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.

北京2022年冬奥会六足冰壶机器人机构设计与运动规划

When a curling rock slides on an ice sheet with an initial rotation,a lateral movement occurs,which is known as the curling phenomenon.The force of friction between the curling rock and the ice sheet changes continually with changes in the environment;thus,the sport of curling requires great skill and experience.The throwing of the curling rock is a great challenge in robot design and control,and existing curling robots usually adopt a combination scheme of a wheel chassis and gripper that differs significantly from human throwing movements.A hexapod curling robot that imitates human kicking,sliding,pushing,and curling rock rotating was designed and manufactured by our group,and completed a perfect show during the Beijing 2022 Winter Olympics Games.Smooth switching between the walking and throwing tasks is realized by the robot’s morphology transformation based on leg configuration switching.The robot’s controlling parameters,which include the kicking velocity v_(k),pushing velocity v_(p),orientation angle θc,and rotation velocityω,are determined by aiming and sliding models according to the estimated equivalent friction coefficientμ_(equ)and ratio e of the front and back frictions.The stable errors between the target and actual stopping points converge to 0.2 and 1.105 m in the simulations and experiments,respectively,and the error shown in the experiments is close to that of a well-trained wheelchair curling athlete.This robot holds promise for helping ice-makers rectify ice sheet friction or assisting in athlete training.

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.

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.

Kinematic Calibration of a Six-Legged Walking Machine Tool

This paper presents the kinematic calibration of a novel six-legged walking machine tool comprising a six-legged mobile robot integrated with a parallel manipulator on the body.Each leg of the robot is a 2-universal-prismatic-spherical(UPS)and UP parallel mechanism,and the manipulator is a 6-PSU parallel mechanism.The error models of both subsystems are derived according to their inverse kinematics.The objective function for each kinematic limb is formulated as the inverse kinematic residual,i.e.,the deviation between the actual and computed joint coordinates.The hip center of each leg is first identified via sphere fitting,and the other kinematic parameters are identified by solving the objective function for each limb individually using the least-squares method.Thus,the kinematic parameters are partially decoupled,and the complexities of the error models are reduced.A calibration method is proposed for the legged robot to overcome the lack of a fixed base on the ground.A calibration experiment is conducted to validate the proposed method,where a laser tracker is used as the measurement equipment.The kinematic parameters of the entire robot are identified,and the motion accuracy of each leg and that of the manipulator are significantly improved after calibration.Validation experiments are performed to evaluate the positioning and trajectory errors of the six-legged walking machine tool.The results indicate that the kinematic calibration of the legs and manipulator improves not only the motion accuracy of each individual subsystem but also the cooperative motion accuracy among the subsystems.

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.

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.

Adaptive Walking of a Quadrupedal Robot Based on Layered Biological Reflexes

A multiple-legged robot is traditionally controlled by using its dynamic model.But the dynamic-model-based approach fails to acquire satisfactory performances when the robot faces rough terrains and unknown environments.Referring animals＇ neural control mechanisms,a control model is built for a quadruped robot walking adaptively.The basic rhythmic motion of the robot is controlled by a well-designed rhythmic motion controller（RMC） comprising a central pattern generator（CPG） for hip joints and a rhythmic coupler（RC） for knee joints.CPG and RC have relationships of motion-mapping and rhythmic couple.Multiple sensory-motor models,abstracted from the neural reflexes of a cat,are employed.These reflex models are organized and thus interact with the CPG in three layers,to meet different requirements of complexity and response time to the tasks.On the basis of the RMC and layered biological reflexes,a quadruped robot is constructed,which can clear obstacles and walk uphill and downhill autonomously,and make a turn voluntarily in uncertain environments,interacting with the environment in a way similar to that of an animal.The paper provides a biologically inspired architecture,with which a robot can walk adaptively in uncertain environments in a simple and effective way,and achieve better performances.

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.

Optimal Design of a 3-Leg 6-DOF Parallel Manipulator for a Specific Workspace

Researchers seldom study optimum design of a six-degree-of-freedom（DOF） parallel manipulator with three legs based upon the given workspace.An optimal design method of a novel three-leg six-DOF parallel manipulator（TLPM） is presented.The mechanical structure of this robot is introduced,with this structure the kinematic constrain equations is decoupled.Analytical solutions of the forward kinematics are worked out,one configuration of this robot,including position and orientation of the end-effector are graphically displayed.Then,on the basis of several extreme positions of the kinematic performances,the task workspace is given.An algorithm of optimal designing is introduced to find the smallest dimensional parameters of the proposed robot.Examples illustrate the design results,and a design stability index is introduced,which ensures that the robot remains a safe distance from the boundary of sits actual workspace.Finally,one prototype of the robot is developed based on this method.This method can easily find appropriate kinematic parameters that can size a robot having the smallest workspace enclosing a predefined task workspace.It improves the design efficiency,ensures that the robot has a small mechanical size possesses a large given workspace volume,and meets the lightweight design requirements.

Footholds optimization for legged robots walking on complex terrain

This paper proposes a novel continuous footholds optimization method for legged robots to expand their walking ability on complex terrains.The algorithm can efficiently run onboard and online by using terrain perception information to protect the robot against slipping or tripping on the edge of obstacles,and to improve its stability and safety when walking on complex terrain.By relying on the depth camera installed on the robot and obtaining the terrain heightmap,the algorithm converts the discrete grid heightmap into a continuous costmap.Then,it constructs an optimization function combined with the robot’s state information to select the next footholds and generate the motion trajectory to control the robot’s locomotion.Compared with most existing footholds selection algorithms that rely on discrete enumeration search,as far as we know,the proposed algorithm is the first to use a continuous optimization method.We successfully implemented the algorithm on a hexapod robot,and verified its feasibility in a walking experiment on a complex terrain.

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 of piezocomposite 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 degree of freedom.The lack of degree of freedom is compensated by a slope of the robot frame relative to the horizontal plane.For the implementation of the self-contained mobile robot,a small power supply circuit is designed and installed on the robot.Experimental results show that the robot can locomote at about 50 mm·s^(-1)with the circuit on board,which can be considered as a significant step toward the goal of building an autonomous legged robot actuated by piezoelectric actuators.

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.

An online terrain classification framework for legged robots based on acoustic signals

Terrain classification information is of great significance for legged robots to traverse various terrains.Therefore,this communication presents an online terrain classification framework for legged robots,utilizing the acoustic signals produced during locomotion.The Mel-Frequency Cepstral Coefficient(MFCC)feature vectors are extracted from the acoustic data recorded by an on-board microphone.Then the Gaussian mixture models(GMMs)are used to classify the MFCC features into different terrain type categories.The proposed framework was validated on a quadruped robot.Overall,our investigations achieved a classification time-resolution of 1 s when the robot trotted over three kinds of terrains,thus recording a comprehensive success rate of 92.7%.

Posture Control of Legged Locomotion Based on Virtual Pivot Point Concept

This paper presents a novel control approach for achieving robust posture control in legged locomotion,specifically for SLIP-like bipedal running and quadrupedal bounding with trunk stabilization.The approach is based on the virtual pendulum concept observed in human and animal locomotion experiments,which redirects ground reaction forces to a virtual support point called the Virtual Pivot Point(VPP)during the stance phase.Using the hybrid averaging theorem,we prove the upright posture stability of bipedal running with a fixed VPP position and propose a VPP angle feedback controller for online VPP adjustment to improve performance and convergence speed.Additionally,we present the first application of the VPP concept to quadrupedal posture control and design a VPP position feedback control law to enhance robustness in quadrupedal bounding.We evaluate the effectiveness of the proposed VPP-based controllers through various simulations,demonstrating their effectiveness in posture control of both bipedal running and quadrupedal bounding.The performance of the VPP-based control approach is further validated through experimental validation on a quadruped robot,SCIT Dog,for stable bounding motion generation at different forward speeds.

Design and Experiments of a Human-Leg-Inspired Omnidirectional Robotic Leg

Bionic-based robotic legs enable the legged robots with elegant and agile mobility in multi-terrain environment,just like natural living beings.And the smart design could efficiently improve the performance of a robotic leg.Inspired by the simplified human leg structure,we present a 3-DOF robotic leg—OmniLeg,that is capable of making omnidirectional legged locomotion while keeping constant posture of the foot.Additionally,the concentrated drive mode,in which all the motor actuators are installed in the torso and do not move with the leg,minimizes the inertia of the robotic leg.In this paper,the modular design,the kinematics model,the structural analysis,the workspace,and the performance evaluation of the OmniLeg are discussed.Furthermore,we build a prototype based on the proposed design,and the precision of it is verified by the error calibration experiment which is conducted by tracking the trajectory of the prototype’s endpoint.Then,we present an OmniLeg-based single legged mobile robot.The capability of omnidirectional legged locomotion of the OmniLeg is demonstrated by the experiments.

Highly adaptive triboelectric tactile sensor on the foot of autonomous wall-climbing robots for detecting the adhesion state and avoiding the hazard

Due to the excellent maneuverability and obstacle crossing of legged robots,it is possible for an autonomous legged wallclimbing robots to replace manual inspection of ship exterior panels.However,when the magnetic adsorption legged wallclimbing robot steps on the convex point or convex line of the wall,or even when the robot missteps,the robot is likely to detach from the ferromagnetic wall.Therefore,this paper proposes a tactile sensor for the legged magnetic adsorption wall-climbing robot to detect the magnetic adsorption state and improve the safety of the autonomous crawling of the robot.The tactile sensor mainly comprises a three-dimensional(3D)-printed shell,a tactile slider,and three isometric sensing units,with an optimized geometry.The experiment shows that the triboelectric tactile sensor can monitor the sliding depth of the tactile slider and control the light-emitting device(LED)signal light.In addition,in the demonstration experiment of detecting the adsorption state of the robot's foot,the triboelectric tactile sensor has strong adaptability to various ferromagnetic wall surfaces.Finally,this study establishes a robot gait control system to verify the feedback control ability of the triboelectric tactile sensor.The results show that the robot equipped with the triboelectric tactile sensor can recognize the dangerous area on the crawling wall and autonomously avoid the risk.Therefore,the proposed triboelectric tactile sensor has great potential in realizing the tactile sensing ability of robots and enhancing the safety and intelligent inspection of ultra-large vessels.

The Merits of Passive Compliant Joints in Legged Locomotion： Fast Learning, Superior Energy Efficiency and Versatile Sensing in a Quadruped Robot

A quadruped robot with four actuated hip joints and four passive highly compliant knee joints is used to demonstrate the potential of underactuation from two standpoints： learning locomotion and perception. First, we show that： （i） forward locomotion on flat ground can be learned rapidly （minutes of optimization time）; （ii） a simulation study reveals that a passive knee configuration leads to faster, more stable, and more efficient locomotion than a variant of the robot with active knees; （iii） the robot is capable of learning turning gaits as well. The merits of underactuation （reduced controller complexity, weight, and energy consumption） are thus preserved without compromising the versatility of behavior. Direct optimization on the reduced space of active joints leads to effective learning of model-free controllers. Second, we find passive compliant joints with po- tentiometers to effectively complement inertial sensors in a velocity estimation task and to outperform inertial and pressure sensors in a terrain detection task. Encoders on passive compliant joints thus constitute a cheap and compact but powerful sensing device that gauges joint position and force/torque, and -- if mounted more distally than the last actuated joints in a legged robot -- it delivers valuable information about the interaction of the robot with the ground.