How to optimize the slope walking motion by the quadruped walking robot

Reduction of the energy consumption is one of the most important problems to utilize quadruped walking robots for various works on rugged terrain. The authors have studied basic strategy to achieve high energy efficiency when the quadruped walking robot do the motion essentially requires positive power by the analysis of body rising motion. This paper discusses the energy efficiency of the slope walking motion by the quadruped walking robot. First, we investigate the walking posture in consideration of ideal actuator characteristics where the robot consumes few negative powers at each joint which causes the main energy loss of the walking robot. Then, we investigate optimal walking posture in consideration of DC motor characteristics by the full search of three gait parameters which define the crawl gait. Furthermore, we derive the optimal walking motion by the optimization of three gait parameters which are kept constant during one cycle gait and instantaneous parameters such as body velocity and supporting forces changed at each moment simultaneously.     

Control and Stability Analysis of Limit Cycles in a Hopping Robot

A new stabilizing nonlinear controller for the vertical motion of an electrically actuated hopping robot is introduced and analyzed. The approach starts by finding reference limit cycles from the "passive dynamics" of a mass-spring system. The controller then modulates the system dynamics via the leg actuator during the stance phase to force the system trajectory to converge to this reference limit cycle. The controlled system dynamics is a continuous yet nonsmooth vector field. A piecewise-continuous Lyapunov function and the general forms of Lasalle's invariance and domain of attraction theorems are used to prove global asymptotic stability of the desired limit cycles. It is also shown that the derived passive dynamic cycles are indeed the positive limit sets of the controlled system. The rate of convergence can be adjusted but is limited by actuator constraints.     

Biped Locomotion by Reduced Ankle Power

Power reduction in the ankle joints of a biped robot is considered inthis paper. Ankles of human beings have small torque and are veryflexible within a certain range of motion (very stiff near and beyondthis range). This characteristic makes foot landing soft and gives agood contact between its sole and the ground. This feature can beimplemented in a biped robot by using a small actuator for the anklejoints. A small actuator consumes less energy and reduces the weightof the leg. With less power in the ankle joints, robot walkingbecomes more difficult to control. This problem can be solved byproviding a feedback control mechanism as presented in this paper. Thecontrol mechanism uses the motion of the body and the swinging leg toeliminate instability caused by the weak ankle. Two locomotionexamples, standing and walking, were investigated respectively toshow the validity of the proposed control scheme. In standing, thecontrol input is the displacement of the ankle joint of thesupporting leg. The control mechanism decides the bending angle ofthe body and the position of the swinging leg. For walking, only thebending angle of the body is used to avoid the discontinuity of thecontrol input. Experimental results are presented to show theeffectiveness of the control mechanism.     

Gait and foot trajectory planning for versatile motions of a six-legged robot

This article deals with the problem of planning and controlling a radially symmetric six-legged walker on an uneven terrain when a smooth time-varying body motion is required. The main difficulties lie on the planning of gaits and foot trajectories. As for the gaits, this article discusses the forward wave gait of a variable duty factor and a variable wave direction. With the commanded body motion, the maximum possible duty factor is computed using the speed limit of the leg swing motion. Guaranteeing this maximum duty factor contributes to obtain higher stability. We prove the “continuity” of this forward wave gait planning algorithm adds the versatility to gaits planned. The foot trajectory planning algorithm dynamically generates a smooth foot trajectory as a function of the instantaneous body motions by modifying standard leg motion templates. The robot can negotiate an uneven terrain by modifying a vertical leg motion by a signal of tactile sensors on the foot. The experiments prove that the robot can successfully track smooth curves with body rotations on an uneven terrain, and thus prove the robustness of the algorithms. © 1997 John Wiley & Sons, Inc.     

基于弹簧-质量模型的仿袋鼠跳跃机器人步态稳定性研究

根据袋鼠跳跃运动的特点,建立了仿袋鼠机器人的弹簧—质量模型．采用拉格朗日法通过线性化近似分析建立了其动力学方程,并对其进行了着地阶段径向与横向运动分析．根据步态运动稳定性的条件,研究了仿袋鼠跳跃机器人顶点反射映像函数、固定点的存在性及其稳定性,获得了仿袋鼠机器人在跳跃过程中满足步态稳定性的各个参数的取值范围,以及各参数之间关系的显式表达式．最后,通过实例证明了采用线性化近似分析的有效性,并获得了仿袋鼠机器人稳定跳跃时各参数之间的变化关系．     

Four-leg independent mechanism for MEMS microrobot

In this paper, the development of a quadruped micro-electro mechanical system (MEMS) microrobot with a four-leg independent mechanism is described. As the actuator mechanism inside small robot bodies is difficult to realize, many microrobots use external field forces such as magnetism and vibration. In this paper, artificial muscle wires that are family of shape memory alloy are used for the force of the actuator. The artificial muscle wire shows the large displacement by passing the electrical current through the material itself. The double four-link mechanism is adopted for the leg system. The link mechanism transforms the linear motion of the artificial muscle wire to the foot step-like pedaling motion. The location of the backward swing motion is lower than that of forward swing motion. This motion generates the locomotion force. As a result, the total length of the constructed quadruped MEMS microrobot was 6 mm. The microrobot could perform similar gait pattern changes as the quadruped animal.     

Demonstration and Analysis of Quadrupedal Passive Dynamic Walking

Animals, including human beings, can travel in a variety of environments adaptively. Legged locomotion makes this possible. However, legged locomotion is temporarily unstable and finding out the principle of walking is an important matter for optimum locomotion strategy or engineering applications. As one of the challenges, passive dynamic walking has been studied on this. Passive dynamic walking is a walking phenomenon in which a biped walking robot with no actuator walks down a gentle slope. The gait is very smooth (like a human) and much research has been conducted on this. Passive dynamic walking is mainly about bipedalism. Considering that there are more quadruped animals than bipeds and a four-legged robot is easier to control than a two-legged robot, quadrupedal passive dynamic walking must exist. Based on the above, we studied saggital plane quadrupedal passive dynamic walking simulation. However, it was not enough to attribute the result to the existence of quadrupedal passive dynamic walking. In this research, quadrupedal passive dynamic walking is experimentally demonstrated by the four-legged walking robot 'Quartet 4'. Furthermore, changing the type of body joint, slope angle, leg length and variety of gaits (characteristics in four-legged animals) was observed passively. Experimental data could not have enough walking time and could not change parameters continuously. Then, each gait was analyzed quantitatively by the experiment and three-dimensional simulation.     

Novel Energy Transfer Mechanism in a Running Quadruped Robot with One Actuator per Leg

In this work we develop a novel method, or mechanism, of energy transfer in a quadruped running robot. The robot possesses only one actuator per leg, for lower weight and greater power autonomy. The developed mechanism ensures correct dispersion of energy to the actuated and the unactuated degrees of freedom of the robot for stable running. In the mechanism design, we address the added problem of running on inclined ground. In conjunction with a pitch control method, the energy transfer mechanism forms a complete control algorithm. Due to the novel dynamics-based design of the mechanism, it allows the arbitrary setting of the motion forward speed and apex height. Further, it may be applied for different robot physical parameters and ground inclines, without extensive controller tuning. This has not been previously possible using only one actuator per leg. Simulations of a detailed three-dimensional model of the robot demonstrate the mechanism on two different robots. The simulations take into account many real-world characteristics, including realistic leg models, energy loss due to feet collisions, foot–ground friction and energy losses in the joints. Results demonstrate that inclines of up to 20° are properly negotiated.     

Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot

The statically stable gait control of a mammal-like quadruped robot that provides an adequate or stable manner of traversing over irregular terrain was addressed. The reinforced wave gait which integrates new parameters of the lateral offset and displacements of the center of gravity (COG) based on the profiles of standard wave gait was investigated. The continuous and discontinuous motion trajectory of a robot’s COG in the periodic reinforced wave gait could be realized. The longitudinal and lateral stability margins of a reinforced wave gait were formulated for the gait generation and control of a quadruped robot. Moreover, the effects of the lateral offset on the stability, velocity and the energy efficiency were studied in details. The reinforced wave gait with lateral sway motion adequately improved the stability, and two particular gait patterns that involve the lateral sway motion for a maximal velocity and maximum achievable stability were described. With consideration of a quadruped robot with asymmetric carrying loads on its body, a scheme that relates to the gait parameters of the displacement of a robot’s COG to avoid losing stability was proposed. The simulation and experimental results about the effects of lateral offset added in the reinforced wave gait on the minimum power consumption during a quadruped robot walking on a flat terrain indicated that the reinforced wave gait with a larger lateral offset would generate a better wave gait with a higher velocity and energy efficiency.     

伸缩腿双足机器人半被动行走控制研究

研究半被动伸缩腿双足机器人行走控制和周期解的全局稳定性问题.使用杆长可变的倒立摆机器人模型,以支撑腿的伸缩作为行走动力源,采用庞加莱映射方法分析了双足机器人行走的不动点及其稳定性.当脚与地面冲击时,假设两腿间的夹角保持为常数,设计了腿伸缩长度的支撑腿角度反馈控制率.证明了伸缩腿双足机器人行走过程不动点的全局稳定性.仿真结果表明,本文提出的腿伸缩长度反馈控制可以实现伸缩腿双足机器人在水平面上的稳定行走,并且周期步态对执行器干扰和支撑腿初始角速度干扰具有鲁棒性.     

Trunk motion control during the flight phase while hopping considering angular momentum of a humanoid

In previous studies, various stabilizing control methods for humanoids during the stance phase while hopping and running were proposed. Although these methods contribute to stability while hopping and running, it is possibility that the control during the flight phase could also affect the stability. In this study, we investigated whether the control during the flight phase can affect the stability of a humanoid while running. To achieve stable hopping, we developed a control system that accounts for the angular momentum of the whole body during the flight phase. In this system, the angular momentum generated by the motion of the lower body in each time interval is calculated during the flight phase, and the trunk joints are controlled to generate the angular momentum necessary to compensate for the deviation of the waist posture, which is used as the reference point for the motion coordinate system of the robot. Once the proposed control system was developed and simulated, we found that the hopping duration in the unconstrained state was extended.     

Stability and joint stiffness analysis of legged robot’s periodic motion driven by McKibben pneumatic actuator

A McKibben-type pneumatic actuator is widely used as a convenient actuator for a robot with a simple actuator model and a simple control method. However, the effect of its characteristics on the stability of robot motion has not been sufficiently discussed. The purpose of our research is to analyze the influence that the various characteristics of a McKibben pneumatic actuator has on the stability of movements generated by the actuator. In this study, we focus on a periodic motion, which is one of the common movements of robots. We introduce a stability criterion for periodic motion similar to our previous work, in which stability of musculo-skeletal system was discussed, and show that the criterion is always satisfied. Next, we focus on a redundancy of air pressure inputs. As one of application of the redundancy, we investigate the joint stiffness of a robot and propose a design procedure of inputs based on a reference period trajectory and the desired joint stiffness. The stability analysis and design of joint stiffness are verified not only through numerical simulations but also through experiments with a developed 1-DOF legged robot.     

基于弹簧负载倒立摆模型的仿袋鼠机器人稳定跳跃控制

仿生跳跃机器人具备很强的越障和环境适应能力,但是由于机器人运动过程中较短的可控时间以及腾空阶段运动的不确定性,运动的稳定性对于仿生跳跃机器人至关重要.本文对仿袋鼠机器人跳跃运动过程中的稳定跳跃控制问题进行了研究.首先采用双质量弹簧负载倒立摆模型(spring-loaded inverted pendulum,SLIP)模型对袋鼠机器人的结构进行简化,建立了机器人系统的动力学模型,并对机器人的运动过程以及着地相与腾空相的切换条件进行了分析.然后采用解耦控制的思想,将SLIP模型的运动控制分解为水平速度控制和跳跃高度控制两个方面,分别通过控制着地角度实现对水平运动速度的控制,通过能量补偿实现对跳跃高度的控制.最后在ADAMS仿真环境中建立机器人模型并进行了机器人运动仿真实验.实验结果表明,本文提出的方法可以实现仿袋鼠机器人稳定的周期性跳跃运动.     

具有2DOF铰接式躯干的仿猎豹四足奔跑机器人

为了探索脊柱运动对腿运动的增强机理,设计了具有2自由度铰接式躯干的仿猎豹四足奔跑机器人。对带腾空相的跳跃（bound）步态奔跑运动的力学过程进行描述,采用阻尼型弹性负载倒立摆（D-SLIP）模型建立了四足机器人动力学模型。依据猎豹的奔跑运动模式,对四足机器人脊柱关节与腿关节的耦合运动进行了轨迹规划。提出一种改进的粒子群优化（PSO）算法,解决了机器人脊柱关节驱动机构尺寸和运动轨迹控制参数之间目标互斥的嵌套优化问题。对四足机器人跳跃奔跑运动进行动力学仿真,结果表明：脊柱与腿的协调运动可以增大奔跑步幅,使机器人产生腾空相,从而提高机器人的奔跑速度。     

A roller-skating/walking mode-based amphibious robot

An amphibious spherical robot capable of motion on land as well as underwater is developed to implement the complicated underwater operations in our previous research. In order to improve the speed performance of the spherical robot on a slope or comparatively smooth terrains, we propose a new roller-skating mode for the robot by equipping a passive wheel on each leg to implement the roller-skating motion in this paper. A braking mechanism is designed to transform the state of each passive wheel between free rolling and braking states by compressing and releasing the spring, which is controlled by the vertical servo motor on each leg. Besides, in order to improve the walking stability of the wheeled robot in longitudinal direction, a closed-loop control method is presented to control the stability of the direction of movement while walking. Therefore, we conduct the experiments on smooth terrains and down a slope to evaluate the performance of the roller-skating motion, including gait stability and velocity. Finally, plenty of walking experiments are conducted to evaluate the ability of directional control.     

Decentralized autonomous control of a quadrupedal locomotion robot using oscillators

This article deals with the design of a control system for a quadrupedal locomotion robot. The proposed control system is composed of a leg motion controller and a gait pattern controller within a hierarchical architecture. The leg controller drives actuators at the joints of the legs using a high-gain local feedback control. It receives the command signal from the gait pattern controller. The gait pattern controller, on the other hand, involves nonlinear oscillators. These oscillators interact with each other through signals from the touch sensors located at the tips of the legs. Various gait patterns emerge through the mutual entrainment of these oscillators. As a result, the system walks stably in a wide velocity range by changing its gait patterns and limiting the increase in energy consumption of the actuators. The performance of the proposed control system is verified by numerical simulations. This work was presented in part at the Fifth International Symposium on Artificial Life and Robotics, Oita, Japan, January 26–28, 2000     

A study of controllable motion of a mobile vibration system moving with breakaway from the surface

We consider a model of a two-mass mechanical system consisting of an external body (box) and an internal body (unbalance), which moves on a rough rigid surface with a breakaway from it. We derive differential equations describing the system motion in the phase of flight and determine the conditions of location on the reference surface. The control parameter is proposed to be the angular velocity of unbalance rotation. To find the dependence of hopping height and length on the control frequency of unbalance rotation, we analyze the equations. An algorithm of numerical integration of the system of differential equations of motion was developed. The numerical solution confirms the theoretical conclusions on the dependence of hopping height and length on rotation frequency. At the same time, the form of trajectory of body mass center was found to depend on the value of the control parameter. Also, we reveal the dependence of the direction of robot motion on hopping height and length, and unbalance (on the ratio of system mass).     

A comparison of three insect-inspired locomotion controllers

This paper compares three insect inspired controllers which were implemented on an autonomous hexapod robot. There is a growing interest in using insect locomotion schemes to control walking robots. Researchers' interest in insect-based controllers ranges from understanding the biological basis of locomotion control in insects to building real-time walking machines which require relatively little computational power. Several models for insect locomotion exist, and robotics researchers tend to adopt one approach and experiment with it.

In contrast, this paper offers a comparison of three insect inspired controllers — all of which were implemented and tested on the same autonomous hexapod robot. Some of the controllers used reflex-based mechanisms whereas others used pattern-based mechanisms. Reflexive controllers exploit sensory stimulus and response reactions to produce leg motion and gait coordination. In contrast, pattern-based controllers depend more upon pre-programmed patterns of behavior which may be influenced by external events. Typically, these pre-programmed patterns of behavior are implemented using central pattern generators (CPGs).

In this work, we compare gait coordination performance of three controllers on flat terrain. We extend the comparison to include leg loading considerations, disabled leg compensation, and externally applied leg perturbations. We discuss the differences between controllers with respect to inconsistent leg retraction velocities, leg design issues, sensing requirements, and computational issues. The robot performed quite differently under varying experimental conditions depending upon which controller was used. We found that controller performance was the most sensitive to robot design parameters. For our case, we had the most success with pattern-based mechanisms given the leg design of our robot and its limitations in controlling the retraction velocity of its legs. The pattern-based mechanisms allowed the robot to remain stable over a variety of gaits while the robot was subjected to loading the legs, disabling a leg, and physically disturbing the legs. The reflexive mechanisms were less successful at maintaining stability when the robot's legs were increasingly disrupted.     

可跳跃式移动机器人机构设计及实现

构建了一个具有跳跃能力的移动式机器人．机器人在较平坦地形下采用轮式移动方式前行；遇到障碍物或沟渠时，可以进行跳跃，从而扩大运动范围．介绍了机器人机械系统的总体结构，给出了机器人的本体结构及起跳姿态，并分析了机器人的运动过程．然后，详细分析了机器人的跳跃机构、跳跃参数调节机构、倾覆翻转机构等关键机构的工作原理，给出了机构设计方案．最后，根据总体设计要求选定了机器人的一些关键参数．     

Computer simulation and dynamic modeling of a quadrupedal pronking gait robot with SLIP model

In this study, a quadrupedal pronking gait robot modeling was carried out with Spring Loaded Inverted Pendulum model in stance phase. This is achieved by solving a natural problem in which the main goal is to enable the robot to walk and run in a stable condition regardless of the environmental conditions. In order to solve this problem, dynamic model and control of a quadrupedal robot were realized for a pronking gait. The stance and flight phase dynamic structures were solved in a sequential closed loop to obtain the equation of motion for pronking gait. Spring Loaded Inverted Pendulum model was used as a dynamic model to simplify the simulation, dynamic locomotion and experimental works of the system, and also to simplify the pronking gait concept. The quadrupedal robot with pronking gait was controlled by proportional-derivative control algorithm. As a result, all computer simulations have shown that the proposed control actions and methods are more effective and make the system control quite easy and successful.