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.

Task-Oriented Topology System Synthesis of Reconfigurable Legged Mobile Lander Integrating Active and Passive Metamorphoses

To explore hostile extraterrestrial landforms and construct an engineering prototype,this paper presents the task-oriented topology system synthesis of reconfigurable legged mobile lander(ReLML)with three operation modes from adjusting,landing,to roving.Compared with our preceding works,the adjusting mode with three rotations(3R)provides a totally novel exploration approach to geometrically matching and securely arriving at complex terrains dangerous to visit currently;the landing mode is redefined by two rotations one translation(2R1T),identical with the tried-and-tested Apollo and Chang'E landers to enhance survivability via reasonable touchdown buffering motion;roving mode also utilizes 2R1T motion for good motion and force properties.The reconfigurable mechanism theory is first brought into synthesizing legged mobile lander integrating active and passive metamorphoses,composed of two types of metamorphic joints and metamorphic execution and transmission mechanisms.To reveal metamorphic principles with multiple finite motions,the finite screw theory is developed to present the procedure from unified mathematical representation,modes and source phase derivations,metamorphic joint and limb design,to final structure assembly.To identify the prototype topology,the 3D optimal selection matrix method is proposed considering three operation modes,five evaluation criteria,and two topological subsystems.Finally,simulation verifies the whole task implementation process to ensure the reasonability of design.

Design and Analysis of a Multi-Legged Robot with Pitch Adjustive Units

The paper proposes a novel multi-legged robot with pitch adjustive units aiming at obstacle surmounting.With only 6 degrees of freedom,the robot with 16 mechanical legs walks steadily and surmounts the obstacles on the complex terrain.The leg unit with adjustive pitch provides a large workspace and empowers the legs to climb up obstacles in large sizes,which enhances the obstacle surmounting capability.The pitch adjustment in leg unit requires as few independent adjusting actuators as possible.Based on the kinematic analysis of the mechanical leg,the biped and quadruped leg units with adjustive pitch are analyzed and compared.The configuration of the robot is designed to obtain a compact structure and pragmatic performance.The uncertainty of the obstacle size and position in the surmounting process is taken into consideration and the parameters of the adjustments and the feasible strategies for obstacle surmounting are presented.Then the 3D virtual model and the robot prototype are built and the multi-body dynamic simulations and prototype experiments are carried out.The results from the simulations and the experiments show that the robot possesses good obstacle surmounting capabilities.

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.

Dynamic Modeling and Analysis of 9-DOF Omnidirectional Legged Vehicle

The omnidirectional legged vehicle with steering-rails has a specific mechanism feature, and it can be controlled flexibly and accurately in omnidirectional motion. Currently there lacks further research in this area. In this paper, the mechanical characteristics of independent walking control and steering control and its kinematics principle are introduced, and a vehicle has a composite motion mode of parallel link mechanism and steering mechanism is presented. The motion direction control of the proposed vehicle is only dependant on its steering rails, so its motion is simple and effective to control. When the relative motion between the walking and steering is controlled cooperatively, the vehicle can walk perfectly. By controlling the steering rails, the vehicle can walk along arbitrary trajectory on the ground. To achieve a good result of motion control, an equivalent manipulator model needs to be built. In terms of the mechanism feature and the kinematic principle, the simplified manipulator model consists of a rail in stance phase, a rail in swing phase, and an equivalent leg. Considering the ground surface slope during walking, a parameter of inclination angle is added. Based on such a RPP manipulator model, the equations of motion are derived by means of Lagrangian dynamic approach. To verify the dynamic equations, the motion of the manipulator model is simulated based on linear and nonlinear motion planning. With the same model and motion parameters, the dynamic equations can be solved by Matlab and the calculation data can be gained. Compared with the simulation data, the result confirms the manipulator dynamic equations are correct. As a result of such special characteristics of the legged mechanism with steering rails, it has a potential broad application prospects. The derivation of dynamics equation could benefit the motion control of the mechanism.

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.

Motion design of a hybrid wheeled/legged robot for lunar exploration

The robot consists of a quadruped mechanism and two active dual-wheel casters possesses the advantages of wheeled and legged mechanism, and can quickly move on the relatively plane ground with the wheeled mechanism, and can walk on the extremely uneven terrain with the legged mechanism. The effectiveness of the motion design of the hybrid robot is iHustrated by simulation results.

A Novel One-legged Robot: Cyclic Gait Synthesis via Optimization

A cyclic flip gait is designed for a novel one legged robot in the paper. Trajectory synthesis of the flip gait is formulized as a problem of numerical optimization subject to nonlinear second order constraints such as positive reaction force of ground and finite torque of the joints. The simulation results are given.

Proposal of Walking to Prevent a Fall of a Planetary Exploration Legged Rover Using Effect of Loose Soil Caused by a Propagation of Vibration

In this study,a walking method that prevents a fall of the planetary exploration-legged rover is proposed.In the proposed walking method,the leg is sunk by giving vibration to the ground.The posture of the rover is changed to prevent a fall of the rover by sinking the leg.First,the relationship between the kind of vibration and the subsidence of the leg is confirmed.In this experimental result,the leg is shown to be easy to sink to the ground by giving vibration.Moreover,the larger the vibratory force is,the easier the leg sinks to the ground.Finally,the legged testbed walks on the loose ground with a slope using the proposed walking method.In this experimental result,the testbed is difficult to fall down when it uses the proposed walking.Moreover,the angle of a slope that the testbed can walk becomes large by using the proposed walking.

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.

Development of Wheel-Legged Biped Robots:A Review

The wheel-legged biped robot is a typical ground-based mobile robot that can combine the high velocity and high efficiency pertaining to wheeled motion and the strong,obstacle-crossing performance associated with legged motion.These robots have gradually exhibited satisfactory application potential in various harsh scenarios such as rubble rescue,military operations,and wilderness exploration.Wheel-legged biped robots are divided into four categories according to the open–close chain structure forms and operation task modes,and the latest technology research status is summarized in this paper.The hardware control system,control method,and application are analyzed,and the dynamic balance control for the two-wheel,biomimetic jumping control for the legs and whole-body control for integrating the wheels and legs are analyzed.In summary,it is observed that the current research exhibits problems,such as the insufficient application of novel materials and a rigid–flexible coupling design;the limited application of the advanced,intelligent control methods;the inadequate understanding of the bionic jumping mechanisms in robot legs;and the insufficient coordination ability of the multi-modal motion,which do not exhibit practical application for the wheel-legged biped robots.Finally,this study discusses the key research directions and development trends for the wheel-legged biped robots.

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.

Dynamic compliance of energy-saving legged elastic parallel joints for quadruped robots:design and realization

Achieving dynamic compliance for energy-efficient legged robot motion is a longstanding challenge.Although recent predictive control methods based on single-rigid-body models can generate dynamic motion,they all assume infinite energy,making them unsuitable for prolonged robot operation.Addressing this issue necessitates a mechanical structure with energy storage and a dynamic control strategy that incorporates feedback to ensure stability.This work draws inspiration from the efficiency of bio-inspired muscle–tendon networks and proposes a controllable torsion spring leg structure.The design integrates a spring-loaded inverted pendulum model and adopts feedback delays and yield springs to enhance the delay effects.A leg control model that incorporates motor loads is developed to validate the response and dynamic performance of a leg with elastic joints.This model provides torque to the knee joint,effectively reducing the robot’s energy consumption through active or passive control strategies.The benefits of the proposed approach in agile maneuvering of quadruped robot legs in a realistic scenario are demonstrated to validate the dynamic motion performance of the leg with elastic joints with the advantage of energy-efficient legs.

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.

A Unified Trajectory Optimization Approach for Long-Term and Reactive Motion Planning of Legged Locomotion

This paper proposes a unified trajectory optimization approach that simultaneously optimizes the trajectory of the center of mass and footholds for legged locomotion.Based on a generic point-mass model,the approach is formulated as a nonlinear optimization problem,incorporating constraints such as robot kinematics,dynamics,ground reaction forces,obstacles,and target location.The unified optimization approach can be applied to both long-term motion planning and the reactive online planning through the use of model predictive control,and it incorporates vector field guidance to converge to the long-term planned motion.The effectiveness of the approach is demonstrated through simulations and physical experiments,showing its ability to generate a variety of walking and jumping gaits,as well as transitions between them,and to perform reactive walking in obstructed environments.

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.

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%.