-controlled Asymmetric Cylinder used on Hydraulic Quadruped Robots

Under the requirement of the force controller of hydraulic quadruped robots,the goal of this work is to accurately track the force commands at the level of the hydraulic drive unit.The main contribution focuses on the development of a force-controlled compensation scheme,which is specifically aimed at the key issues affecting the hydraulic quadrupedal locomotion.With this idea,based on a P-Q valve-controlled asymmetric cylinder,we first establish a mathematical model for the hydraulic drive unit force control system.With the desired force commands,a force feed-forward algorithm is presented to improve the dynamic performance of the system.Meanwhile,we propose a disturbance compensation algorithm to reduce the influence induced by external disturbances due to foot-ground impacts.Afterwards,combining with a variable gain PI controller,a series of experiments are implemented on a force control performance test platform to verify the proposed scheme.The results demonstrate that the force-controlled compensation scheme has the ability to notably improve the force tracking accuracy,reduce the response time and redundant force.