Optimal three-dimensional biped walking pattern generation based on geodesics

The innovative three-dimensional humanoid biped gait planning method using geodesics is introduced in this article. In order to control three-dimensional walking, the three-dimensional linear inverted pendulum model is studied in our energy-optimal gait planning based on geodesics. The kinetic energy of the three-dimensional linear inverted pendulum model is calculated at first. Based on this kinetic energy model, the Riemannian metric is defined and the Riemannian surface is further determined by this Riemannian metric. The geodesic is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the center of gravity because the kinetic energy along the geodesic is invariant according to the geometric property of geodesics and the walking is energy-saving. Finally, a simulation experiment using a 12-degree-of-freedom biped robot model is implemented. The gait sequences of the simulated RoboErectus humanoid robot are obtained in the ROS (Robot Operating System) Gazebo environment. The proposed geodesics approach is compared with the traditional sinusoidal interpolation method by analyzing the torque feedback of each joint of both legs, and our geodesics optimization gait planning method for three-dimensional linear inverted pendulum model walking control is verified by the assessment results.

Hierarchical Sliding Mode Algorithm for Athlete Robot Walking

Dynamic equations and the control law for a class of robots with elastic underactuated MIMO system of legs, athlete Robot, are discussed in this paper. The dynamic equations are determined by Euler-Lagrange method. A new method based on hierarchical sliding mode for controlling postures is also introduced. Genetic algorithm is applied to design the oscillator for robot motion. Then, a hierarchical sliding mode controller is implemented to control basic posture of athlete robot stepping. Successful simulation results show the motion of athlete robot.

A Parametric Optimization Approach to Walking Pattern Synthesis

Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C3fitted at knots uniformly distributed along the motion time. This high-order differentiability eliminates jerky variations of actuating torques. Through connecting conditions, spline polynomial coefficients are determined as a linear function of the joint coordinates at knots. These values are then dealt with as optimization parameters. An optimal control problem is formulated on the basis of a performance criterion to be minimized, representing an integral quadratic amount of driving torques. Using the above spline approximations, this primary problem is recast into a constrained non-linear optimization problem of mathematical programming, which is solved using a computing code implementing an SQP algorithm. As numerical simulations, complete gait cycles are generated for a seven-link planar biped. The only kinematic data to be accounted for are the walking speeds. Optimization of both phases of gait is carried out globally; it includes the optimization of transition configurations of the biped between successive phases of the gait cycle.

Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications

The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rotation, we hypothesize that the FRI will closely track the ZMP in early single support when the foot remains flat on the ground, but will then significantly diverge from the ZMP in late single support as the foot rolls during heel-off. Additionally, since spin angular momentum has been shown to remain small throughout the walking cycle, we hypothesize that the CMP will never leave the ground support base throughout the entire gait cycle, closely tracking the ZMP. We test these hypotheses using a morphologically realistic human model and kinetic and kinematic gait data measured from ten human subjects walking at self-selected speeds. We find that the mean separation distance between the FRI and ZMP during heel-off is within the accuracy of their measurement (0.1% of foot length). Thus, the FRI point is determined not to be an adequate measure of foot rotational acceleration and a modified FRI point is proposed. Finally, we find that the CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking.

A springy pendulum could describe the swing leg kinetics of human walking

The dynamics of human walking during various walking conditions could be qualitatively captured by the springy legged dynamics, which have been used as a theoretical framework for bipedal robotics applications. However, the spring-loaded inverted pendulum model describes the motion of the center of mass (CoM), which combines the torso, swing and stance legs together and does not explicitly inform us as to whether the inter-limb dynamics share the springy legged dynamics characteristics of the CoM. In this study, we examined whether the swing leg dynamics could also be represented by springy mechanics and whether the swing leg stiffness shows a dependence on gait speed, as has been observed in CoM mechanics during walking. The swing leg was modeled as a spring-loaded pendulum hinged at the hip joint, which is under forward motion. The model parameters of the loaded mass were adopted from body parameters and anthropometric tables, whereas the free model parameters for the rest length of the spring and its stiffness were estimated to best match the data for the swing leg joint forces. The joint forces of the swing leg were well represented by the springy pendulum model at various walking speeds with a regression coefficient of R(2)>0.8. The swing leg stiffness increased with walking speed and was correlated with the swing frequency, which is consistent with previous observations from CoM dynamics described using the compliant leg. These results suggest that the swing leg also shares the springy dynamics, and the compliant walking model could be extended to better present swing leg dynamics.

Motion and Walking Stabilization of Humanoids Using Sensory Reflex Control

Humanoid robots are versatile robot platforms that can carry out intelligent tasks and services for humans, including intimate interactions. For high mobility, a robust stabilization of motion including biped walking is crucial. This paper employs and elaborates on sensory reflex control to stabilize standing motion and biped walking using basic sensors such as an inertial measurement unit (IMU) and a force-sensing resistor (FSR). Specifically, normalized zero-moment points processed from FSR data are used in the reflexive control of a simple motion of swinging the whole body while standing, and the measured inclination angle of the trunk, filtered from IMU data, is used for biped walking on a sloped floor. The proposed control scheme is validated through experiments with the commercial humanoid robot, ROBOTIS-OP.

Multi-contact bipedal robotic locomotion

This paper presents a formal framework for achieving multi-contact bipedal robotic walking, and realizes this methodology experimentally on two robotic platforms: AMBER2 and Assume The Robot Is A Sphere (ATRIAS). Inspired by the key feature encoded in human walking—multi-contact behavior—this approach begins with the analysis of human locomotion and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. Human-inspired outputs are extracted from reference locomotion data to characterize the human model or the spring-loaded invert pendulum (SLIP) model, and then employed to develop the human-inspired control and an optimization problem that yields stable multi-domain walking. Through a trajectory reconstruction strategy motivated by the process that generates the walking gait, the mathematical constructions are successfully translated to the two physical robots experimentally.

A Switching Control Strategy for Energy Efficient Walking on Uneven Surfaces

This paper studies the problem of achieving an energy efficient walking on an uneven surface for a compass-like biped robot with flat feet. To this end, reference walking gaits, which consist of two phases including the static foot phase and the foot rotation phase, are designed on several typical slopes via minimizing the dimensionless specific mechanical cost of transport. Moreover, for other slopes, a simple transformation method is proposed to generate interim reference walking gaits from the reference ones on those typical slopes. Then an input–output feedback linearization approach is considered to design a tracking control law in the static foot phase and a time-scaling approach is adopted to construct a tracking control law in the foot rotation phase as the dynamics in this phase is underactuated. By switching the control law at different phases and switching the reference walking gaits on different slopes, a compass-like robot can achieve energy efficient walking on uneven surfaces. The validity of our method is illustrated by numerical simulations.

Optimal gait planning for humanoids with 3D structure walking on slippery surfaces

In this study, a gait optimization routine is developed to generate walking patterns which demand the lowest friction forces for implementation. The aim of this research is to fully address the question “which walking pattern demands the lowest coefficient of friction amongst all feasible patterns?”. To this end, first, the kinematic structure of the considered 31 DOF (Degrees of Freedom) humanoid robot is investigated and a closed-form dynamics model for its lower-body is developed. Then, the medium through which the walking pattern generation is conducted is presented. In this medium, after designing trajectories for the feet and the pelvis, the joint space variables are obtained, using the inverse kinematics. Finally, by employing a genetic algorithm (GA), an optimization process is conducted to generate walking patterns with the minimum Required Coefficient Of Friction (RCOF). Six parameters are adopted to parameterize the pelvis trajectory and are exploited as the design variables in this optimization procedure. Also, a parametrical study is accomplished to address the effects of some other variables on RCOF. For comparison purposes, a tip-over Stability Margin (SM) is defined, and an optimization procedure is conducted to maximize this margin. Finally, the proposed gait planning procedure is implemented on SURENA III, a humanoid robot designed and fabricated in CAST, to validate the developed simulation procedure. The obtained results reveal merits of the proposed optimal gait planning procedure in terms of RCOF.

Multi-level control of zero-moment point-based humanoid biped robots: a review

Researchers dream of developing autonomous humanoid robots which behave/walk like a human being. Biped robots, although complex, have the greatest potential for use in human-centred environments such as the home or office. Studying biped robots is also important for understanding human locomotion and improving control strategies for prosthetic and orthotic limbs. Control systems of humans walking in cluttered environments are complex, however, and may involve multiple local controllers and commands from the cerebellum. Although biped robots have been of interest over the last four decades, no unified stability/balance criterion adopted for stabilization of miscellaneous walking/running modes of biped robots has so far been available. The literature is scattered and it is difficult to construct a unified background for the balance strategies of biped motion. The zero-moment point (ZMP) criterion, however, is a conservative indicator of stabilized motion for a class of biped robots. Therefore, we offer a systematic presentation of multi-level balance controllers for stabilization and balance recovery of ZMP-based humanoid robots.

High-DOF Robots in Dynamic Environments Using Incremental Trajectory Optimization

We present a novel optimization-based motion planning algorithm for high degree-of-freedom (DOF) robots in dynamic environments. Our approach decomposes the high-dimensional motion planning problem into a sequence of low-dimensional sub-problems. We compute collision-free and smooth paths using optimization-based planning and trajectory perturbation for each sub-problem. The overall algorithm does not require a priori knowledge about global motion or trajectories of dynamic obstacles. Rather, we compute a conservative local bound on the position or trajectory of each obstacle over a short time and use the bound to incrementally compute a collision-free trajectory for the robot. The high-DOF robot is treated as a tightly coupled system, and we incrementally use constrained coordination to plan its motion. We highlight the performance of our planner in simulated environments on robots with tens of DOFs.

Gait motion stabilization tuning approach of biped robot based on augmented reality

Zero moment point (ZMP) is the most popular concept that is applied to stabilize the gait motion of a biped robot. This paper utilizes ZMP with the augmented-reality (AR) method to improve the stability of gait motion of a biped robot. The 3ds Max computer software package is used to build a virtual robot. Under an achieved joint angle data of solid robot to produce an animation of the robot's trajectory, the joint angle data are transmitted to the virtual robot to analyze the offset of the trunk. Furthermore, this investigation adopts AR to allow the user to make direct comparisons between the solid and virtual robot before and after the gait motion is corrected. The animated trajectories of the virtual robot are compared and the relevant data provide feedback to the solid robot to adjust the joint angle and further correct its posture. The experimental results reveal that the proposed scheme can improve gait motion, even when the biped robot is affected by an unexpected loading disturbance. As well as improving the stability of gait motion of a biped robot, the results of this study can also be used to teach the application of the proposed method in a robotics class.

Coupling effect analysis between the central nervous system and the CPG network with proprioception

Human rhythmic movement is generated by central pattern generators (CPGs), and their application to robot control has attracted interest of many scientists. But the coupling relationship between the central nervous system and the CPG network with external inputs is still not unveiled. According to biological experiment results, the CPG network is controlled by the neural system; in other words, the interaction between the central nervous system and the CPG network can control human movement effectively. This paper offers a complex human locomotion model, which illustrates the coupling relationship between the central nervous system and the CPG network with proprioception. Based on Matsuoka's CPG model (K. Matsuoka, Biol. Cybern. 52(6), 367–376 (1985)), the stability and robustness of the CPG network are analyzed with external inputs. In order to simulate the coupling relationship, the Radial Basis Function (RBF) neural network is used to simulate the cerebral cortex, and the Credit-Assignment Cerebellar Model Articulation Controller algorithm is employed to realize the locomotion mode conversion. A seven-link biped robot is chosen to simulate the walking gait. The main discoveries include: (1) the output of a new CPG network, which is stable and robust, can be treated as proprioception. Proprioception provides the central nervous system with the information about all joint angles; (2) analysis on a new locomotion model reveals that the cerebral cortex can modulate CPG parameters, leading to adjustment in walking gait.

DEVELOPMENT AND WALKING CONTROL OF EMOTIONAL HUMANOID ROBOT, KIBO

This paper deals with the mechanical design, system integration, and dynamic walking algorithm of KIBO, an emotional biped humanoid robot that has a facial expression mechanism and various human-interactive devices. To emphasize the aesthetic features and marketability of KIBO, the mechanical design was performed after the exterior design stage to conform to all requirements, particularly constraints imposed by the external appearance and human-like link dimensions. For flexible biped walking, a walking pattern generator with variable walking parameters was developed. The walking pattern generator generates both a walking pattern and a corresponding reference zero-moment point (ZMP) pattern simultaneously. For stable biped walking, a walking control strategy using the ZMP and inertial sensor data was developed. In the strategy, we newly proposed a dual ZMP control approach and a posture control approach using an equivalent body inclination, which is calculated from the ZMP and inertial sensor data for robust walking on non-level ground. Finally, the hardware, software architecture, and dynamic walking performance of KIBO were verified through several walking experiments.

Online Joint Trajectory Generation of Human-like Biped Walking

Biped walking has long been studied in the area of gait analysis and robotic locomotion. The goal of this paper is to establish a systematic methodology for human-like natural walking by fusing the measured human joint data and optimal pattern generation techniques based on a full-body humanoid model. To this end, this paper proposes an adaptive two-stage gait pattern by which the step length and walking velocity can be changed with two scaling factors. In addition, to cope with the situations involving passing over a small obstacle, the joint trajectories of the swing foot can be adjusted with a novel concept of differential angle trajectory using a reliable optimization method, viz. particle swarm optimization. The feasibility of the proposed walking scheme is validated by walking experiments with the robot platform DARwIn-OP.

Modeling, stability and walking pattern generators of biped robots: a review

Biped robots have gained much attention for decades. A variety of researches have been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. This paper discusses the main challenges encountered in the design of biped robots, such as modeling, stability and their walking patterns. The subject is difficult to deal with because the biped mechanism intervenes with mechanics, control, electronics and artificial intelligence. In this paper, we collect and introduce a systematic discussion of modeling, walking pattern generators and stability for a biped robot.

Theoretical analysis of the state of balance in bipedal walking

This paper presents a theoretical analysis based on classic mechanical principles of balance of forces in bipedal walking. Theories on the state of balance have been proposed in the area of humanoid robotics and although the laws of classical mechanics are equivalent to both humans and humanoid robots, the resulting motion obtained with these theories is unnatural when compared to normal human gait. Humanoid robots are commonly controlled using the zero moment point (ZMP) with the condition that the ZMP cannot exit the foot-support area. This condition is derived from a physical model in which the biped must always walk under dynamically balanced conditions, making the centre of pressure (CoP) and the ZMP always coincident. On the contrary, humans follow a different strategy characterized by a 'controlled fall' at the end of the swing phase. In this paper, we present a thorough theoretical analysis of the state of balance and show that the ZMP can exit the support area, and its location is representative of the imbalance state characterized by the separation between the ZMP and the CoP. Since humans exhibit this behavior, we also present proof-of-concept results of a single subject walking on an instrumented treadmill at different speeds (from slow 0.7 m/s to fast 2.0 m/s walking with increments of 0.1 m/s) with the motion recorded using an optical motion tracking system. In order to evaluate the experimental results of this model, the coefficient of determination (R2) is used to correlate the measured ground reaction forces and the resultant of inertial and gravitational forces (anteroposterior R² = 0.93, mediolateral R² = 0.89, and vertical R² = 0.86) indicating that there is a high correlation between the measurements. The results suggest that the subject exhibits a complete dynamically balanced gait during slow speeds while experiencing a controlled fall (end of swing phase) with faster speeds. This is quantified with the root-mean-square deviation (RMSD) between the CoP and the ZMP, a relationship that grows exponentially, suggesting that the ZMP exits the support area earlier with faster walking speeds (relative to the stride duration). We conclude that the ZMP is a significant concept that can be exploited for the analysis of bipedal balance, but we also challenge the control strategy adopted in humanoid robotics that forces the ZMP to be contained within the support area causing the robot to follow unnatural patterns.

Prototyping and Real-Time Implementation of Bipedal Humanoid Robots

This chapter is aimed at describing a contemporary bipedal humanoid robot prototyping technology, accompanied with a mathematically rigorous method to generate real-time walking, jumping, and running trajectories that can be applied to this type of robots. The main strategy in this method is to maintain the overall dynamic equilibrium and to prevent undesired rotational actions for the purpose of smooth maneuvering capabilities while the robot is in motion. In order to reach this goal, Zero Moment Point criterion is utilized in spherical coordinates, so that it is possible to fully exploit its properties by the help of Euler’s equations of motions. Such a strategy allows for characterization of the rotational inertia and therefore the associated angular momentum rate change terms, so that undesired torso angle fluctuations during walking and running are well suppressed. It enables prevention of backwards-hopping actions during jumping as well. To validate the proposed approach, the authors performed simulations using a precise 3D simulator and conducted experiments on an actual bipedal robot. Results indicated that the method is superior to classical methods in terms of suppressing undesired rotational actions, such as torso angle fluctuations and backwards-hopping.

Stable walking control of a 3D biped robot with foot rotation

In order to obtain a more human-like walking and less energy consumption, ait foot rotation phaseis considered in the single support phase of a 3D biped robot, in which the stance heel lifts from the ground and the stance foot rotates about the toe. Since there is no actuation at the toe, a walking phase of the robot is composed of a fully actuated phase and an under-actuated phase. The objective of this paper is to present an asymptotically stable walking controller that integrates these two phases. To get around the under-actuation issue, a strict monotonic parameter of the robot is used to describe the reference trajectory instead of using the time parameter. The overall control law consists of a zero moment point (ZMP) controller, a swing ankle rotation controller and a partial joint angles controller. The ZMP controller guarantees that the ZMP follows the desired ZMP. The swing ankle rotation controller assures a flat-foot impact at the end of the swinging phase. Each of these controllers creates two constraints on joint accelerations. In order to determine all the desired joint accelerations from the control law, a partial joint angles controller is implemented. A word “partial” emphasizes the fact that not all the joint angles can be controlled. The outputs controlled by a partial joint angles controller are defined as a linear combination of all the joint angles. The most important question addressed in this paper is how this linear combination can be defined in order to ensure walking stability. The stability of the walking gait under closed-loop control is evaluated with the linearization of the restricted Poincaré map of the hybrid zero dynamics. Finally, simulation results validate the effectiveness of the control law even in presence of initial errors and modelling errors.

Model-based reinforcement of Kinect depth data for human motion capture applications

Motion capture systems have recently experienced a strong evolution. New cheap depth sensors and open source frameworks, such as OpenNI, allow for perceiving human motion on-line without using invasive systems. However, these proposals do not evaluate the validity of the obtained poses. This paper addresses this issue using a model-based pose generator to complement the OpenNI human tracker. The proposed system enforces kinematics constraints, eliminates odd poses and filters sensor noise, while learning the real dimensions of the performer's body. The system is composed by a PrimeSense sensor, an OpenNI tracker and a kinematics-based filter and has been extensively tested. Experiments show that the proposed system improves pure OpenNI results at a very low computational cost.

Application of phase-plane method in generating minimum time solution for stable walking of biped robot with specified pattern of motion

Walking with a maximum speed is an interesting subject in the field of biped motion. Giving an answer to the question of “what is the maximum achievable speed of a certain biped walking with a physically acceptable pattern?” is the main objective of this work. In this paper, minimum time motion of biped was studied during one step that consists of single support phase (SSP) and double support phase (DSP). The minimum time problem is formulated with stability and non-slip conditions along with actuator limits expressed as some inequality constraints. In addition, certain kinematic constraints in terms of hip joint position are considered that ensure an acceptable walking pattern. A phase-plane technique is used to find the minimum time solution. A numerical simulation is given to shed some light on how the proposed method works. Validity and effectiveness of the method are verified by comparing the results with those of other researches.

A SYSTEMATIC GAIT-PLANNING FRAMEWORK NEGOTIATING BIOMECHANICALLY MOTIVATED CHARACTERISTICS OF A PLANAR BIPEDAL ROBOT

Natural human walking possesses three characteristics: (i) gait repeatability, (ii) postural balance, and (iii) highly regulated centroidal angular momentum (CAM). In this paper, a systematic gait-planning framework is presented for the gait planning of a five-link bipedal robot, negotiating those three characteristics. The framework employs a set of task-space variables and a set of gait parameters. Five kinematic and dynamic objective functions are selected, corresponding to the biped's five degrees of freedom (DOFs), incorporating three characteristics. Fusing the equations of five objective functions together, two ordinary differential equations called the framework equations are derived. Assigning desired values to the gait parameters, the framework equations are integrated across the gait cycle, rendering the motion profiles of the task-space variables. A set of simulation results shows that the framework presents gait that successfully negotiates three characteristics. A parametric analysis is then carried out to study the effect of changing the gait parameters on the joint angular displacements and velocities, the postural balance, and the regulation of CAM of the bipedal robot.

The Mechanism of Yaw Torque Compensation in the Human and Motion Design for Humanoid Robots

When a humanoid robot walks fast or runs, the yaw torque is so large that the supporting foot slips easily and the robot may become unstable. The compensation for the yaw torque is important for fast humanoid walking and many studies have been focusing on yaw torque compensation. However, the issue of humanoid robot motion design that can make the movements of the robot more human-like, as well as guarantee the stability of the robot, has not been studied in-depth. In this paper, the mechanism of yaw torque compensating for human walking is firstly studied. Then we propose a method to compensate yaw torque for a humanoid robot through the motion of the arms and waist joint based on the human yaw torque compensation mechanism and ZMP stability citation. Finally, the effectiveness of the proposed method is demonstrated by the results from the simulation and walking experiments on the newly developed BHR humanoid robot.

Kinesiology-Based Robot Foot Design for Human-Like Walking

Compared with the conventional flat foot, the flexible foot is advantageous in implementing human-like walking and much reduces energy consumption. In this paper, from an anatomical and kinesiological point of view, a flexible foot with toes and heels is investigated for a bipedal robot and three critical design parameters for walking stability are drawn, which include stiffness of toes and heels, frontal toe position, and ankle joint position. In addition, a human-like walking trajectory compatible with the flexible foot is proposed by mimicking a human walking pattern. First of all, the zero moment point (ZMP) trajectory continuously moves forward without stopping, even in the single support phase. Secondly, the centre of mass (CoM) trajectory includes vertical motion similar to that seen in human beings. Thirdly, the ankle trajectory follows the rotational motion of a human foot while being lifted from and landing on the ground. Through the simulation study, it is shown that the suggested design parameters can be applied as useful indices for the mechanical design of biped feet; interestingly, the vertical motion of the centre of mass tends to compensate for the transient response in the initial walking step.

Passive and dynamic gait measures for biped mechanism: formulation and simulation analysis

Understanding and mimicking human gait is essential for design and control of biped walking robots. The unique characteristics of normal human gait are described as passive dynamic walking, whereas general human gait is neither completely passive nor always dynamic. To study various walking motions, it is important to quantify the different levels of passivity and dynamicity, which have not been addressed in the current literature. In this paper, we introduce the initial formulations of Passive Gait Measure (PGM) and Dynamic Gait Measure (DGM) that quantify passivity and dynamicity, respectively, of a given biped walking motion, and the proposed formulations will be demonstrated for proof-of-concepts using gait simulation and analysis. The PGM is associated with the optimality of natural human walking, where the passivity weight functions are proposed and incorporated in the minimization of physiologically inspired weighted actuator torques. The PGM then measures the relative contribution of the stance ankle actuation. The DGM is associated with the gait stability, and quantifies the effects of inertia in terms of the Zero-Moment Point and the ground projection of center of mass. In addition, the DGM takes into account the stance foot dimension and the relative threshold between static and dynamic walking. As examples, both human-like and robotic walking motions during single support phase are generated for a planar biped system using the passivity weights and proper gait parameters. The calculated PGM values show more passive nature of human-like walking as compared with the robotic walking. The DGM results verify the dynamic nature of normal human walking with anthropomorphic foot dimension. In general, the DGMs for human-like walking are greater than those for robotic walking. The resulting DGMs also demonstrate their dependence on the stance foot dimension as well as the walking motion; for a given walking motion, smaller foot dimension results in increased dynamicity. Future work on experimental validation and demonstration will involve actual walking robots and human subjects. The proposed results will benefit the human gait studies and the development of walking robots.

A Novel Sensory Mapping Design for Bipedal Walking on a Sloped Surface

This paper presents an environment recognition method for bipedal robots using a time-delay neural network. For a robot to walk in a varying terrain, it is desirable that the robot can adapt to any environment encountered in real-time. This paper aims to develop a sensory mapping unit to recognize environment types from the input sensory data based on an artificial neural network approach. With the proposed sensory mapping design, a bipedal walking robot can obtain real-time environment information and select an appropriate walking pattern accordingly. Due to the time-dependent property of sensory data, the sensory mapping is realized by using a time-delay neural network. The sensory data of earlier time sequences combined with current sensory data are sent to the neural network. The proposed method has been implemented on the humanoid robot NAO for verification. Several interesting experiments were carried out to verify the effectiveness of the sensory mapping design. The mapping design is validated for the uphill, downhill and flat surface cases, where three types of environment can be recognized by the NAO robot online.

Biped walking control using a trajectory library

This paper presents biped walking control using a library of optimal trajectories. Biped walking control is formulated as an optimal control problem. We use a parametric trajectory optimization method to find the periodic steady-state walking trajectory. As a second stage, we use Differential Dynamic Programming to generate a library of optimal trajectories and locally linear models of the optimal control law, which are used to construct a more global control law. The proposed controller is compared with a trajectory tracking controller using optimal gains. The utility and performance of the proposed method are evaluated using simulated walking control of a planar five-link biped robot.

Multilevel Cognitive Machine-Learning-Based Concept for Artificial Awareness: Application to Humanoid Robot Awareness Using Visual Saliency

As part of “intelligence,” the “awareness” is the state or ability to perceive, feel, or be mindful of events, objects, or sensory patterns: in other words, to be conscious of the surrounding environment and its interactions. Inspired by early-ages human skills developments and especially by early-ages awareness maturation, the present paper accosts the robots intelligence from a different slant directing the attention to combining both “cognitive” and “perceptual” abilities. Within such a slant, the machine (robot) shrewdness is constructed on the basis of a multilevel cognitive concept attempting to handle complex artificial behaviors. The intended complex behavior is the autonomous discovering of objects by robot exploring an unknown environment: in other words, proffering the robot autonomy and awareness in and about unknown backdrop.

CONTRIBUTION TO THE INTEGRATED CONTROL OF BIPED LOCOMOTION MECHANISMS

This work is concerned with the integrated dynamic control of humanoid locomotion mechanisms based on the spatial dynamic model of the humanoid mechanism, a servo system model, and an environment model. The control scheme was synthesized using the centralized model of the system and the hierarchical principle, with tactical and executive control levels. The proposed structure of the dynamic controller involves four feedback loops: position-velocity feedback at the robotic mechanism joints, dynamic reaction feedback at Zero-Moment Point, impact force feedback at the instant when the foot strikes the ground, and the load feedback of the mechanism joints. Simulation experiments are carried out for a number of characteristic examples. The numerical results obtained, along with theoretical study, serve as the basis for a critical evaluation of the performance of the devised controller.

A UNIVERSAL BIPED WALKING GENERATOR FOR COMPLEX ENVIRONMENTS WITH PATTERN FEASIBILITY CHECKING

In this paper, we propose a universal biped walking generator that can plan smooth and flexible walking motions in complex environments, including stairs, slopes, and obstacles. In addition to generating collision-free patterns while keeping the balance of the robot, this generator also checks whether the patterns are achievable for the robot. Aiming at this goal, we introduce a simplified walking method to specify the complete biped motions with the unit of a walking step, instead of a time step of the robot's working time used in usual methods. The zero moment point sampling search is also proposed as an efficient method to determine the walking solution for a feasible footstep plan while simultaneously considering dynamic balance and feasibility. Furthermore, another sampling-based algorithm is proposed to revise unfeasible footstep plans to feasible ones. The feasibility and the efficiency of our proposed approach are demonstrated by experiments on simulated and real Nao robots.

GAIT GENERATION AND OPTIMIZATION USING THE ESTIMATION OF DISTRIBUTION ALGORITHM FOR TEENSIZE HUMANOID SOCCER ROBOT RESr-1

This paper gives an overview of locomotion planning and control of a TeenSize humanoid soccer robot, Robo-Erectus Senior (RESr-1), which has been developed as an experimental platform for human–robot interaction and cooperative research in general and robotics soccer games in particular. The locomotion planning and control, along with an introduction of hierarchical control architecture, vision-based behavior and its application in the Humanoid TeenSize soccer challenge, are elaborated. The Estimation of Distribution Algorithm (EDA) is used in locomotion generation and optimization to achieves dynamically stable walk and a powerful kick. By setting different objective functions, smooth walking and powerful kicking can be generated quickly. RESr-1 made its debut at RoboCup 2007, and got fourth place in the Humanoid TeenSize penalty kick competition. In addition, some experimental results on RESr-1's walking, tracking and kicking are presented.

DYNAMICALLY BALANCED ASCENDING AND DESCENDING GAITS OF A TWO-LEGGED ROBOT

The present paper deals with dynamically balanced ascending and descending gait generations of a 7 DOF biped robot negotiating a staircase. During navigation, the foot of the swing leg is assumed to follow a trajectory, after ensuring its kinematic constraints. Dynamic balance margin of the gaits are calculated by using the concept of zero-moment point (ZMP). In the present work, an approach different from the well-known semi-inverse method has been developed for trunk motion generation, in which it is initially generated based on static balance and then checked for its dynamic balance. The joint torques are determined utilizing the Lagrange–Euler formulation, and the average power consumption at each joint is calculated. Moreover, variations of the dynamic balance margin are studied for both the ascending as well as descending gaits of the biped robot. Average dynamic balance margin and average power consumption in the ascending gait are found to be more than that of the descending gait. The effect of trunk mass on the dynamic balance margin and average power consumption for both the ascending and descending gaits are studied. The dynamic balance margin and average power consumption are found to decrease and increase, respectively with the increase in the trunk mass.

GENERATING OPTIMAL WALKING CYCLES USING SPLINE-BASED STATE-PARAMETERIZATION

Optimal gait cycles are generated for a seven-link biped using a parametric optimization method. A sagittal walking pattern, including a double-support phase divided into two sub-phases, is considered. Generalized joint coordinates are approximated by three-time differentiable spline-functions. These are the concatenation of 4-order polynomials linked together up to their third derivatives at connecting points — or knots — distributed along the motion time of each phase. Optimization parameters are the values of joint coordinates at the knots, plus the joint velocities, and possibly the joint accelerations, at transitions between successive phases. An integral amount of driving torques is minimized throughout the walking cycle. During the double support, constraint forces in the kinematically closed locomotion system are dealt with as additional actuating forces. For this reason, these are also minimized. Using the above optimization parameters, this basic optimal control problem is transformed into an optimization problem of mathematical programming. The latter is efficiently solved using a Sequential Quadratic Programming algorithm. The only kinematic data required for generating a gait cycle is the walking speed. Postural configurations between successive phases, step length, and relative length of single and double supports are optimized with respect to a given walking speed.

THE CHALLENGE OF MOTION PLANNING FOR SOCCER PLAYING HUMANOID ROBOTS

Motion planning for humanoids faces several challenging issues: high dimensionality of the configuration space, necessity to address balance constraints in single and double support mode, higher levels of planning for coordination of different skills, etc. While the above challenges hold for any humanoid robot, the soccer scenario adds difficulties rarely addressed in humanoid motion planning research, as for example: dynamic environments with active opponents, the requirement to perform short- and long-term plans for performing soccer-relevant actions, and the necessity to plan movements purposely terminating with a collision with the ball. These aspects open a completely new scenario for researchers. This paper surveys state-of-the-art research in motion planning for humanoid robots with a focus on outlining connections, differences, and identifying the key aspects that ought to be addressed when developing effective humanoid soccer players.