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.

Gait Definition and Successive Gait-transition Method Based on Energy Consumption for a Quadruped

In nature,to realize the smooth motion for different speeds,the continuous gait transition is usually required for the quadrupeds.Thus,the gait simulation of quadrupeds is a requisite step to obtain the stable and energy-efficient gait for the walking machines.In this paper,the definitions of the two gait parameters,phasic difference and duty factor are presented,which can determine the gait of the quadrupeds.Then,several typical gaits of the quadrupeds are analyzed such that the seven standard gaits and corresponding parameters are summarized.Additionally,the variance law of the two parameters,which determine the relationship of gait transition,is analyzed.Furthermore,the quadruped gait derivative spectrum (QGDS) is proposed and the gait definition of the quadrupeds is presented.To minimize the power consumption,the choice criterion of gait,the optimal gait in terms of the motion speed,duty factory,and power consumption for the walking machines,is developed.Last,the continuous variance of the gait is implemented by the simulation of the gait transition from walk to trot,which evaluate the choice criterion and transition of gait.

Gait Analysis of Quadruped Robot Using the Equivalent Mechanism Concept Based on Metamorphosis

The previous research regarding the gait planning of quadruped robot focuses on the sequence for lifting o and placing the feet, but neglects the influence of body height. However, body height a ects gait performance significantly, such as in terms of the stride length and stability margin. We herein study the performance of a quadruped robot using the equivalent mechanism concept based on metamorphosis. Assuming the constraints between standing feet and the ground with hinges, the ground, standing legs and robot body are considered as a parallel mechanism, and each swing leg is regarded as a typical serial manipulator. The equivalent mechanism varies while the robot moves on the ground. One gait cycle is divided into several periods, including step forward stages and switching stages. There exists a specific equivalent mechanism corresponding to each gait period. The robot's locomotion can be regarded as the motion of these series of equivalent mechanisms. The kinematics model and simplified model of the equivalent mechanism is established. A new definition of the multilegged robot stability margin, based on friction coe cient, is presented to evaluate the robot stability. The stable workspaces of the equivalent mechanism in the step forward stage of trotting gait under di erent friction coe cients are analyzed. The stride length of the robots is presented by analyzing the relationship between the stable workspaces of the equivalent mechanisms of two adjacent step forward stages in one gait cycle. The simulation results show that the stride length is larger with increasing friction coe cient. We herein propose a new method based on metamorphosis, and an equivalent mechanism to analyze the stability margin and stable workspace of the multilegged robot.

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.

Path planning based on sliding window and variant A* algorithm for quadruped robot

In order to improve the adaptability of the quadruped robot in complex environments,a path planning method based on sliding window and variant A* algorithm for quadruped robot is presented. To improve the path planning efficiency and robot security,an incremental A* search algorithm( IA*) and the A* algorithm having obstacle grids extending( EA*) are proposed respectively. The IA* algorithm firstly searches an optimal path based on A* algorithm,then a new route from the current path to the new goal projection is added to generate a suboptimum route incrementally. In comparison with traditional method solving path planning problem from scratch,the IA* enables the robot to plan path more efficiently. EA* extends the obstacle by means of increasing grid g-value,which makes the route far away from the obstacle and avoids blocking the narrow passage. To navigate the robot running smoothly,a quadratic B-spline interpolation is applied to smooth the path.Simulation results illustrate that the IA* algorithm can increase the re-planning efficiency more than 5 times and demonstrate the effectiveness of the EA* algorithm.

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.

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 method and the improvement of the adaptation of quadruped robots on rough terrain.

Stable Transition of Quadruped Rhythmic Motion Using the Tracking Differentiator

Since the quadruped robot possesses predominant environmental adaptability,it is expected to be employed in nature environments. In some situations,such as ice surface and tight space,the quadruped robot is required to lower the height of center of gravity( COG) to enhance the stability and maneuverability. To properly handle these situations,a quadruped controller based on the central pattern generator( CPG) model,the discrete tracking differentiator( TD) and proportional-derivative( PD) sub-controllers is presented. The CPG is used to generate basic rhythmic motion for the quadruped robot. The discrete TD is not only creatively employed to implement the transition between two different rhythmic medium values of the CPG which results in the adjustment of the height of COG of the quadruped robot,but also modified to control the transition duration which enables the quadruped robot to achieve the stable transition. Additionally,two specific PD sub-controllers are constructed to adjust the oscillation amplitude of the CPG,so as to avoid the severe deviation in the transverse direction during transition locomotion. Finally,the controller is validated on a quadruped model. A tunnel with variable height is built for the quadruped model to travel through. The simulation demonstrates the severe deviation without the PD sub-controllers,and the reduced deviation with the PD sub-controllers.

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.

Simulation Platform of Underwater Quadruped Walking Robot Based on MotionGenesis Kane 5.3 and Central Pattern Generator

It will still in lack of a simulation platform used to learn the walking of underwater quadruped walking robot. In order to alleviate this shortage,a simulation platform for the underwater quadruped walking robot based on Kane dynamic model and CPG-based controller is constructed. The Kane dynamic model of the underwater quadruped walking robot is processed with a commercial package MotionGenesis Kane 5. 3. The forces between the feet and ground are represented as a spring and damper. The relation between coefficients of spring and damper and stability of underwater quadruped walking robot in the stationary state is studied. The CPG-based controller consisted of Central Pattern Generator( CPG) and PD controller is presented,which can be used to control walking of the underwater quadruped walking robot. The relation between CPG parameters and walking speed of underwater quadruped walking robot is investigated. The relation between coefficients of spring and damper and walking speed of underwater quadruped walking robot is studied. The results show that the simulation platform can imitate the stable walking of the underwater quadruped walking robot.

Mechanism of Spine Motion About Contact Time in Quadruped Running

The current research of quadruped robot focuses on the quadruped robot with spine motion. Contact time is a very important part of system performance. However, the mechanism of spine motion about contact time has not been clearly elucidated. In this paper, the e ect of spine motion on contact time is studied deeply from dynamic view.Firstly, a simplified model of the quadruped robot with spine joint is set up, its dynamic equations are derivated, and a method that can generate passive periodic locomotion is proposed. Secondly, according to the vertical spring oscillator model, the two-dimension planar locomotion of the simplified model is regarded as a special vibration in the vertical direction, and the approximate formula of calculating contact time is obtained. Finally, the approximate formula of calculating contact time is verified by the simulation results of passive periodic locomotion, and the e ect of spine motion on contact time is deeply discussed based on the approximate formula of calculating contact time. The discussion proves that spine motion indeed has little e ect on contact time, but spine motion can slightly reduce body pith movement and regulate the leg sti ness in leg contact phase. This research proposes an e ective research method which can be used to study the motion mechanism of the quadruped robot with spine motion,and the mechanism of spine motion about contact time is clearly elucidated which is helpful to set the parameters of mechanical structure and study control algorithm about the quadruped robot with spine motion.

Piezoelectrically Actuated Biomimetic Self-Contained Quadruped Bounding Robot

This paper presents the development of a mesoscale self-contained quadruped mobile robot that employs two pieces ofpiezocomposite actuators for the bounding locomotion.The design of the robot leg is inspired by legged insects and animals,and the biomimetic concept is implemented in the robot in a simplified form,such that each leg of the robot has only one degreeof freedom.The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane.For theimplementation of the self-contained mobile robot,a small power supply circuit is designed and installed on the robot.Experimentalresults show that the robot can locomote at about 50 mm·s-1with the circuit on board,which can be considered as asignificant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators.

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.

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 cosimulation 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.

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 analyzed 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-objective 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.

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.

Qualitative Comparison between Rats and Humans in Quadrupedal and Bipedal Locomotion

Bipedal (Bp) locomotion is one of the most characteristic motor behaviors in human beings. Innate quadrupedal (Qp) four-legged animals also often walk bipedally. The walking posture, however, is significantly different between the two. This suggests that although both have a potential to walk bipedally, however, the human has a body scheme suitable for Bp locomotion, probably its skeletal system. The skeletal system includes the lumbar lordosis, sacral kyphosis, a round pelvis, a large femur neck angle, short feet, and so on. To verify this hypothesis, we compared kinematic and EMG activities between rats and humans during Qp and Bp locomotion on a treadmill belt. The rat is a representative Qp animal, but it is able to acquire Bp walking capability with motor learning. Although the mobile ranges of the hindlimb joint are different during each locomotor pattern between rats and humans, both showed replicable flexion and extension excursion patterns for each joint depending on the locomotor phase. There are many phase-locked EMG bursts between rats and humans during the same walking task and these are observed in the proximal rather than the distal muscles. This suggests that both rats and humans utilize similar neuronal systems for the elaboration of Qp and Bp locomotion. It was interesting that both subjects showed more muscle activities during non-natural locomotor patterns;Qp < Bp for rats and Bp < Qp for humans. This indicates that rat Bp and human Qp walking need more effort and we may be able to find its reason in their skeletal system.

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.