Bionic lightweight design of limb leg units for hydraulic quadruped robots by additive manufacturing and topology optimization

Galloping cheetahs,climbing mountain goats,and load hauling horses all show desirable locomotion capability,which motivates the development of quadruped robots.Among various quadruped robots,hydraulically driven quadruped robots show great potential in unstructured environments due to their discrete landing positions and large payloads.As the most critical movement unit of a quadruped robot,the limb leg unit(LLU)directly affects movement speed and reliability,and requires a compact and lightweight design.Inspired by the dexterous skeleton–muscle systems of cheetahs and humans,this paper proposes a highly integrated bionic actuator system for a better dynamic performance of an LLU.We propose that a cylinder barrel with multiple element interfaces and internal smooth channels is realized using metal additive manufacturing,and hybrid lattice structures are introduced into the lightweight design of the piston rod.In addition,additive manufacturing and topology optimization are incorporated to reduce the redundant material of the structural parts of the LLU.The mechanical properties of the actuator system are verified by numerical simulation and experiments,and the power density of the actuators is far greater than that of cheetah muscle.The mass of the optimized LLU is reduced by 24.5%,and the optimized LLU shows better response time performance when given a step signal,and presents a good trajectory tracking ability with the increase in motion frequency.

Dynamic Bending of Bionic Flexible Body Driven by Pneumatic Artificial Muscles(PAMs) for Spinning Gait of Quadruped Robot

The body of quadruped robot is generally developed with the rigid structure. The mobility of quadruped robot depcnds on the mechanical properties of the body mechanism, It is difficult for quadruped robot with rigid structure to achieve better mobility walking or running in the unstructured environment. A kind of bionic flexible body mechanism for quadruped robot is proposed, which is composed of one bionic spine and four pneumatic artificial muscles（PAMs）. This kind of body imitates the four-legged creatures＇ kinematical structure and physical properties, which has the characteristic of changeable stiff＇hess, lightweight, flexible and better bionics. The kinematics of body bending is derived, and the coordinated movement between the flexible body and legs is analyzed. The relationship between the body bending angle and the PAM length is obtained. The dynamics of the body bending is derived by the floating coordinate method and Lagrangian method, and the driving tbrce of PAM is determined. The experiment of body bending is conductcd, and the dynamic bending characteristic of bionic flexible body is evaluated. Experimental results show that the bending angle of the bionic flexible body can reach 18. An innovation body mechanism for quadruped robot is proposed, which has the characteristic of flexibility and achieve bending by changing gas pressure of PAMs. The coordinated movement of the body and legs can achieve spinning gait in order to improve the mobility of quadruped robot.

Energy Efficiency Analysis of Quadruped Robot with Trot Gait and Combined Cycloid Foot Trajectory

Quadruped robots consume a lot of energy, which is one of the factors restricting their application. Energy efficiency is one of the key evaluating indicators for walking robots. The relationship between energy and elastic elements of walking robots have been studied, but different walking gait patterns and contact status have important influences on locomotion energy efficiency, and the energy efficiency considering the foot-end trajectory has not been reported. Therefore, the energy consumption and energy efficiency of quadruped robot with trot gait and combined cycloid foot trajectory are studied. The forward and inverse kinematics of quadruped robot is derived. The combined cycloid function is proposed to generate horizontal and vertical foot trajectory respectively, which can ensure the acceleration curve of the foot-end smoother and more successive, and reduce the contact force between feet and environment. Because of the variable topology mechanism characteristic of quadruped robot, the leg state is divided into three different phases which are swing phase, transition phase and stance phase during one trot gait cycle. The non-continuous variable constraint between feet and environment of quadruped robot is studied. The dynamic model of quadruped robot is derived considering the variable topology mechanism characteristic, the periodic contact and elastic elements of the robot. The total energy consumption of walking robot during one gait cycle is analyzed based on the dynamic model. The specific resistance is used to evaluate energy efficiency of quadruped robot. The calculation results show the relationships between specific resistance and gait parameters, which can be used to determine the reasonable gait parameters.

Gait Planning for a Quadruped Robot with One Faulty Actuator

Fault tolerance is essential for quadruped robots when they work in remote areas or hazardous environments. Many fault-tolerant gaits planning method proposed in the past decade constrained more degrees of freedom（DOFs） of a robot than necessary. Thus a novel method to realize the fault-tolerant walking is proposed. The mobility of the robot is analyzed first by using the screw theory. The result shows that the translation of the center of body（CoB） can be kept with one faulty actuator if the rotations of the body are controlled. Thus the DOFs of the robot body are divided into two parts： the translation of the CoB and the rotation of the body. The kinematic model of the whole robot is built, the algorithm is developed to actively control the body orientations at the velocity level so that the planned CoB trajectory can be realized in spite of the constraint of the faulty actuator. This gait has a similar generation sequence with the normal gait and can be applied to the robot at any position. Simulations and experiments of the fault-tolerant gait with one faulty actuator are carried out. The CoB errors and the body rotation angles are measured. Comparing to the traditional fault-tolerant gait they can be reduced by at least 50%. A fault-tolerant gait planning algorithm is presented, which not only realizes the walking of a quadruped robot with a faulty actuator, but also efficiently improves the walking performances by taking full advantage of the remaining operational actuators according to the results of the simulations and experiments.

Development of a Biomimetic Quadruped Robot

This paper presents the design and prototype of a small quadruped robot whose walking motion is realized by two piezocomposite actuators. In the design, biomimetic ideas are employed to obtain the agility of motions and sustainability of a heavy load. The design of the robot legs is inspired by the leg configuration of insects, two joints （hip and knee） of the leg enable two basic motions, lifting and stepping. The robot frame is designed to have a slope relative to the horizontal plane, which makes the robot move forward. In addition, the bounding locomotion of quadruped animals is implemented in the robot. Experiments show that the robot can carry an additional load of about 100 g and run with a fairly high velocity. The quadruped prototype can be an important step towards the goal of building an autonomous mobile robot actuated by piezocomposite actuators.

NOVEL FORMULATION OF STATIC STABILITY FOR A WALKING QUADRUPED ROBOT

By defining the static stable area for foot placement, a new approach toanalysis of quadruped robot stability is presented. Unlike conventionally, the method avoids solvingcomplicated direct kinematics of quadruped robot and shows the information on the robot stabilityand the selection of swing leg. Especially, the proposed algorithm can be used as real-timeoperation for on-line gait generation and control for quadruped robots. The effectiveness of theproposed approach is shown through a practical crawling experiment of the quadruped robotTITAN-VIII.

Bionic Quadruped Robot Dynamic Gait Control Strategy Based on Twenty Degrees of Freedom

Quadruped robot dynamic gaits have much more advantages than static gaits on speed and efficiency, however high speed and efficiency calls for more complex mechanical structure and complicated control algorithm. It becomes even more challenging when the robot has more degrees of freedom.As a result, most of the present researches focused on simple robot, while the researches on dynamic gaits for complex robot with more degrees of freedom are relatively limited. The paper is focusing on the dynamic gaits control for complex robot with twenty degrees of freedom for the first time. Firstly, we build a relatively complete 3 D model for quadruped robot based on spring loaded inverted pendulum(SLIP) model, analyze the inverse kinematics of the model, plan the trajectory of the swing foot and analyze the hydraulic drive. Secondly, we promote the control algorithm of one-legged to the quadruped robot based on the virtual leg and plan the state variables of pace gait and bound gait. Lastly, we realize the above two kinds of dynamic gaits in ADAMS-MATLAB joint simulation platform which testify the validity of above method.

Co-simulation of a quadruped robot's mechanical and hydraulic systems based on ADAMS and AMESim

In order to observe the change and fluctuation in flow and pressure of a hydraulic quadruped robot＇s hydraulic system when the robot walks on trot gait,a co-simulation method based on ADAMS and AMESim is proposed. Firstly,the change rule in each swing angle of the hydraulic quadruped robot＇s four legs is analyzed and converted to the displacement change of the hydraulic cylinder by calculating their geometric relationship.Secondly,the robot＇s dynamic model is built in ADAMS and its hydraulic and control system models are built in AMESim. The displacement change of the hydraulic cylinder in the hydraulic system is used as the driving function of the dynamics model in ADAMS,and the driving force of the dynamics model is used as the loads of the hydraulic system in AMESim. By introducing the PID closed-loop control in the control system,the co-simulation between hydraulic system and mechanical system is implemented. Finally,the curve of hydraulic cylinders＇ loads,flow and pressure are analyzed and the results show that they fluctuate highly in accordance with the real situation. The study provides data support for the development of a hydraulic quadruped robot＇s physical prototype.

Bionic Design and Analysis of a Novel Quadruped Robot with a Multistage Buffer System

Large quadruped mammals,such as ruminants,have outstanding motion ability,including running and bounding.These advanced motion abilities are related to the buffer effect of their complicated musculoskeletal systems.However,the buffer effect of most bio-robots is not satisfactory owing to the simple design of their buffer systems.In this paper,a physiological analysis of the ruminant musculoskeletal system is presented to explain the intrinsic buffer mechanism of motion.Based on the physical buffer parts of the ruminant limbs,the corresponding bionic mappings were determined.These mappings were used to guide the mechanism design of the robot multistage buffer system.The multistage buffer system includes two main buffer mechanisms:the first stage and the second stage.The buffer mechanism analysis of the first stage and multiple stages is discussed in theory to compare the effects between the normal single buffer system and the novel multistage buffer system.Then,the detailed mechanical structure of the limbs was designed based on the limb mechanism design.To further verify the superior efficacy of the multistage buffer system,the corresponding walking simulation experiments were conducted after the virtual prototype of a quadruped robot with a novel limb was built completely.Both theoretical analysis and simulation experiments prove that the bionic robot design with the novel multistage buffer system achieves better motion performance than the traditional robot buffer design and can be regarded as the design template of the robot limb.

Inter-limb and intra-limb coordination control of quadruped robots

To realize the coordinated and stable rhythmic motion of quadruped robots （QRs）, the locomotion control method of QRs based on central pattern generator （CPG） was explored. In tradi- tional control strategies based on CPG, few CPG models care about the intra-limb coordination of QRs, and the durations of stance phase and swing phase are always equal. In view of these deficien- cies, a new and simpler multi-joint coordinated control method for both inter-limb and intra-limb was proposed in this paper. A layered CPG control network to realize the locomotion control of QRs was constructed by using modified Hopf oscillators. The coupled relationships among hip joints of all limbs and between hip joint and knee joint within a limb were established. Using the co-simulation method of ADAMS and MATLAB/Simulink, various gait simulation experiments were carried out and the effectiveness of the designed control network was tested. Simulation results show that the pro- posed control method is effective for QRs and can meet the control requirements of QRs＇ gaits with different duty factors.

Continuous and smooth gait transition in a quadruped robot based on CPG

To improve the smoothness of motion control in a quadruped robot, a continuous and smooth gait transition method based on central pattern generator （CPG） was presented to solve the unsmooth or failed problem which may result in phase-locked or sharp point with direct replacement of the gait matrix. Through improving conventional weight matrix, a CPG network and a MATLAB/ Simulink model were constructed based on the Hopf oscillator for gait generation and transition in the quadruped robot. A co-simulation was performed using ADAMS/MATLAB for the gait transition between walk and trot to verify the correctness and effectiveness of the proposed CPG gait generation and transition algorithms. Related methods and conclusions can technically support the motion control technology of the quadruped robot.

Fuzzy adaptive PID control on hydraulic servo system of quadruped robot

Quadruped robot driven by high power density hydraulic device works in unstructured en- vironment. With variable load and various external disturbance, the hydraulic servo system has fea- tures such as nonlinear, time-varying parameters. Traditional control method has some limitation. In order to help the hydraulic servo system of the quadruped robot to adapt to harsh environments, and to obtain high control quality and control precision, an incremental fuzzy adaptive PID controller based on position feedback is designed to solve the related technical problems. Matlab/Simulink sim- ulation and experimental results show that the incremental fuzzy adaptive PID controller improves the dynamic performance of the system, enhances the respond speed and precision of the hydraulic ser- vo system, and has some theory significance and practical value.

Stable walking of quadruped robot on unknown rough terrain

Quadruped robot is considered to be the most practical locomotion machine to negotiate uneven terrain, and shows superb stability during static walking. To improve the ability to go over rough terrain, this paper is focused on the stable walking and balance control of quadruped robots. 24 kinds of walking gaits are analyzed in order to derive the most stable and smoothest walking gait. Considering the inefficiency to model a terrain by its specified appearance, a uniform terrain model is established and by means of kinematic analysis, a method to adjust the body posture and center of gravity （COG） height is presented. Simulations demonstrate the effectiveness of the proposed meth- od and the improvement of the adaptation of quadruped robots on rough terrain.

Design of trotting controller for the position-controlled quadruped robot

This work presents a controller designed for position-controlled quadrupedal dynamic locomotion,aiming at simple and robust trotting control. The controller takes the torso attitude angles and velocities into planning foot trajectories. Firstly design of the servo motor actuated quadruped robot is introduced and the kinematic equations are deduced. Then a scheme is presented for controlling the robot torso attitude based on the virtual leg model. Furthermore,it demonstrates the design of the controller which enables the robot to have a wide range of trotting gaits and omni-directional motions. Finally,results of robust trotting in various speeds,path tracking and push recovery in simulation are reported,and results of trotting on real quadruped robots will be studied.

Joint space compliance control for a hydraulic quadruped robot based on force feedback

In the realm of quadruped robot locomotion,compliance control is imperative to handle impacts when negotiating unstructured terrains.At the same time,kinematic tracking accuracy should be guaranteed during locomotion.To meet both demands,ajoint space compliance controller is designed,so that compliance can be achieved in stance phase while position tracking performance can be guaranteed in swing phase.Unlike operational space compliance control,the joint space compliance control method is easy to implement and does not depend on robot dynamics.As for each joint actuator,high performance force control is of great importance for compliance design.Therefore,a nonlinear PI controller based on feedback linearization is proposed for the hydraulic actuator force control.Besides,an outer position loop（compliance loop）is closed for each joint.Experiments are carried out to verify the force controller and compliance of the hydraulic actuator.The robot leg compliance is assessed by a virtual prototyping simulation.

Gait planning and intelligent control for a quadruped robot

We present a method for designing free gaits for a structurally symmetrical quadruped robot capable of performing statically stable, omnidirectional walking on irregular terrain. The robot＇s virtual model is constructed and a control algorithm is proposed by applying virtual components at some strategic locations. The deliberative-based controller can generate flexible sequences of leg transferences while maintaining walking speed, and choose optimum foothold for moving leg based on integration data of exteroceptive terrain profile. Simulation results are presented to show the gait＇s efficiency and system＇s stability in adapting to an uncertain terrain.

Turning methods for quadruped robot with two degrees of freedom per leg

With the target at simplicity like facilitating the mechanical system,the quadruped robots usually have limited degrees of freedom per leg.Addressing the robot whose legs have only two degrees of freedom,this paper explores several turning strategies including altering the median value,changing the phase difference,and modifying the amplitude.The insights of the proposed methods are that we break down the symmetries which exist during the process of the robot locomotion and rebuild them.Since we probe into the turning feasibility from the points of the median value,phase difference and amplitude in the sine functions,these turning methods are feature of universality.In order to evaluate these methods,this paper presents a new way to weigh the stability,which can be easily applied to practical robots.Experiments demonstrate that the quadruped turns around with little effort and endeavor.

Multi-objective optimization design for leg mechanism of hydraulic-actuated quadruped robot

In order to improve the robot＇ s abilities of bearing heavy burdens and transporting in complex terrains, the multi-objective optimization design for leg mechanism of the quadruped robot with hydraulic actuated is studied in this paper. The kinematics and dynamics of the robot are ana- lyzed and the two-dimensional linear inverted pendulum model is adopted in planning the trajectories of joints. Then the mathematical model of valve-controlled asymmetric cylinder and control model of single leg are proposed respectively. In the end, NSGA-Ⅱ algorithm is used to achieve the multi^ob- jective optimization design of parameters concerning single leg mechanism and PD torque control. The results prove that the optimized leg mechanism can significantly reduce the required maximum power of hydraulic system, thus decrease its own weight and lead to the obtaining of good dynamic performance.

A desired landing points walking method enablinga planner quadruped robot to walk on rough terrain

It is necessary for legged robots to walk stably and smoothly on rough terrain.In this paper,a desired landing points(DLP) walking method based on preview control was proposed in which an off-line foot motion trace and an on-line modification of the trace were used to enable the robot to walk on rough terrain.The on-line modification was composed of speed modification,foot lifting-off height modification,step length modification,and identification and avoidance of unsuitable landing terrain.A planner quadruped robot simulator was used to apply the DLP walking method.The correctness of the method was proven by a series of simulations using the Adams and Simulink.

Slope Terrain Locomotion Control of a Quadruped Robot Based on Biological Reflex CPG Model

Inspired by the neuronal principles underlying the tetrapod locomotion,this paper proposed a biomimetic vestibular reflex central pattern generator（ CPG） model to improve motion performance and terrain adaptive ability of a quadruped robot in complex situations,which is on the basis of central pattern generator（ CPG） model constructed by modified Hopf oscillators. The presented reflex model was modified in the light of the particular joint configuration of the quadruped robot and the trot gait pattern. Focusing on slop locomotion of the quadruped robot with trot gaits,the cosimulations of the ADAMS virtual prototype,CPG mathematical expressions with vestibular reflex and Simulink control model were conducted. The simulation results demonstrated that the presented CPG controller with vestibular reflex was more efficient and stable for the quadruped robot trotting on slopes,c ompared with the different trotting control models.