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.     

Numerical and experimental study of the virtual quadrupedal walking robot-semiquad

SemiQuad is a prototyped walking robot with a platform and two double-link legs. Thus, it is a five-link mechanism. The front leg models identical motions of two quadruped's front legs, the back leg models identical motions of two quadruped's back legs. The legs have passive (uncontrolled) feet that extend in the frontal plane. Due to this the robot is stable in the frontal plane. This robot can be viewed as a "virtual" quadruped. Four DC motors drive the mechanism. Its control system comprises a computer, hardware servo-systems and power amplifiers. The locomotion of the prototype is planar curvet gait. In the double support our prototype is statically stable and over actuated. In the single support it is unstable and under actuated system. There is no flight phase. We describe here the scheme of the mechanism, the characteristics of the drives and the control strategy. The dynamic model of the planar walking is recalled for the double, single support phases and for the impact instant. An intuitive control strategy is detailed. The designed control strategy overcomes the difficulties appeared due to unstable and under actuated motion in the single support.Due to the control algorithm the walking regime consists of the alternating different phases. The sequence of these phases is the following. A double support phase begins. A fast bend and unbend of the front leg allows a lift-off of the front leg. During the single support on the back leg the distance between the two leg tips increases. Then an impact occurs and a new double support phase begins. A fast bend and unbend of the back leg allows the lift-off of the back leg. During the single support on the front leg the distance between the two leg tips decreases to form a cyclic walking gait.The experiments give results that are close to those of the simulation.Funding for SemiQuad was primarily provided by the CNRS and the region Pays de La Loire.     

Study on Roller-Walker — Improvement of Locomotive Efficiency of Quadruped Robots by Passive Wheels

Abstract

Roller-Walker is a leg–wheel hybrid mobile robot using a passive wheel equipped on the tip of each leg. The passive wheel can be transformed into sole mode by rotating the ankle roll joint when Roller-Walker walks on a rough terrain. This paper discusses the energy efficiency of locomotion in wheeled mode. We define a leg trajectory to produce forward straight propulsion, and discuss the relationships between the parameters of the leg trajectory and energy efficiency of the propulsion using a dynamics simulator. We find optimum parameter sets where optimization criterion is specific resistance. The results indicate that faster locomotion achieves higher energy efficiency. We then carry out hardware experiments and empirically derive the experimental specific resistance. We show that wheeled locomotion has an 8-times higher energy efficiency than the ordinary crawl gait. Finally, we compare the specific resistance of Roller-Walker with other walking robots described in the literature.     

变长度弹性伸缩腿双足机器人半被动起步行走仿人控制

传统双足机器人行走使用轨迹跟踪控制,而人类行走大部分时间处于被动状态.针对半被动变长度弹性伸缩腿双足机器人从静止状态开始起步行走的问题,提出了一种起步行走仿人控制方法.首先,使用串联弹性驱动双足弹簧负载倒立摆(B-SLIP)模型;然后,利用拉格朗日方法建立行走动力学方程,并利用模型的自稳定性在双支撑阶段采用能量误差比例...     

双足机器人动态步行实时步态生成

针对双足机器人动态步行生成关节运动轨迹复杂问题,提出了一种简单直观的实时步态生成方案。建立了平面五杆双足机器人动力学模型,通过模仿人类步行主要运动特征并根据双足机器人动态步行双腿姿态变化的要求,将动态步行复杂任务分解为顺序执行的四个过程,在关节空间相对坐标系下设计了躯干运动模式、摆动腿和支撑腿动作及步行速度调整模式,结合当前步行控制结果反馈实时产生稳定的关节运动轨迹。仿真实验验证了该方法的有效性,简单易实现。     

正弦驱动与传感反馈结合的双足机器人仿生行走控制

提出了一种正弦驱动与传感反馈结合的双足机器人仿生行走控制方法．所有关节由正弦振荡器驱动, 较之相互耦合的神经元振荡器更加简单;控制参数具有明晰的物理意义,便于对运动模式进行调节．传感反馈表征 了机器人的运动状态,对于保证机器人的稳定行走起着至关重要的作用．将机器人碰地、碰膝等关键运动状态作为 相位反馈,对控制力矩进行相位重置,协调各关节动作,进而实现控制器、机器人、环境的耦合．同时,从节省能量 和仿生的角度,考虑了关节运动的被动特性,确定了各关节力矩的作用区间．仿真结果表明,该控制方法能实现机 器人稳定行走,并具有良好的能效性和自稳定性.     

基于能量的蛇形机器人蜿蜒运动控制方法的仿真与实验研究

能量作为最基本的物理量之一, 联系着蛇形机器人蜿蜒运动的各个方面. 能量耗散描述了环境交互作用, 能量转换对应着运动的动力学过程, 能量平衡反映了蜿蜒运动的协调性. 提出一种基于能量的蛇形机器人蜿蜒运动控制方法-被动蜿蜒. 通过输出关节力矩控制机器人蜿蜒运动, 由机器人的能量状态调整力矩的大小. 仿真结果显示了被动蜿蜒控制下机器人的构形、角度、力矩、能量状态和转弯特性, 并对控制力矩进行了递归分析. 基于Optotrak运动测量系统构建了被动蜿蜒控制的模拟/物理混合实验系统. 进行了移动实验和拖动实验, 前者改变环境的摩擦特性,后者改变机器人的负载. 仿真和实验验证了蛇形机器人被动蜿蜒控制的有效性和适应性.     

Mechanical Design of a Trunk with Redundant and Viscoelastic Joints for Rhythmic Quadruped Locomotion

Passive mechanisms, such as free joints and viscoelastic components, enable natural oscillation of the robot body, which allows rhythmic locomotion with low energy and computational costs. In particular, joint viscoelasticity can be a powerful candidate for changing natural oscillation and so influence the operation performance of locomotion. The present study considers the passive mechanism of a trunk, and investigates the contributions of a trunk mechanism with redundant joints and tunable viscoelasticity to quadruped locomotion. A physical quadruped robot with a trunk mechanism is developed, and the walking performance of this robot for various gait patterns and joint viscoelasticities is investigated. A simulation model is also constructed based on the physical robot, and the contribution of the viscoelasticity to trunk oscillation and the appropriate joint viscoelasticity and number of trunk joints are discussed. Experimental results obtained using the physical robot indicate that the proposed trunk mechanism contributes to successful locomotion as compared to a robot with a rigid trunk and that the velocity is influenced by not only the gait pattern, but also the joint viscoelasticity (i.e., there are appropriate couplings of the joint viscoelasticity and gait pattern). The simulation results indicate that the trunk mechanism requires joint viscoelasticity in order to achieve oscillation and that a greater number of joints having a smaller joint viscoelasticity enables higher velocity. These results suggest that, in addition to the leg mechanism and the controller design, the design of the trunk mechanism is also important.     

Formation control of underactuated bio-inspired snake robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.     

Adaptive splitbelt treadmill walking of a biped robot using nonlinear oscillators with phase resetting

To investigate the adaptability of a biped robot controlled by nonlinear oscillators with phase resetting based on central pattern generators, we examined the walking behavior of a biped robot on a splitbelt treadmill that has two parallel belts controlled independently. In an experiment, we demonstrated the dynamic interactions among the robot mechanical system, the oscillator control system, and the environment. The robot produced stable walking on the splitbelt treadmill at various belt speeds without changing the control strategy and parameters, despite a large discrepancy between the belt speeds. This is due to modulation of the locomotor rhythm and its phase through the phase resetting mechanism, which induces the relative phase between leg movements to shift from antiphase, and causes the duty factors to be autonomously modulated depending on the speed discrepancy between the belts. Such shifts of the relative phase and modulations of the duty factors are observed during human splitbelt treadmill walking. Clarifying the mechanisms producing such adaptive splitbelt treadmill walking will lead to a better understanding of the phase resetting mechanism in the generation of adaptive locomotion in biological systems and consequently to a guiding principle for designing control systems for legged robots.     

A new algorithm to maintain lateral stabilization during the running gait of a quadruped robot

This paper presents a new uncoupled controller (based on a Kinetic Momentum Management Algorithm, KMMA) which allows a quadrupedal robot, whose operation is simple and fast, to run using a symmetrical gait patterns in a wide variety of scenarios. It consists of two tasks: calculating the lateral position and speed of the fore swinging leg when it next makes contact with the ground; and controlling the roll angle by mean of inertia forces using the stance legs.The KMMA provides the benefits of modulation and the synchronization typically presented in CPG (Central Pattern Generation) models. Furthermore, it is able to maintain the locomotion parameters (such as stroke frequency of gait pattern) when the robot runs in a highly disturbed environment, thus resulting in a lower energy consumption. Additionally, the uncoupled scheme of the leg makes the operation computationally cheap, thus avoiding the use of a Virtual Actuator Control or a Hybrid Zero Dynamics.The performance of the KMMA has been verified by means of co-simulation (using ADAMS and MATLAB) with a highly realistic model of a quadruped robot with uncoupled legs. The performance of the algorithm has been tested in different situations in which the following variables have been varied: frontal velocity, turning ratio, payload, external disturbances and terrain slope. Successful results in terms of stability, energy efficiency, and adaptability to a complex locomotion environment have been obtained.     

Dynamic modelling & simulation of a four legged jumping robot with compliant legs

Legged locomotion is used by most animals and human beings on Earth. Legged locomotion is preferred over the wheeled locomotion as it can be used for both flat and rough terrains. In this paper, an attempt has been made for the dynamic modelling and simulation of four legged jumping robots with compliant legs. Sagittal plane and bounding gait has been considered for the simulation. For energy saving, passive dynamics has been used with the help of compliant legs (linear spring). Different state variables have been obtained for analysis. Control strategies have been implemented on dynamic modelling for forward velocity control.     

Energy-preserving control of a passive one-legged running robot

Fast and energy-efficient control is an increasingly important and attractive area of research in legged locomotion. In this paper, we present a new simple controller for a planar one-legged passive running robot having a springy leg and a compliant hip joint. The most distinctive advantage of the controller over previously proposed ones is it does not require any pre-planned trajectories nor target dynamics. Instead, it utilizes exact non-linear dynamics. Our results are summarized as follows. First, we propose an energy-preserving control strategy for energy-efficient and autonomous gait generation. This strategy is successfully implemented as a new touchdown controller at the flight phase. Simulation results show that the robot can hop from a wide set of initial conditions. Moreover, the running gaits generated are found to be quasi-periodic orbits, which can be seen in Hamiltonian systems. Since the controlled running gaits exist for every admissible energy level, they have some robustness against disturbances. Next, it is shown that an adaptive control of the touchdown angle, which is similar to a delayed feedback controller for a chaotic system, can asymptotically stabilize these quasi-periodic gaits to the periodic ones of the desired period, with some limitations. In particular, for one-periodic gait, by using some additional adaptive controllers, the robot eventually hops without any control inputs. Since our energy-preserving strategy is clear and implementation of the controller is straightforward, we believe it can be easily applied to a wide class of legged mechanisms.     

Optimal control of a half-circular compliant legged monopod

This paper investigates an optimal control strategy for the dynamic locomotion of a simplified planar compliant half-circular legged monopod model. We first present a novel planar leg model which incorporates rolling kinematics and a new compliance model, motivated by the use of similar leg designs on existing platforms. Two locomotion tasks, moving at a prescribed horizontal velocity and a one-shot jump to maximum possible height or length, are then investigated within this model. The designs of two high-level optimal controllers for these tasks are then described to investigate the performance and stability of resulting behaviors, based on the optimization of trajectory parameters for a closed-loop low-level Proportional-Derivative controller at the hip. Our results show that with these optimized parameters the robot can achieve stable locomotion at a desired horizontal velocity and can successfully jump over and across a specified height and length. Finally, the composition of objective functions capturing multiple criteria is also investigated for the one-shot jump task.     

Stable running with a two-segment compliant leg

This research presents a two-segment compliant leg model for understanding fast running locomotion of animals and extending to quadruped robot later. We introduce an approach toward a full understanding of the model by investigating the energy of the system and constructing a set of data, called Limit Cycle Set. The set is computed via optimization procedures and includes all the configurations of the model that contribute to its periodic, stable running locomotion. By introducing the creative design of the configurations, the two-segment compliant model is sufficiently general to be extended to other similar two-segment leg models. Along with the computation, we investigate the system stability and discover that it is possible to achieve stability of a compliant leg in real environments with a simple control strategy. The stable motion is successfully validated in real experiments.     

Contextual Policy Search for Linear and Nonlinear Generalization of a Humanoid Walking Controller

We investigate learning of flexible robot locomotion controllers, i.e., the controllers should be applicable for multiple contexts, for example different walking speeds, various slopes of the terrain or other physical properties of the robot. In our experiments, contexts are desired walking linear speed of the gait. Current approaches for learning control parameters of biped locomotion controllers are typically only applicable for a single context. They can be used for a particular context, for example to learn a gait with highest speed, lowest energy consumption or a combination of both. The question of our research is, how can we obtain a flexible walking controller that controls the robot (near) optimally for many different contexts? We achieve the desired flexibility of the controller by applying the recently developed contextual relative entropy policy search(REPS) method which generalizes the robot walking controller for different contexts, where a context is described by a real valued vector. In this paper we also extend the contextual REPS algorithm to learn a non-linear policy instead of a linear policy over the contexts which call it RBF-REPS as it uses Radial Basis Functions. In order to validate our method, we perform three simulation experiments including a walking experiment using a simulated NAO humanoid robot. The robot learns a policy to choose the controller parameters for a continuous set of forward walking speeds.     

Functional Redesign of Mantis 2.0, a Hybrid Leg-Wheel Robot for Surveillance and Inspection

The paper discusses the redesign of the second version of the Mantis hybrid leg-wheel mobile robot, conceived for surveillance and inspection tasks in unstructured indoor and outdoor environments. This small-scale ground mobile robot is characterized by a main body equipped with two front actuated wheels, a passive rear axle and two rotating legs. Motion on flat and even ground is purely wheeled in order to obtain high speed, high energetic efficiency and stable camera vision; only in case of obstacles or ground irregularities the front legs realize a mixed leg-wheel locomotion to increase the robot climbing ability; in particular, the outer profile of the legs, inspired by the praying mantis, is specially designed to climb square steps. The multibody simulations and the experimental tests on the first prototype have shown the effectiveness of the mixed leg-wheel locomotion not only for step climbing, but also on uneven and yielding terrains. Nevertheless, extensive experimental tests have shown that the front wheels may slip in the last phase of step climbing in case of contact with some materials. In order to overcome this problem, the leg design has been modified with the introduction of auxiliary passive wheels, which reduce friction between legs and step upper surface; these wheels are connected to the legs by one-way bearings, in order to rotate only when they are pulled by the front wheels, and remaining locked when they have to push forward the robot. The influence of the auxiliary wheels on the front wheels slippage is investigated by means of theoretical analysis and multibody simulations.     

Evolving gaits for hexapod robots using cyclic genetic algorithms

A major facet of multi-legged robot control is locomotion. Each leg must move in such a manner that it efficiently produces thrust and provides maximum support. The motion of all the legs must be coordinated so that they are working together to provide constant stability while propelling the robot forward. In this paper, we discuss the use of a cyclic genetic algorithm (CGA) to evolve control programs that produce gaits for actual hexapod robots. Tests done in simulation and verified on the actual robot show that the CGA successfully produces gaits for both fully capable and disabled robots.     

Position-based impedance control of a biped humanoid robot

This paper describes position-based impedance control for biped humanoid robot locomotion. The impedance parameters of the biped leg are adjusted in real-time according to the gait phase. In order to reduce the impact/contact forces generated between the contacting foot and the ground, the damping coefficient of the impedance of the landing foot is increased largely during the first half double support phase. In the last half double support phase, the walking pattern of the leg changed by the impedance control is returned to the desired walking pattern by using a polynomial. Also, the large stiffness of the landing leg is given to increase the momentum reduced by the viscosity of the landing leg in the first half single support phase. For the stability of the biped humanoid robot, a balance control that compensates for moments generated by the biped locomotion is employed during a whole walking cycle. For the confirmation of the impedance and balance control, we have developed a life-sized humanoid robot, WABIAN-RIII, which has 43 mechanical d.o.f. Through dynamic walking experiments, the validity of the proposed controls is verified.     

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.