Multimode Design and Analysis of an Integrated Leg-Arm Quadruped Robot with Deployable Characteristics

To improve locomotion and operation integration, this paper presents an integrated leg-arm quadruped robot(ILQR) that has a reconfigurable joint. First, the reconfigurable joint is designed and assembled at the end of the legarm chain. When the robot performs a task, reconfigurable configuration and mode switching can be achieved using this joint. In contrast from traditional quadruped robots, this robot can stack in a designated area to optimize the occupied volume in a nonworking state. Kinematics modeling and dynamics modeling are established to evaluate the mechanical properties for multiple modes. All working modes of the robot are classified, which can be defined as deployable mode, locomotion mode and operation mode. Based on the stability margin and mechanical modeling, switching analysis and evaluation between each mode is carried out. Finally, the prototype experimental results verify the function realization and switching stability of multimode and provide a design method to integrate and perform multimode for quadruped robots with deployable characteristics.

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.

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.

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.

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.

Effect of Spine Motion on Mobility in Quadruped Running

Most of current running quadruped robots have similar construction： a stiff body and four compliant legs. Many researches have indicated that the stiff body without spine motion is a main factor in limitation of robots’ mobility. Therefore, investigating spine motion is very important to build robots with better mobility. A planar quadruped robot is designed based on cheetahs’ morphology. There is a spinal driving joint in the body of the robot. When the spinal driving joint acts, the robot has spine motion; otherwise, the robot has not spine motion. Six group prototype experiments with the robot are carried out to study the effect of spine motion on mobility. In each group, there are two comparative experiments： the spinal driving joint acts in one experiment but does not in the other experiment. The results of the prototype experiments indicate that the average speeds of the robot with spine motion are 8.7%–15.9% larger than those of the robot without spine motion. Furthermore, a simplified sagittal plane model of quadruped mammals is introduced. The simplified model also has a spinal driving joint. Using a similar process as the prototype experiments, six group simulation experiments with the simplified model are conducted. The results of the simulation experiments show that the maximum rear leg horizontal thrusts of the simplified mode with spine motion are 68.2%–71.3% larger than those of the simplified mode without spine motion. Hence, it is found that spine motion can increase the average running speed and the intrinsic reason of speed increase is the improvement of the maximum rear leg horizontal thrust.

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.

Robust force tracking control via backstepping sliding mode control and virtual damping control for hydraulic quadruped robots

In order to improve the force tracking performance of hydraulic quadruped robots in uncertain and unstructured environments,an impedance-based adaptive reference trajectory generation scheme is used.Secondly,in order to improve the robustness to environmental changes and reduce the contact force errors caused by trajectory tracking errors,the backstepping sliding mode controller is combined with the adaptive reference trajectory generator.Finally,a virtual damping control based on velocity and pressure feedback is proposed to solve the problem of contact force disappearance and stall caused by sudden environmental change.The simulation results show that the proposed scheme has higher contact force tracking accuracy when the environment is unchanged;the contact force error can always be guaranteed within an acceptable range when the environment is reasonably changed;when the environment suddenly changes,the drive unit can move slowly until the robot re-contacts the environment.

Learning Gait of Quadruped Robot without Prior Knowledge of the Environment

Walking is the basic skill of a legged robot, and one of the promising ways to improve the walking performance and its adaptation to environment changes is to let the robot learn its walking by itself. Currently, most of the walking learning methods are based on robot vision system or some external sensing equipment to estimate the walking performance of certain walking parameters, and therefore are usually only applicable under laboratory condition, where environment can be pre-defined. Inspired by the rhythmic swing movement during walking of legged animals and the behavior of their adjusting their walking gait on different walking surfaces, a concept of walking rhythmic pattern（WRP） is proposed to evaluate the walking specialty of legged robot, which is just based on the walking dynamics of the robot. Based on the onboard acceleration sensor data, a method to calculate WRP using power spectrum in frequency domain and diverse smooth filters is also presented. Since the evaluation of WRP is only based on the walking dynamics data of the robot＇s body, the proposed method doesn＇t require prior knowledge of environment and thus can be applied in unknown environment. A gait learning approach of legged robots based on WRP and evolution algorithm（EA） is introduced. By using the proposed approach, a quadruped robot can learn its locomotion by its onboard sensing in an unknown environment, where the robot has no prior knowledge about this place. The experimental result proves proportional relationship exits between WRP match score and walking performance of legged robot, which can be used to evaluate the walking performance in walking optimization under unknown environment.

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.

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.

Dynamic stability of quadruped robot walking on slope with trot gait

The dynamic stability of a quadruped robot trotting on slope was analyzed.Compared with crawl gait,trot gait can improve walking speed of quadruped robots.When a quadruped robot trots,each leg is in the alternate state of swing phase or supporting phase,and two legs in the diagonal line are in the same phase.The feet in the supporting phase form a supporting region on the ground.When a quadruped robot walks on slope,the vertical distance from zero moment point(ZMP) to the supporting diagonal line is defined as ZMP offset distance.Whether this distance is less than the maximum offset distance or not,the stability of robot trotting on slope can be judged.The foot trajectory was planned with the sinusoidal function.Based on the kinematic analysis,the ZMP offset distance of quadruped robot under different slope angles,step length and step height was calculated,then the reasonable slope angle,step length and step height for quadruped robot trotting on slope to keep dynamic stability can be determined.On the other hand,the posture angle of quadruped robot should be controlled within the desired range.Computer simulations were executed to verify the theoretical analysis.The study will provide reference for determining reasonable step parameters of the quadruped robot.

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.

Compliant landing of a trotting quadruped robot based on hybrid motion/force robust control

A compliant landing strategy for a trotting quadruped robot on unknown rough terrains based on contact force control is presented. Firstly, in order to lower the disturbance caused by the landing impact force, a landing phase is added between the swing phase and the stance phase, where the desired contact force is set as a small positive constant. Secondly, the joint torque optimization of the stance legs is formulated as a quadratic programming(QP) problem subject to equality and inequality/bound constraints. And a primal-dual dynamical system solver based on linear variational inequalities(LVI) is applied to solve this QP problem. Furthermore, based on the optimization results, a hybrid motion/force robust controller is designed to realize the tracking of the contact force, while the constraints of the stance feet landing angles are fulfilled simultaneously. Finally, the experiments are performed to validate the proposed methods.

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.

Study on the musculoskeletal body for quadruped robots with spinning gait

The walking creatures' athletic ability is related to their body' s musculoskeletal system.A kind of musculoskeletal body for quadruped robots is developed,which will be used to assist the leg mechanism to achieve spinning gait in order to improve the robot mobility in unstructured environment.A bionic-flexible-spine model driven by pneumatic artificial muscles(PAMs) is proposed.Because the body has the flexible property,the robot can achieve spinning gait quickly,which is similar to walking creatures by coordinated movement between body bending and legs side-swing.The kinematics of the bending of the musculoskeletal body and side-swing of leg mechanism of quadruped robot for spinning gait are studied.According to the stability analysis of spinning gait,the relationship between body bending angle and leg swing angle can be determined.The PID controller is designed to conduct the bending experiment,and the bending characteristic of the musculoskeletal body is studied.Experimental results show that the biggest bending angle of the musculoskeletal body can reach 30°.

A gait generation and transition method for quadruped walking machine

In nature, quadrupeds as horses or cats change their gait to be suited to their motion speed. This fact is very important to realize smooth motion with different gaits. In this article a method of the gait transition for the quadruped walking machine is proposed. With analyzing the accustomed gaits of quadruped, some standard gaits and the relationships between duty factor and the phasic differences of the legs corresponding to the first leg could be concluded. With this, the gaits transferring could be continuous. Besides, celerity and on line method for generation and modifying gaits is studied, which can make the robot have a smooth motion to adapt the uncharted rough terrain.