Fuzzy neural network approaches for robotic gait synthesis

In this paper, a learning scheme using a fuzzy controller to generate walking gaits is developed. The learning scheme uses a fuzzy controller combined with a linearized inverse biped model. The controller provides the control signals at each control time instant. The algorithm used to train the controller is "backpropagation through time". The linearized inverse biped model provides the error signals for backpropagation through the controller at control time instants. Given prespecified constraints such as the step length, crossing clearance, and walking speed, the control scheme can generate the gait that satisfies these constraints. Simulation results are reported for a five-link biped robot.     

双足机器人自适应常值驱动与传感反馈结合的仿生行走控制

为了将双足机器人的混沌步态控制收敛到稳定的周期步态,提出一种控制策略。首先用庞卡莱截面法研究斜坡倾角变化对步态的影响,结果表明,坡度增大会导致倍周期步态到混沌步态的产生;然后以人类步行的生物力学为仿生依据,根据延迟反馈控制的基本思路,设计了自适应常值驱动与传感反馈相结合的仿生行走控制策略,并依据当前步和前两步初始状态对控制器参数进行逐步调节,最终将混沌步态控制收敛到周期步态。仿真结果表明了所提出算法的有效性。     

Dynamically balanced optimal gaits of a ditch-crossing biped robot

This paper deals with the generation of dynamically balanced gaits of a ditch-crossing biped robot having seven degrees of freedom (DOFs). Three different approaches, namely analytical, neural network (NN)-based and fuzzy logic (FL)-based, have been developed to solve the said problem. The former deals with the analytical modeling of the ditch-crossing gait of a biped robot, whereas the latter two approaches aim to maximize the dynamic balance margin of the robot and minimize the power consumption during locomotion, after satisfying a constraint stating that the changes of joint torques should lie within a pre-specified value to ensure its smooth walking. It is to be noted that the power consumption and dynamic balance of the robot are also dependent on the position of the masses on various links and the trajectory followed by the hip joint. A genetic algorithm (GA) is used to provide training off-line, to the NN-based and FL-based gait planners developed. Once optimized, the planners will be able to generate the optimal gaits on-line. Both the NN-based and FL-based gait planners are able to generate more balanced gaits and that, too, at the cost of lower power consumption compared to those yielded by the analytical approach. The NN-based and FL-based approaches are found to be more adaptive compared to the other approach in generating the gaits of the biped robot.     

Path Planning for a Statically Stable Biped Robot Using PRM and Reinforcement Learning

In this paper path planning and obstacle avoidance for a statically stable biped robot using PRM and reinforcement learning is discussed. The main objective of the paper is to compare these two methods of path planning for applications involving a biped robot. The statically stable biped robot under consideration is a 4-degree of freedom walking robot that can follow any given trajectory on flat ground and has a fixed step length of 200 mm. It is proved that the path generated by the first method produces the shortest smooth path but it also increases the computational burden on the controller, as the robot has to turn at almost all steps. However the second method produces paths that are composed of straight-line segments and hence requires less computation for trajectory following. Experiments were also conducted to prove the effectiveness of the reinforcement learning based path planning method.     

Intelligent trajectory control using recurrent averaging learning

In this article, robotic trajectory control using artificial intelligence techniques is developed. The learning strategy is called recurrent averaging learning. It takes the average of initial states and final states after a cycle of training and sets this value as the new initial and final states for next training cycle. A three-layer neural network is used as a controller, it provides the control signals in each stage of a walking gait. A linearized inverse biped model is derived. This model calculates the error signals that will be used to back propagate to the controller in each stage. Through learning, the robot can develop skills to walk along a predefined path with specified step length, walking speed, and crossing clearance. This proposed scheme is tested with simulations of the BLR-G1 walking robot on horizontal and sloping surfaces.     

仿人机器人相似性运动轨迹跟踪控制研究

提出一种基于带观测器的条件状态反馈控制的仿人机器人相似性运动轨迹跟踪控制方法.首先,分析了7连杆双足机器人动力学模型,阐述了其运动能量方程与动力学特征方程; 其次,基于带观测器的状态反馈控制器原理,构建起三维倒立摆平衡控制模型; 最后,由线性二次型调节器确定状态反馈增益矩阵,使机器人轨迹跟踪误差最小化,以复现出较高相似度的双足步行运动效果.实验验证了该方法的有效性.     

Biped robots: Correlations between technological design and dynamic behavior

The authors of the paper have collaborated in a joint project involving four French control, mechanics and computer-science laboratories. In the paper, various mechanical architectures of biped robots are examined in detail, showing that their walking capabilities are closely linked to the kinematic characteristics of the mechanical structure. Then, it is shown that the geometrical and inertial parameters of the mechanical systems strongly affect the gait. In particular, the influence of the biped inertia on the lateral stability of the system, as well as the conditions of the existence of passive pendular gaits during the swing phase, are computationally analyzed. Extending the ideas previously developed, some characteristics of the mechanical architecture and design of the BIP project can be clearly justified. It turns out that a kinematic structure with 15 degrees of freedom is necessary in order for the biped robot to develop anthropomorphic gaits. Furthermore, as an anthropometric mass distribution can improve the walking abilities of the robot, special transmitters have been designed in order to help to fulfil this requirement.     

基于Fuzzy–CPG的双足机器人适应性行走控制

为提高双足机器人的环境适应性, 本文提出了一种基于模糊控制与中枢模式发生器(CPG)的混合控制策 略, 称之为Fuzzy–CPG算法. 高层控制中枢串联模糊控制系统, 将环境反馈信息映射为行走步态信息和CPG幅值参 数. 低层控制中枢CPG根据高层输出命令产生节律性信号, 作为机器人的关节控制信号. 通过机器人运动, 获取环境 信息并反馈给高层控制中枢, 产生下一步的运动命令. 在坡度和凹凸程度可变的仿真环境中进行混合控制策略的 实验验证, 结果表明, 本文提出的Fuzzy–CPG控制方法可以使机器人根据环境的变化产生适应的行走步态, 提高了 双足机器人的环境适应性行走能力.     

Stability analysis and time-varying walking control for an under-actuated planar biped robot

This paper presents two walking controllers for a planar biped robot with unactuated point feet. The control is based on the tracking of reference motions expressed as a function of time. First, the reference motions are adapted at each step in order to create a hybrid zero dynamic (HZD) system. Next, the stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the HZD. When the controlled outputs are selected to be the actuated coordinates, most periodic walking gaits for this robot are unstable, that is, the eigenvalues of the linearized Poincaré map (ELPM) is larger than one. Therefore, two control strategies are explored to produce stable walking. The first strategy uses an event-based feedback controller to modify the ELPM and the second one is based on the choice of controlled outputs. The stability analysis show that, for the same robot and for the same reference trajectory, the stability of the walking (or ELPM) can be modified by some pertinent choices of controlled outputs. Moreover, by studying some walking characteristics of many stable cases, a necessary condition for stable walking is proposed. It is that the height of swing foot is nearly zero at the desired moment of impact. Based on this condition, the duration of the step is almost constant in presence of initial error, so a method for choosing controlled outputs for the second controller is given. By using this method, two stable domains for the controlled outputs selection are obtained.     

Inverse kinematics and inverse dynamics for control of a biped walking machine

Analytical techniques are presented for the motion planning and control of a 12 degree-of-freedom biped walking machine. From the Newton-Euler equations, joint torques are obtained in terms of joint trajectories, and the inverse dynamics are developed for both the single-support and double-support cases. Physical admissibility of the biped trajectory is characterized in terms of the equivalent force-moment and zero-moment point. This methodology has been used to obtain reference inputs and implement the feedforward control of walking robots. A simulation example illustrates the application of the techniques to plan the forward-walking trajectory of the biped robot. The implementation of a prototype mechanism and controller is also described.     

Control of a Biped Walking Robot during the Double Support Phase

This paper discusses the control problem of a biped walking robotduring the double-support phase. Motion of a biped robot during thedouble-support phase can be formulated as motion of robotmanipulators under holonomic constraints. Based on the formulation,the walking gait is generated by controlling the position of thetrunk of the robot to track a desired trajectory, referenced in theworld frame. Constrained forces at both feet were controlled suchthat firm contact is preserved between the feet and ground by using asimplified model of the double-support phase. The control scheme wasevaluated experimentally.     

Simultaneous design of optimal gait pattern and controller for a bipedal robot

Nowadays, biped robotics becomes an interesting topic for many control researchers. The biped robot is more adaptable than the other mobile robots in a varied environment and can have more diverse possibilities in planning the motion. However, it falls down easily and its control for stable walking is difficult. Therefore, generation of a desired walking pattern for the biped robot in the presence of some model uncertainties is an important problem. The proposed walking pattern should be also achievable by the designed controller. To achieve this aim and to reach the best control performance, the walking pattern and controller should be designed simultaneously rather than separately. In the present study, an optimal walking pattern is proposed to be tracked by a designed sliding mode controller. In this respect, a genetic algorithm (GA) is utilized to determine the walking pattern parameters and controller coefficients simultaneously. Here, high stability, minimum energy consumption, good mobility properties, and actuator limitations are considered as the important indexes in optimization. Simulation results indicate the efficiency of the proposed scheme in walking the understudy biped robot.     

Toward the enhancement of biped locomotion and control techniques: walking pattern classification

A new walking pattern classification method is proposed for a 5-link 7-DOF biped robot walking on an uneven floor. This method extracts the patterns in the current floor position of the stance foot and the transitioning floor conditions of the swing foot during locomotion. When a global path composed of stairs, obstacles, etc., and certain walking parameters, such as the speed of walking and the total walking time, are put into the system, the guidance controller unit determines the trajectory of the footsteps in terms of step patterns by using a genetic algorithm-based optimization technique while ensuring the biped’s stability criterion. A demonstration of the biped with different pattern classes was realized by a dynamic simulator.     

A framework for the control of stable aperiodic walking in underactuated planar bipeds

This paper presents a new definition of stable walking for point-footed planar bipedal robots that is not necessarily periodic. The inspiration for the definition is the commonly-held notion of stable walking: the biped does not fall. Somewhat more formally, biped walking is shown to be stable if the trajectory of each step places the robot in a state at the end of the step for which a controller is known to exist that generates a trajectory for the next step with this same property. To make the definition useful, an algorithm is given to verify if a given controller induces stable walking in the given sense. Also given is a framework to synthesize controllers that induce stable walking. The results are illustrated on a 5-link biped ERNIE in simulation and experiment.     

Construction of a Gait Adaptation Model in Human Split-Belt Treadmill Walking Using a Two-Dimensional Biped Robot

A number of studies have measured kinematics, dynamics and oxygen uptake while a person walks on a treadmill. In particular, during walking on a split-belt treadmill, in which the left and right belts have different speeds, remarkable differences in kinematics are observed between normal subjects and subjects with cerebellar disease. In order to construct a gait adaptation model of such human split-belt treadmill walking, we proposed a simple control model and developed a new two-dimensional biped robot walk on a split-belt treadmill. We combined the conventional limit-cycle-based control consisting of joint PD control, cyclic motion trajectory planning and a stepping reflex with a newly proposed adjustment of P-gain at the hip joint of the stance leg. The data obtained in experiments on the robot (normal subject model and cerebellum disease subject model) have highly similar ratios and patterns to data obtained in experiments on normal subjects and subjects with cerebellar disease carried out by Bastian et al. We also showed that the P-gain at the hip joint of the stance leg was the control parameter of adaptation for symmetric gaits in split-belt walking and that P-gain adjustment corresponded to muscle stiffness adjustment by the cerebellum. Consequently, we successfully proposed a gait adaptation model for human split-belt treadmill walking, and confirmed the validity of our hypotheses and the proposed model using the biped robot.     

Overview of the Lucy Project: Dynamic Stabilization of a Biped Powered by Pneumatic Artificial Muscles

This paper gives an overview of the Lucy project. What is special is that the biped is not actuated with the classical electrical drives, but with pleated pneumatic artificial muscles. In an antagonistic setup of such muscles both the torque and the compliance are controllable. From human walking there is evidence that joint compliance plays an important role in energy-efficient walking and running. To be able to walk at different walking speeds and step lengths, a trajectory generator and joint trajectory tracking controller are combined. The first generates dynamically stable trajectories based on the objective locomotion parameters which can be changed from step to step. The joint trajectory tracking unit controls the pressure inside the muscles so the desired motion is followed. It is based on a computed torque model and takes the torque–angle relation of the antagonistic muscle setup into account. With this strategy the robot is able to walk at a speed up to 0.15 m/s. A compliance controller is developed to reduce the energy consumption by combining active trajectory control with the exploitation of the natural dynamics. A mathematical formulation was developed to find an optimal compliance setting depending on the desired trajectory and physical properties of the system. This strategy is experimentally evaluated on a single pendulum structure and not implemented on the real robot because the walking speed of the robot is currently too slow. At the end a discussion is given about the pros and cons of building a pneumatic biped, and the control architecture used.     

Near Optimal PID Controllers for the Biped Robot While Walking on Uneven Terrains

The execution of the gaits generated with the help of a gait planner is a crucial task in biped locomotion. This task is to be achieved with the help of a suitable torque based controller to ensure smooth walk of the biped robot. It is important to note that the success of the developed proportion integration differentiation (PID) controller depends on the selected gains of the controller. In the present study, an attempt is made to tune the gains of the PID controller for the biped robot ascending and descending the stair case and sloping surface with the help of two non-traditional optimization algorithms, namely modified chaotic invasive weed optimization (MCIWO) and particle swarm optimization (PSO) algorithms. Once the optimal PID controllers are developed, a simulation study has been conducted in computer for obtaining the optimal tuning parameters of the controller of the biped robot. Finally, the optimal gait angles obtained by using the best controller are fed to the real biped robot and found that the biped robot has successfully negotiated the said terrains.     

An approach to analyzing biped locomotion dynamics and designing robot locomotion controls

An approach to analyzing biped locomotion problems is presented. This approach applies the principles of Lagrangian dynamics to derive the equations of motion of locomotion gaits, state-variable techniques to analyze locomotion dynamics, and multivariable feedback to design locomotion controls. A robot model which has no knee joints or feet and is constrained to motion in the sagittal plane is chosen as a sufficiently simple model of a biped to illustrate the approach. A goal of the analysis is the design of a locomotion control for the robot which produces a walking gait having a velocity and stride length similar to those of a human walking gait. The principle feature of the approach is a much deeper understanding of the dynamics of biped locomotion than previous approaches have provided.     

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。