Inverted Modelling:An Effective Way to Support Motion Planning of Legged Mobile Robots

This paper presents an effective way to support motion planning of legged mobile robots—Inverted Modelling,based on the equivalent metamorphic mechanism concept.The difference from the previous research is that we herein invert the equivalent parallel mechanism.Assuming the leg mechanisms are hybrid links,the body of robot being considered as fixed platform,and ground as moving platform.The motion performance is transformed and measured in the body frame.Terrain and joint limits are used as input parameters to the model,resulting in the representation which is independent of terrains and particular poses in Inverted Modelling.Hence,it can universally be applied to any kind of legged robots as global motion performance framework.Several performance measurements using Inverted Modelling are presented and used in motion performance evaluation.According to the requirements of actual work like motion continuity and stability,motion planning of legged robot can be achieved using different measurements on different terrains.Two cases studies present the simulations of quadruped and hexapod robots walking on rugged roads.The results verify the correctness and effectiveness of the proposed method.

Smart Gait:A Gait Optimization Framework for Hexapod Robots

The current gait planning for legged robots is mostly based on human presets,which cannot match the flexible characteristics of natural mammals.This paper proposes a gait optimization framework for hexapod robots called Smart Gait.Smart Gait contains three modules:swing leg trajectory optimization,gait period&duty optimization,and gait sequence optimization.The full dynamics of a single leg,and the centroid dynamics of the overall robot are considered in the respective modules.The Smart Gait not only helps the robot to decrease the energy consumption when in locomotion,mostly,it enables the hexapod robot to determine its gait pattern transitions based on its current state,instead of repeating the formalistic clock-set step cycles.Our Smart Gait framework allows the hexapod robot to behave nimbly as a living animal when in 3D movements for the first time.The Smart Gait framework combines offline and online optimizations without any fussy data-driven training procedures,and it can run efficiently on board in real-time after deployment.Various experiments are carried out on the hexapod robot LittleStrong.The results show that the energy consumption is reduced by 15.9%when in locomotion.Adaptive gait patterns can be generated spontaneously both in regular and challenge environments,and when facing external interferences.

Type Design and Behavior Control for Six Legged Robots

The research on legged robots attracted much attention both from the academia and industry. Legged robots are multi-input multi-output with multiple end-e ector systems. Therefore,the mechanical design and control framework are challenging issues. This paper reviews the development of type synthesis and behavior control on legged robots; introduces the hexapod robots developed in our research group based on the proposed type synthesis method. The control framework for legged robots includes data driven layer,robot behavior layer and robot execution layer. Each layer consists several components which are explained in details. Finally,various experiments were conducted on several hexapod robots. The summarization of the type synthesis and behavior control design constructed in this paper would provide a unified platform for communications and references for future advancement for legged robots.

Type Synthesis of Walking Robot Legs

Walking robots use leg structures to overcome obstacles or move on complicated terrains. Most robots of current researches are equipped with legs of simple structure. The specific design method of walking robot legs is seldom studied. Based on the generalized-function(GF) set theory, a systematic type synthesis process of designing robot legs is introduced. The specific mobility of robot legs is analyzed to obtain two main leg types as the goal of design.Number synthesis problem is decomposed into two stages, actuation and constraint synthesis by name,corresponding to the combinatorics results of linear Diophantine equations. Additional restrictions are discussed to narrow the search range to propose practical limb expressions and kinematic-pair designs. Finally, all the fifty-one leg structures of four subtypes are carried out, some of which are chosen to make up robot prototypes, demonstrating the validity of the method. This paper proposed a novel type synthesis methodology, which could be used to systematically design various practical robot legs and the derived robots.

Typical Gait Analysis of a Six-legged Robot in the Context of Metamorphic Mechanism Theory

The equivalent mechanism of the system is often considered as one specific mechanism in most existing studies of multi-legged robots, however the equivalent mechanism is varying while the robot moves on the ground. Four typical tripod period gaits of a radial symmetrical six-legged robot are analyzed. Similar to the metamorphic mechanism, the locomotion of multi-legged robot is considered as a series of varying hybrid serial-parallel mechanisms by assuming the constraints of the feet on the ground with hinges. One gait cycle is divided into several periods, and in different walking period there is a specific equivalent mechanism corresponding to it, and the walking process of multi-legged robot is composed by these series of equivalent mechanisms. Walking performance can be got by analyzing these series of equivalent mechanisms. Kinematics model of the equivalent mechanism is established, workspaces of equivalent mechanisms are illustrated by simulation and a concept of static stability workspace is proposed to evaluate the static stability of these four gaits. A new method to calculate the stride length of multi-legged robots is presented by analyzing the relationship between the workspace of two adjacent equivalent parallel mechanisms in one gait cycle. The stride lengths of four gaits are given by simulations. Comparison of stride length and static stability among these four typical tripod gaits are given. It has been proved that mixed gait and insect-wave gait II have better static stability than mammal kick-off gait and insect-wave gait I. Insect-wave gait II displays its advantage on stride length while the height of robot body lower than 87 mm, mammal kick-off gait has superiority on stride length while the height of robot body higher than 115 mm, and insect-wave gait I shows its shortcoming in stride length. The proposed method based on metamorphic theory and combining the footholds and body height of robot provides a new method to comprehensive analyze the performance of multi-legged robot.

Dynamics and Wheel's Slip Ratio of a Wheel-legged Robot in Wheeled Motion Considering the Change of Height

The existing research on dynamics and slip ratio of wheeled mobile robot （WMR） are derived without considering the effect of height, and the existing models can not be used to analyze the dynamics performance of the robot with variable height while moving such as NOROS- Ⅱ. The existing method of dynamics modeling is improved by adding the constraint equation between perpendicular displacement of body and horizontal displacement of wheel into the constraint conditions. The dynamic model of NOROS- Ⅱ in wheel motion is built by the Lagrange method under nonholonomic constraints. The inverse dynamics is calculated in three different paths based on this model, and the results demonstrate that torques of hip pitching joints are inversely proportional to the height of robot. The relative error of calculated torques is less than 2% compared with that of ADAMS simulation, by which the validity of dynamic model is verified, Moreover, the relative horizontal motion between fore/hind wheels and body is produced when the height is changed, and thus the accurate slip ratio can not be obtained by the traditional equation. The improved slip ratio equations with the parameter of the vertical velocity of body are introduced for fore wheels and hind wheels respectively. Numerical simulations of slip ratios are conducted to reveal the effect of varied height on slip ratios of different wheels. The result shows that the slip ratios of fore/hind wheels become larger/smaller respectively as the height increases, and as the height is reduced, the reverse applies. The proposed research of dynamic model and slip ratio based on the robot height provides the effective method to analyze the dynamics of WMRs with varying height.

Method for Analyzing Articulated Torques of Heavy-duty Six-legged Robot

The accuracy of an articulated torque analysis influences the comprehensive performances of heavy-duty multi-legged robots. Currently, the extremal estimation method and some complex methods are employed to calculate the articulated torques, which results in a large safety margin or a large number of calculations. To quickly obtain accurate articulated torques, an analysis method for the articulated torque is presented for an electrically driven heavy-duty six-legged robot. First, the rearmost leg that experiences the maximum normal contact force is confirmed when the robot transits a slope. Based on the ant-type and crab-type tripod gaits, the formulas of classical mechanics and MATLAB software are employed to theoretically analyze the relevant static torques of the joints. With the changes in the joint angles for the abductor joint, hip joint, and knee joint, variable tendency charts and extreme curves are obtained for the static articulated torques. Meanwhile, the maximum static articulated torques and the corresponding poses of the robot are also obtained. According to the poses of the robot under the maximum static articulated torques, ADAMS software is used to carry out a static simulation analysis. Based on the relevant simulation curves of the articulated torques, the maximum static articulated torques are acquired. A comparative analysis of the maximum static articulated torques shows that the theoretical calculation values are higher than the static simulation values, and the maximum error value is approximately 10%. The proposed method lays a foundation for quickly determining accurate articulated torques to develop heavy-duty six-legged robots.

Human-Tracking Strategies for a Six-legged Rescue Robot Based on Distance and View

Human tracking is an important issue for intelligent robotic control and can be used in many scenarios, such as robotic services and human-robot cooperation. Most of current human-tracking methods are targeted for mobile/tracked robots, but few of them can be used for legged robots. Two novel human-tracking strategies, view priority strategy and distance priority strategy, are proposed specially for legged robots, which enable them to track humans in various complex terrains. View priority strategy focuses on keeping humans in its view angle arrange with priority, while its counterpart, distance priority strategy, focuses on keeping human at a reasonable distance with priority. To evaluate these strategies, two indexes（average and minimum tracking capability） are defined. With the help of these indexes, the view priority strategy shows advantages compared with distance priority strategy. The optimization is done in terms of these indexes, which let the robot has maximum tracking capability. The simulation results show that the robot can track humans with different curves like square, circular, sine and screw paths. Two novel control strategies are proposed which specially concerning legged robot characteristics to solve human tracking problems more efficiently in rescue circumstances.

Explosive Electric Actuator and Control for Legged Robots

Unmanned systems such as legged robots require fast-motion responses for operation in complex envi-ronments.These systems therefore require explosive actuators that can provide high peak speed or high peak torque at specific moments during dynamic motion.Although hydraulic actuators can provide a large force,they are relatively inefficient,large,and heavy.Industrial electric actuators are incapable of providing instant high power.In addition,the constant reduction ratio of the reducer makes it difficult to eliminate the tradeoff between high speed and high torque in a given system.This study proposes an explosive electric actuator and an associated control method for legged robots.First,a high-power-density variable transmission is designed to enable continuous adjustment of the output speed to torque ratio.A heat-dissipating structure based on a composite phase-change material(PCM)is used.An integral torque control method is used to achieve periodic and controllable explosive power output.Jumping experiments are conducted with typical legged robots to verify the effectiveness of the proposed actuator and control method.Single-legged,quadruped,and humanoid robots jumped to heights of 1.5,0.8,and 0.5 m,respectively.These are the highest values reported to date for legged robots powered by electric actuators.

Extended Evolutionary Fast Learn-to-Walk Approach for Four-Legged Robots

Robot locomotion is an active research area. In this paper we focus on the locomotion of quadruped robots. An effective walking gait of quadruped robots is mainly concerned with two key aspects, namely speed and stability. The large search space of potential parameter settings for leg joints means that hand tuning is not feasible in general. As a result walking parameters are typically determined using machine learning techniques. A major shortcoming of using machine learning techniques is the significant wear and tear of robots since many parameter combinations need to be evaluated before an optimal solution is found. This paper proposes a direct walking gait learning approach, which is specifically designed to reduce wear and tear of robot motors, joints and other hardware. In essence we provide an effective learning mechanism that leads to a solution in a faster convergence time than previous algorithms. The results demonstrate that the new learning algorithm obtains a faster convergence to the best solutions in a short run. This approach is significant in obtaining faster walking gaits which will be useful for a wide range of applications where speed and stability are important. Future work will extend our methods so that the faster convergence algorithm can be applied to a two legged humanoid and lead to less wear and tear whilst still developing a fast and stable gait.

Motion Error Compensation of Multi-legged Walking Robots

Existing errors in the structure and kinematic parameters of multi-legged walking robots,the motion trajectory of robot will diverge from the ideal sports requirements in movement.Since the existing error compensation is usually used for control compensation of manipulator arm,the error compensation of multi-legged robots has seldom been explored.In order to reduce the kinematic error of robots,a motion error compensation method based on the feedforward for multi-legged mobile robots is proposed to improve motion precision of a mobile robot.The locus error of a robot body is measured,when robot moves along a given track.Error of driven joint variables is obtained by error calculation model in terms of the locus error of robot body.Error value is used to compensate driven joint variables and modify control model of robot,which can drive the robots following control model modified.The model of the relation between robot＇s locus errors and kinematic variables errors is set up to achieve the kinematic error compensation.On the basis of the inverse kinematics of a multi-legged walking robot,the relation between error of the motion trajectory and driven joint variables of robots is discussed.Moreover,the equation set is obtained,which expresses relation among error of driven joint variables,structure parameters and error of robot＇s locus.Take MiniQuad as an example,when the robot MiniQuad moves following beeline tread,motion error compensation is studied.The actual locus errors of the robot body are measured before and after compensation in the test.According to the test,variations of the actual coordinate value of the robot centroid in x-direction and z-direction are reduced more than one time.The kinematic errors of robot body are reduced effectively by the use of the motion error compensation method based on the feedforward.

Ground substrates classification and adaptive walking through interaction dynamics for legged robots

Adaptive locomotion in different types of surfaces is of critical importance for legged robots.The knowledge of various ground substrates,especially some geological properties,plays an essential role in ensuring the legged robots'safety.In this paper,the interaction between the robots and the environments is investigated through interaction dynamics with the closed-loop system model,the compliant contact model,and the friction model,which unveil the influence of environment's geological characteristics for legged robots'locomotion.The proposed method to classify substrates is based on the interaction dynamics and the sensory-motor coordination.The foot contact forces,joint position errors,and joint motor currents,which reflect body dynamics,are measured as the sensing variables.We train and classify the features extracted from the raw data with a multilevel weighted k-Nearest Neighbor(kNN) algorithm.According to the interaction dynamics,the strategy of adaptive walking is developed by adjusting the touchdown angles and foot trajectories while lifting up and dropping down the foot.Experiments are conducted on five different substrates with quadruped robot FROG-I.The comparison with other classification methods and adaptive walking between different substrates demonstrate the effectiveness of our approach.

Novel Door-opening Method for Six-legged Robots Based on Only Force Sensing

Current door-opening methods are mainly developed on tracked, wheeled and biped robots by applying multi-DOF manipulators and vision systems. However, door-opening methods for six-legged robots are seldom studied, especially using 0-DOF tools to operate and only force sensing to detect. A novel door-opening method for six-legged robots is developed and imple- mented to the six-parallel-legged robot. The kinematic model of the six-parallel-legged robot is established and the model of measuring the positional relationship between the robot and the door is proposed. The measurement model is completely based on only force sensing. The real- time trajectory planning method and the control strategy are designed. The trajectory planning method allows the maximum angle between the sagittal axis of the robot body and the normal line of the door plane to be 45°. A 0-DOF tool mounted to the robot body is applied to operate. By integrating with the body, the tool has 6 DOFs and enough workspace to operate. The loose grasp achieved by the tool helps release the inner force in the tool. Experiments are carried out to validate the method. The results show that the method is effective and robust in opening doors wider than 1 m. This paper proposes a novel door-opening method for six-legged robots, which notably uses a O-DOF tool and only force sensing to detect and open the door.

Kinematics and Dynamics Analysis of a Quadruped Walking Robot with Parallel Leg Mechanism

It is desired to require a walking robot for the elderly and the disabled to have large capacity,high stiffness,stability,etc.However,the existing walking robots cannot achieve these requirements because of the weight-payload ratio and simple function.Therefore,Improvement of enhancing capacity and functions of the walking robot is an important research issue.According to walking requirements and combining modularization and reconfigurable ideas,a quadruped/biped reconfigurable walking robot with parallel leg mechanism is proposed.The proposed robot can be used for both a biped and a quadruped walking robot.The kinematics and performance analysis of a 3-UPU parallel mechanism which is the basic leg mechanism of a quadruped walking robot are conducted and the structural parameters are optimized.The results show that performance of the walking robot is optimal when the circumradius R,r of the upper and lower platform of leg mechanism are 161.7 mm,57.7 mm,respectively.Based on the optimal results,the kinematics and dynamics of the quadruped walking robot in the static walking mode are derived with the application of parallel mechanism and influence coefficient theory,and the optimal coordination distribution of the dynamic load for the quadruped walking robot with over-determinate inputs is analyzed,which solves dynamic load coupling caused by the branches’ constraint of the robot in the walk process.Besides laying a theoretical foundation for development of the prototype,the kinematics and dynamics studies on the quadruped walking robot also boost the theoretical research of the quadruped walking and the practical applications of parallel mechanism.

Static Force Analysis of Foot of Electrically Driven Heavy-Duty Six-Legged Robot under Tripod Gait

The electrically driven six-legged robot with high carrying capacity is an indispensable equipment for planetary exploration, but it hinders its practicability because of its low efficiency of carrying energy. Meanwhile, its load capacity also affects its application range. To reduce the power consumption, increase the load to mass ratio, and improve the stability of robot, the relationship between the walking modes and the forces of feet under the tripod gait are researched for an electrically driven heavy-duty six-legged robot. Based on the configuration characteristics of electrically driven heavy-duty six-legged, the typical walking modes of robot are analyzed. The mathematical models of the normal forces of feet are respectively established under the tripod gait of typical walking modes. According to the MATLAB software, the variable tendency charts are respectively gained for the normal forces of feet. The walking experiments under the typical tripod gaits are implemented for the prototype of electrically driven heavy-duty six-legged robot. The variable tendencies of maximum normal forces of feet are acquired. The comparison results show that the theoretical and experimental data are in the same trend. The walking modes which are most available to realize the average force of distribution of each foot are confirmed. The proposed method of analyzing the relationship between the walking modes and the forces of feet can quickly determine the optimal walking mode and gait parameters under the average distribution of foot force, which is propitious to develop the excellent heavy-duty multi-legged robots with the lower power consumption, larger load to mass ratio, and higher stability.

Free gait generation method for omnidirectional locomotion on abrupt terrain with multi-legged biomimetic robot

In order to achieve omnidirectional locomotion on rough terrain with multi-legged biomimetic robot,a free gait generation approach is proposed based on local rules.The phase coordinates of each operation leg was established according to the motion task and a universal depiction of leg-end locomotion was implemented;the mathematical relation of gait pattern and walking velocity of multi-legged robot was put forward;combined polynomial curve was adopted to generate the leg-end trajectory,which was capable of accomplishing walking missions and accommodating to landform conditions;a distributed network of local rules for gait control was constructed based on a set of local rules operating between adjacent legs.In the simulation experiments,adaptive regulation of inter-leg phase sequence,omnidirectional locomotion and ground accommodation were realized.Moreover,statically stable free gait was obtained simultaneously,which provided multi-legged robot with the capability of walking on irregular terrain reliably and expeditiously.

Research of 6-DOF Serial-Parallel Mechanism Platform for Stability Training of Legged-Walking Robot

The concept of legged-robot stability training with a training platform is proposed and a serial-parallel mechanism platform with 6 degrees of freedom is designed for this target. The designed platform is composed of 4-DOF parallel mechanism with spherical joints and prismatic pairs,and 2-DOF serial mechanism with prismatic pairs. With this design,the platform has advantages of low platform countertop,big workspace,high carrying capacity and high stiffness. On the basis of DOF analysis and computation of space mechanism,weight supporting auxiliary mechanism and raceways-balls supporting mechanism are designed,so as to improve the stiffness of designed large platform and payload capacity of servo motors. And then the whole structure design work of the platform is done. Meanwhile,this paper derives the analytical solutions of forward kinematics, inverse kinematics and inverse dynamics. The error analysis model of position and orientation is established. And then the simulation is done in ADAMS to ensure the correctness and feasibility of this design.

Design and Optimization of Wheel-legged Robot:Rolling-Wolf

Though the studies of wheel-legged robots have achieved great success, the existing ones still have defects in load distribution, structure stability and carrying capacity. For overcoming these shortcomings, a new kind of wheel-legged robot（Rolling-Wolf） is designed. It is actuated by means of ball screws and sliders, and each leg forms two stable triangle structures at any moment, which is simple but has high structure stability. The positional posture model and statics model are built and used to analyze the kinematic and mechanical properties of Rolling-Wolf. Based on these two models, important indexes for evaluating its motion performance are analyzed. According to the models and indexes, all of the structure parameters which influence the motion performance of Rolling-Wolf are optimized by the method of Archive-based Micro Genetic Algorithm（AMGA） by using Isight and Matlab software. Compared to the initial values, the maximum rotation angle of the thigh is improved by 4.17%, the maximum lifting height of the wheel is improved by 65.53%, and the maximum driving forces of the thigh and calf are decreased by 25.5% and 12.58%, respectively. The conspicuous optimization results indicate that Rolling-Wolf is much more excellent. The novel wheel-leg structure of Rolling-Wolf is efficient in promoting the load distribution, structure stability and carrying capacity of wheel-legged robot and the proposed optimization method provides a new approach for structure optimization.

The Kinematics and Force Analysis of a New Leg Mechanism for Multi-legged Wall-Climbing Robot

This paper presents a new kind of leg mechanism with which the wall climbing robot can easily perform the ground to wall transition by itself.To get its walking envelope and limit position,the forward/inverse kinematics and the statics of the mechanism are solved.All of these lay the foundation for ground to wall transition gait programing,mechanism parameter selection and optimization.

STUDY ON THE INCREASE OF SLOPE-WALKING ABILITY OF MULTI－LEGGED ROBOT

The stable slope-walking ability of legged robot walking in any direction on slope is analysed. The contacting angle and leaving angle of leg to the ground are presented. A method to increase the slope-walking ability is proposed only by changing the contacting angle and leaving angle of the leg to the ground.