Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> The focus of this paper is the problem of foot rotation in biped robots during the single-support phase. Foot rotation is an indication of postural instability, which should be carefully treated in a dynamically stable walk and avoided altogether in a statically stable walk. We introduce the foot-rotation indicator (FRI) point, which is a point on the foot/ground-contact surface where the net ground-reaction force would have to act to keep the foot stationary. To ensure no foot rotation, the FRI point must remain within the convex hull of the foot-support area. In contrast with the ground projection of the center of mass (GCoM), which is a static criterion, the FRI point incorporates robot dynamics. As opposed to the center of pressure (CoP)—better known as the zero-moment point (ZMP) in the robotics literature—which may not leave the support area, the FRI point may leave the area. In fact, the position of the FRI point outside the footprint indicates the direction of the impending rotation and the magnitude of rotational moment acting on the foot. Owing to these important properties, the FRI point helps not only to monitor the state of postural stability of a biped robot during the entire gait cycle, but indicates the severity of instability of the gait as well. In response to a recent need, the paper also resolves the misconceptions surrounding the CoP/ZMP equivalence. <s> BIB001 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> A bipedal locomotion system is synthesized to characterize some of the previously overlooked aspects of the locomotion process, specifically standing/balance and initiation and stopping. The locomotion system is described by a three-element three-dimensional model consisting of two lower limbs and an upper body. The system equations of motion are derived using variational methods, and are retained in their nonlinear form. The impulsive contact events of impact of the swing limb with the ground and transfer of support are incorporated into the model. Bipedal locomotion is synthesized through numerical simulations. Several control inputs are studied for establishing and sustaining the standing/balance gait. Subsequent motion is analyzed via phase-space portraits. It is shown that an impulsive torque is sufficient for establishing and controlling the standing/balance gait as well as steady locomotion. <s> BIB002 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In this paper, a new application of the ZMP (Zero Moment Point) control law is presented. The objective of this control method is to obtain a smooth and soft motion based on a real-time control. In the controller, the ZMP is treated as an actuating signal. The coordinates of the robot body are fed back to obtain its position. The proposed control method was applied on two different biped robots, and its validity is verified experimentally. <s> BIB003 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Abstract The formulation and optimization of joint trajectories for humanoid robots is quite different from this same task for standard robots because of the complexity of humanoid robots’ kinematics and dynamics. In this paper we exploit the similarity between human motion and humanoid robot motion to generate joint trajectories for humanoids. In particular, we show how to transform human motion information captured by an optical tracking device into a high dimensional trajectory for a humanoid robot. We propose an automatic approach to relate humanoid robot kinematic parameters to the kinematic parameters of a human performer. Based on this relationship we infer the desired trajectories in robot joint space. B-spline wavelets are utilized to efficiently represent the trajectories. The density of the basis functions on the time axis is selected automatically. Large-scale optimization techniques are employed to solve the underlying computational problems efficiently. We applied our method to the task of teaching a humanoid robot how to make various naturally looking movements. <s> BIB004 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper introduces an open architecture humanoid robotics platform (OpenHRP for short) on which various building blocks of humanoid robotics can be investigated. OpenHRP is a virtual humanoid robot platform with a compatible humanoid robot, and consists of a simulator of humanoid robots and motion control library for them which can also be applied to a compatible humanoid robot as it is. OpenHRP also has a view simulator of humanoid robots on which humanoid robot vision can be studied. The consistency between the simulator and the robot are enhanced by introducing a new algorithm to simulate repulsive force and torque between contacting objects. OpenHRP is expected to initiate the exploration of humanoid robotics on an open architecture software and hardware, thanks to the unification of the controllers and the examined consistency between the simulator and a real humanoid robot. <s> BIB005 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Abstract Design and construction of compact body humanoid robots and various biped locomotion control strategies implemented onto them in the ESYS humanoid project at the Engineering Systems Laboratory are presented. Design concepts and hardware specifications of the constructed compact size humanoid robots from Mk.1 to Mk.5 are discussed. As for the biped walk control, four biped locomotion control strategies all of which have various advantages such as versatility, high-energy efficiency, smooth loading on hardware, and real-time gait generation, are proposed. 3D biped dynamic walking of the constructed humanoids is realized by implementing the proposed biped control strategies onto them. Results of evaluation experiments on the proposed control strategies are reported. <s> BIB006 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> The authors studied the self-excited walking of a four-link biped mechanism that possesses an actuated hip joint and passive knee joints with stoppers. They showed that the self-excitation control enables the three-degree-of-freedom planar biped model to walk on level ground by numerical simulation. From the parameter study, it was found that stable walking locomotion is possible over a wide range of feedback gain and link parameter values and that the walking period is almost independent of the feedback gain. Various characteristics of the self-excited walking of a biped mechanism were examined in relation to leg length, and length and mass ratios of the shank. Next, a biped mechanism was manufactured similar to the analytical model. After parameter modification, the authors demonstrated that the biped robot can perform natural dynamic walking on a plane with a 0.8 degree inclination. The simulated results also agree with the experimental walking locomotion. <s> BIB007 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> A humanoid robot is expected to be a rational form of machine to act in the real human environment and support people through interaction with them. Current humanoid robots, however, lack in adaptability, agility, or high-mobility enough to meet the expectations. In order to enhance high-mobility, the humanoid motion should be generated in real-time in accordance with the dynamics, which commonly requires a large amount of computation and has not been implemented so far. We have developed a real-time motion generation method that controls the center of gravity (COG) by indirect manipulation of the zero moment point (ZMP). The real-time response of the method provides humanoid robots with high-mobility. In the paper, the algorithm is presented. It consists of four parts, namely, the referential ZMP planning, the ZMP manipulation, the COG velocity decomposition to joint angles, and local control of joint angles. An advantage of the algorithm lies in its applicability to humanoids with a lot of degrees of freedom. The effectiveness of the proposed method is verified by computer simulations. <s> BIB008 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Trunk motions are typically used in biped robots to stabilize the locomotion. However, they can be very large for some leg trajectories unless they are carefully designed. This paper proposes a fuzzy-logic zero-moment-point (ZMP) trajectory generator that would eventually reduce the swing motion of the trunk significantly even though the leg trajectory is casually designed, for example, simply to avoid obstacles. The fuzzy-logic ZMP trajectory generator uses the leg trajectory as an input. The resulting ZMP trajectory is similar to that of a human one and continuously moves forward in the direction of the locomotion. The trajectory of the trunk to stabilize the locomotion is determined by solving a differential equation with the ZMP trajectory and the leg trajectory known. The proposed scheme is simulated on a 7-DOF biped robot in the sagittal plane. The simulation results show that the ZMP trajectory generated by the proposed fuzzy-logic generator increases the stability of the locomotion and thus reduces the motion range of the trunk significantly. <s> BIB009 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In Vol. 1, No. 1 of Int. J. Humanoid Rubotics, we gave a review of the Zero-Moment Point (ZMP) concept, on the occasion of thirty five years of its use in modeling dynamics of the biped gait. At the time of writing this article, we thought that thirty five years was a long enough period in which all confusions, if they existed, could be cleared up. However, we were not quite right, and we will indicate here some of the most important points concerning the concept. A survey of the literature that appeared in the last several years related to the widely accepted ZMP method reveals a diversity of terms used to describe the state in which the biped system performs “regular” gait, safe from overturning. The terms in use are: stability (stable gait), dynamic balance, and dynamic equilibrium. Stability is a customary term in the theory of automatic control, and in this domain it has its well-defined meaning and usage, so that it is not appropriate to use it in some other instances, straying from its basic meaning. The term dynamic equilibrium is also unsuitable because it is used in the D’Alambert principle to transform dynamic equations into a static form, with a zero on the right-hand side — hence the term equilibrium. Therefore, dynamic balance remains the most appropriate term, as it fully reflects the nature of the related notion, and is not in use in other areas. We ourselves did not make clear this terminological distinction in the aforementioned article, which would have been prudent. Another issue we want to address is the situation illustrated in Fig. 4 in the paper — to make it easier to follow the explanation we repeat it here — concerning the notions of ZMP and fictitious ZMP (FZMP). As is well known, the crucial characteristic of a dynamically balanced gait is that the point at which the conditions ΣMx = 0, ΣMy = 0 are fulfilled is within the support polygon (Fig. 4), whereby <s> BIB010 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Abstract This paper presents humanoid robotics platform that consists of a humanoid robot and an open architecture software platform developed in METI’s Humanoid Robotics Project (HRP). The final version of the robot, called HRP-2, has 1540 mm height, 58 kg weight and 30 degrees of the freedom. The software platform includes a dynamics simulator and motion controllers of the robot for biped locomotion, falling and getting up motions. The platform has been used to develop various applications and is expected to initiate more humanoid robotics research. <s> BIB011 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In this paper we present a theoretical and experimental study of the self-excited walking of a biped mechanism with knees and feet on level ground. This biped mechanism possesses a single motor at the hip joint and active lock mechanisms at both knee joints. We first show that the self-excitation control enables the three-degrees-of-freedom planar biped model with feet to walk on level ground, and that a stable walking locomotion is possible over a wide range of feedback gain and a foot radius of up to 0.3 m. Subsequently, we describe the manufactured biped Robot 2 which is similar to the analytical model and we show that the biped robot can perform natural dynamic walking on a level floor. It is also shown that the simulated results agree well with the experimental results. We further describe the wireless-controlled biped Robot 3, which can walk on a level floor carrying batteries and electronic circuits inside the thighs. <s> BIB012 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Abstract This paper describes our research efforts aimed at understanding human being walking functions. Using a motion-capture system, force plates and distributed force sensors, walk motion of both human being and humanoid H7 was captured. Experimental results are shown. Comparisons in between human being and H7 walk made using the following characteristics: (1) ZMP trajectories; (2) torso movement; (3) free leg trajectories; (4) joint angle usage; (5) joint torque usage. Furthermore, implications of the comparisons to the humanoid robot are discussed. <s> BIB013 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In this paper we present the experimental validation of a framework for the systematic design, analysis, and performance enhancement of controllers that induce stable walking in N -link underactuated planar biped robots. Controllers designed via this framework act by enforcing virtual constraints—holonomic constraints imposed via feedback—on the robot’s configuration, which create an attracting two-dimensional invariant set in the full walking model’s state space. Stability properties of resulting walking motions are easily analyzed in terms of a two-dimensional subdynamic of the full walking model. A practical introduction to and interpretation of the framework is given. In addition, in this paper we develop the ability to regulate the average walking rate of the biped to a continuum of values by modification of within-stride and stride-boundary characteristics, such as step length. <s> BIB014 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Principal mechanisms of passive dynamic walking are studied from the mechanical energy point of view, and novel gait generation and control methods based on passive dynamic walking are proposed. First, a unified property of passive dynamic walking is derived, which shows that the walking system's mechanical energy increases proportionally with respect to the position of the system's center of mass. This yields an interesting indeterminate equation that determines the relation between the system's control torques and its center of mass. By solving this indeterminate equation for the control torque, active dynamic walking on a level can then be realized. In addition, the applications to the robust energy referenced control are discussed. The effectiveness and control performances of the proposed methods have been investigated through numerical simulations. <s> BIB015 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> 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-... <s> BIB016 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> 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. <s> BIB017 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In this paper, we analyze the balance of a humanoid robot during manipulation tasks. By defining the generalized zero-moment point (GZMP), we obtain the region of it for keeping the balance of the robot during manipulation. During manipulation, the convex hull of the supporting points forms the 3-D convex polyhedron. The region of the GZMP is obtained by considering the infinitesimal displacement and the moment about the edges of the convex hull. We show that we can determine whether or not the robot may keep balance for several styles of manipulation tasks, such as pushing and pulling an object. The effectiveness of our proposed method is demonstrated by simulation. <s> BIB018 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper proposes a universal stability criterion of the foot contact of legged robots. The proposed method checks if the sum of the gravity and the inertia wrench applied to the COG of the robot, which is proposed to be the stability criterion, is inside the polyhedral convex cone of the contact wrench between the feet of a robot and its environment. The criterion can be used to determine the strong stability of the foot contact when a robot walks on an arbitrary terrain and/or when the hands of the robot are in contact with it under the sufficient friction assumption. The determination is equivalent to check if the ZMP is inside the support polygon of the feet when the robot walks on a horizontal plane with sufficient friction. The criterion can also be used to determine if the foot contact is sufficiently weakly stable when the friction follows a physical law. Therefore, the proposed criterion can be used to judge what the ZMP can, and it can be used in more universal cases <s> BIB019 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper proposes the walking pattern generation method, the kinematic resolution method of center of mass (CoM) Jacobian with embedded motions, and the design method of posture/walking controller for humanoid robots. First, the walking pattern is generated using the simplified model for bipedal robot. Second, the kinematic resolution of CoM Jacobian with embedded motions makes a humanoid robot balanced automatically during movement of all other limbs. Actually, it offers an ability of whole body coordination to humanoid robot. Third, the posture/walking controller is completed by adding the CoM controller minus the zero moment point controller to the suggested kinematic resolution method. We prove that the proposed posture/walking controller brings the disturbance input-to-state stability for the simplified bipedal walking robot model. Finally, the effectiveness of the suggested posture/walking control method is shown through experiments with regard to the arm dancing and walking of humanoid robot. <s> BIB020 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper proposes a control method to absorb the landing force or the ground reaction force for a stable dynamic walking of a humanoid robot. Humanoid robot may become unstable during walking due to the impulsive contact force of the sudden landing of its foot. Therefore, a control method to decrease the landing force is required. In this paper, time-domain passivity control approach is applied for this purpose. Ground and the foot of the robot are modeled as two one-port network systems that are connected, and exchange energy with each other. The time-domain passivity controller with admittance causality is implemented, which has the landing force as input and foot's position to trim off the force as output. The proposed landing force controller can enhance the stability of the walking robot from simple computation. The small-sized humanoid robot, HanSaRam-VII that has 27 DOFs, is developed to verify the proposed scheme through dynamic walking experiments. <s> BIB021 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper presents the virtual height inverted pendulum mode (VHIPM), which is a simple and effective trajectory generation method for the stable walking of biped robots. VHIPM, which is based on the inverted pendulum mode (IPM), can significantly reduce the zero moment point (ZMP) error by adjusting the height in the inverted pendulum. We show the relationship between VHIPM and other popular trajectory generation methods, and compare the ZMP errors in walking when trajectories are generated by various methods including VHIPM. We also investigate the sensitivity of the ZMP error in VHIPM to the step length, walking period and mass distribution of a robot. The simulation results show that VHIPM significantly reduces the ZMP errors compared to other methods under various circumstances. <s> BIB022 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper presents a biped humanoid robot that is able to walk on a rough terrain while touching a handrail. The contact wrench sum (CWS for short) is used as the criterion to judge if the contact between the robot and the environment is strongly stable under the sufficient friction assumption, where the contact points are not coplanar and the normal vectors at the points are not identical. It is confirmed that the proposed pattern generator can make the robot walk as desired in dynamics simulations and experiments, and the motions can be improved by a hand position control and using waist joints. <s> BIB023 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> In order to handle complex navigational commands, this paper proposes a novel algorithm that can modify a walking period and a step length in both sagittal and lateral planes. By allowing a variation of zero moment point (ZMP) over the convex hull of foot polygon, it is possible to change the center of mass (CM) position and velocity independently throughout the single support phase. This permits a range of dynamic walking motion, which is not achievable using the 3-D linear inverted pendulum mode (3D-LIPM). In addition, the proposed algorithm enables to determine the dynamic feasibility of desired motion via the construction of feasible region, which is explicitly computed from the current CM state with simple ZMP functions. Moreover, adopting the closed-form functions makes it possible to calculate the algorithm in real time. The effectiveness of the proposed algorithm is demonstrated through both computer simulation and experiment on the humanoid robot, HanSaRam-VII, developed at the Robot Intelligence Technology (RIT) laboratory, Korea Advanced Institute of Science and Technology (KAIST). <s> BIB024 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper presents a motion pattern generator of humanoid robots that walks on a flat plane, steps and a rough terrain. It is guaranteed rigorously that the desired contact between a humanoid robot and terrain should be maintained by keeping the contact wrench sum between them inside the contact wrench cone under the sufficient friction assumption. A walking pattern is generated by solving the contact wrench equations and by applying the resolved momentum control. <s> BIB025 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> We clarified that the common necessary condition for generating a dynamic gait results from the requirement to restore mechanical energy through studies on passive dynamic walking mechanisms. This paper proposes a novel method of generating a dynamic gait that can be found in the mechanism of a swing inspired by the principle of parametric excitation using telescopic leg actuation. We first introduce a simple underactuated biped model with telescopic legs and semicircular feet and propose a law to control the telescopic leg motion. We found that a high-speed dynamic bipedal gait can easily be generated by only pumping the swing leg mass. We then conducted parametric studies by adjusting the control and physical parameters and determined how well the basic gait performed by introducing some performance indexes. Improvements in energy efficiency by using an elastic-element effect were also numerically investigated. Further, we theoretically proved that semicircular feet have a mechanism that decreases the energy dissipated by heel-strike collisions. We provide insights throughout this paper into how zero-moment-point-free robots can generate a novel biped gait. <s> BIB026 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper presents an overview of the recent progress and development of the humanoid robot, HanSaRam series, which have been developed in the Robot Intelligence Technology (RIT) Laboratory, KAIST since 2000. The HanSaRam series have been designed and developed as a small-sized robot for researching walking gate generation, navigation, task planning and HuroCup of FIRA. In particular, the performance of the 7th and 8th versions have been remarkably improved in the aspect of walking pattern generation and task planning. This paper describes the overall design and architecture of recently developed two versions of HanSaRam along with a developed vision simulator tool and the real-time walking gate generation scheme, modifiable walking pattern generator. <s> BIB027 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This article presents a novel observer-based control system to achieve reactive motion generation for dynamic biped walking. The proposed approach combines a feedback controller with an online generated feet pattern to assure a stable gait. Using the desired speed of the robot, a preview control system derives the dynamics of the robot's body, and thereby the trajectory of its center of mass, to ensure a zero moment point (ZMP) movement, which results in a stable execution of the calculated step pattern. Extending the control system by an observer, based on this knowledge and the measured sensor values, compensates for errors in the model parameters and disturbances encountering while walking. <s> BIB028 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper reports the applicability of our passivity-based contact force control framework for biped humanoids. We experimentally demonstrate its adaptation to unknown rough terrain. Adaptation to uneven ground is achieved by optimally distributed antigravitational forces applied to preset contact points in a feedforward manner, even without explicitly measuring the external forces or the terrain shape. Adaptation to unknown inclination is also possible by combining an active balancing controller based on the center-of-mass (CoM) measurements with respect to the inertial frame. Furthermore, we show that a simple impedance controller for supporting the feet or hands allows the robot to adapt to low-friction ground without prior knowledge of the ground friction. This presentation includes supplementary experimental videos that show a full-sized biped humanoid robot balancing on uneven ground or time-varying inclination. <s> BIB029 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> This paper presents the hardware design and gait generation of humanoid soccer robot Stepper-3D. Virtual Slope Walking, inspired by Passive Dynamic Walking, is introduced for gait generation. In Virtual Slope Walking, by actively extending the stance leg and shortening the swing leg, the robot walks on level ground as it walks down a virtual slope. In practical, Virtual Slope Walking is generated by connecting three key frames in the sagittal plane with sinusoids. Aiming for improving the walking stability, the parallel double crank mechanism are adopted in the leg structure. Experimental results show that Stepper-3D achieves a fast forward walking speed of 0.5 m/s and accomplishes omnidirectional walking. Stepper-3D performed fast and stable walking in the RoboCup 2008 Humanoid competitions. <s> BIB030 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes under-actuated is not present during the walk of humanoid robots. The objective of this study is to determine if this phase is useful to reduce the energy consumed in the walking. In order to study the efficiency of this phase, six cyclic gaits are presented for a planar biped robot. The simplest cyclic motion is composed of successive single support phases with flat stance foot on the ground. The most complex cyclic motion is composed of single support phases that include a sub-phase of rotation of the stance foot about the toe and of finite time double support phase. For the synthesis of these walking gaits, optimal motions with respect to the torque cost, are defined by taking into account given performances of actuators. It is shown that for fast motions a foot rotation sub-phase is useful to reduce the criteria cost. In the optimization process, under-actuated phase (foot rotation phase), fully-actuated phase (flat foot phase) and over-actuated phase (double support phase) are considered. <s> BIB031 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> Research on humanoid robotics in Mechatronics and Automation (MA) Laboratory, Electrical and Computer Engineering (ECE), National University of Singapore (NUS) was started at the beginning of this decade. Various research prototypes for humanoid robots have been designed and are going through evolution over these years. These humanoids have been successfully participating in various robotic soccer competitions. In this paper, three major research and development aspects of the above humanoid research are discussed. The paper focuses on various practical and theoretical considerations involved in processing architecture, gait generation and vision systems. <s> BIB032 </s> Intelligent Approaches in Locomotion - A Review <s> Biped trajectories <s> 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. <s> BIB033
Bipedal movement starts from a simple premise -if the feet are placed in a forward moving pattern, and the rest of the body remains supported without falling to the ground, then the whole mass of the system will be moved forward continuously. Bipedal motion is therefore a combination of gait and whole (and especially upper) body stability. A typical procedure for constructing bipedal motion would be: Plan a path to determine foot placements;  Apply stability constraints to determine the Centre of Gravity (CoG) trajectory, based on a model of the weight distribution;  Construct a plausible gait algorithm, addressing the double support (both feet on the ground) and single support (one foot off the ground) phases;  Solve any remaining degrees of freedom (DoF) by any sensible manner. Methods may include copying human movement, simplifying movement, or even producing something that 'looks right'. The first and most common stability constraint is the Zero Moment Point (ZMP) BIB010 . It is calculated as the point under the foot where the ground reaction force will completely negate the effects of moments and forces on the foot from the rest of the body (assuming sufficient friction). If the ZMP exists under the foot, then the system is stable, but if the calculated point is outside the foot, then the ZMP does not exist and the body (robot) will topple, rotating around an edge of the foot. The ZMP equations are used to ensure that the robot remains upright as the feet are moved. They are combined with a model of the mass distribution in order to determine a trajectory for the CoG. The model is often simplified to make deriving the equations simpler. A common model is the inverted pendulum model (IPM), which has a single point mass connected to the ground by a weightless rod BIB008 . In two dimensions this is given as: The gait algorithm is anything that raises a foot (now labelled as belonging to the swing leg) off the ground, moves it forwards, and places it back on the ground. Often, the mass models used assume that all of the mass is contained above the hip. Therefore, the CoG trajectory, as determined by the ZMP constraint, defines the hip angle trajectory. This is calculated to produce the CoG position relative to the hip position, which in turn is specified by the foot placements and leg joint angles. The foot trajectories are used to determine the leg joint angles and the overall motion is determined by the desired ZMP. It is located under the support foot in the single support phase and transitions to the other foot during the double support phase. Solving for the final trajectories is covered in BIB020 . Variations to the above procedure involve alterations to the stability constraint, alterations to the mass distribution model and alterations to the gait algorithm. Some of these variations are discussed below. Equation (1) is a general form of the ZMP inverted pendulum constraint, but in many experiments it is simplified with the condition that there is no vertical movement of the CoG (i.e., ). This is often referred to as the Three Dimensional Linear Inverted Pendulum Model (3D-LIPM). The simplicity of the 3D-LIPM algorithm made it popular in BIB020 , BIB011 , BIB021 , BIB005 , BIB027 (with an emphasis on controllability including steering), BIB028 (with an observation system added), and BIB024 (using ZMP trajectory modification based on an analysis on the feasible ZMP region). In BIB022 , a comparison was made between several different mass models. The authors found that all of the models could be written in the form of equation 1 but with α varying depending on which mass model was used. Since different mass models will result in varying levels of accuracy to the true model, the identification of the constant α allows the mass model to be fine tuned. By experimentally varying α, the ZMP error can be reduced. As α multiplies the height zCoG, the model was called a Virtual Height Inverted Pendulum. A simple error minimisation procedure was used to find optimal values for α for different step periods. The procedure involved incrementing or decrementing α by a fixed amount, if the ZMP error was outside a threshold interval. To further increase the accuracy, more complicated mass models can be used, at the expense of increased complexity of analysis. For example, multi-mass models were used in BIB009 , BIB006 . In BIB006 , three different bipedal control methods were evaluated and validated by comparing them to a reference multi-mass model with ZMP constraint. The compared models used polynomial interpolation between start and end states, actuator driving in the double-support phase, and a combined approach with added toe support and shock absorption, respectively. The toe support phase is omitted in normal ZMP based methods because it is, by definition, a failure with the foot beginning to rotate about the front edge. The authors included it to allow real-time freedom of choice for placing the landing foot. They argued this would allow for better walking on uneven ground. Often, the ZMP is required to be under the centre of the foot during the single support phase, transitioning to the other foot in the double support phase. However, this is not the only way to position it as the ZMP can exist anywhere in the support polygon. Given this wider range of possible ZMPs, a control law for the ZMP was developed in BIB003 . The motion was based on the inverted pendulum model but the ZMP and vertical reaction forces were assigned control laws that allowed the centre of mass (CoM) to closely track a reference trajectory, allowing for real-time control and smooth motion. In an attempt to generate more natural looking and efficient gaits, an energy control method was developed in  , BIB015 . The mechanical energy of the system was controlled to track a reference energy trajectory, which accounted for energy losses during the interactions between the robot and the surface. Trajectories based on conserving potential energy were developed in  , and ease of analysis was suggested as an advantage of this method. Energy efficiency can be increased by creating self-excited behaviour in the swing leg BIB007 , BIB012 . The ZMP constraint was developed for simple environment interaction, where the ground is even and the contact is only between the feet and the environment. Solutions to deal with uneven ground include an active balancing system based on distributing appropriate antigravitational forces to the contact points BIB029 , and a modified ZMP technique using a nearest possible point to the desired ZMP during times when it cannot be found under the support polygon BIB008 . Extensions to the ZMP have been presented to deal with cases where other parts of the system are in contact with the environment. These include the Generalized Zero Moment Point BIB018 , and Contact Wrench Sum BIB023 , BIB019 , BIB025 . Both of these techniques involve the relationship between all of the contacts made with the environment (feet, hands, etc...) and the forces through the system, with the goal of preventing unwanted rotations. They allow locomotion on uneven floors and the use of supports, such as handrails. The ZMP can only be used to classify a state as stable or unstable. More informative alternatives include the Foot Rotation Indicator (FRI) BIB001 , used to determine the stability margin or degree of instability, and the Centroidal Moment Point (CMP) BIB016 , which provides information on the whole body rotational. After analysing how the various stability constraints performed for a human gait, 0 CoG z  the authors of BIB016 recommended a modified FRI that was more sensitive, and that the CMP and ZMP should both be used, for human-like locomotion. A reason to improve upon ZMP control is illustrated in BIB013 , where significant differences were found between human and ZMP gaits, such as CoG trajectory, free leg trajectory, and the position of the ZMP under the foot. Inspired by passive downhill walking systems, an active system was controlled, using a virtual slope walking gait in BIB030 . The system used knee bending and straightening to develop a relationship between the legs on level ground, that was the same as a normal gait on a downwards slope. The physical design of the robot helped with stability and the control mechanism was found to be able to produce fast gaits. Quick gaits were also generated using a polynomial trajectory approach, with algebraic optimisation based on ZMP evaluation, torque and velocity limits BIB031 . If the system is dynamically stable, or controlled in a way to easily guarantee stability, then stability constraints are not needed BIB017 . In BIB026 , a robot was designed that did not have actuators at the ankle and was stable enough not to require the ZMP constraint. Furthermore, to easily enable a high speed gait, each leg contained a telescopic actuator which pumped the swing leg. The authors of BIB002 investigated initiating movement, stopping, and standing, to cope with real world state changes. Other transitions (e.g., for dealing with slopes) were examined in  , where the algorithm had to control the walking on a flat ground, on a slope, and the transition between the two. To help with walk stability, a method to control foot landing force was presented in BIB021 . It consisted of a system that measured impact force and outputted a foot height in order to absorb the collision. Full jumping and landing control was developed in  where, because of the point model used, ZMP or similar constraints were not possible due to the lack of a support polygon. Convergence to a known stable state guaranteed stability in the different phases of the motion. Another control algorithm for point feet was given in  . To avoid the over-constrained nature of ZMP type criteria, a different analytical framework was used in  - BIB014 . The analysis was based on transforming the problem into a task of driving a set of dynamic outputs to zero. Zero dynamics equations were produced for the swing and impact phases. The two phases were combined into a complete model that was called the hybrid zero dynamics (HZD). A suitable cost function of the HZD was defined and used to drive the motion into the swing and impact phases. Additional constraints were also imposed, such as minimal ground reaction force, foot landing only at the end of the swing, plus various boundary condition constraints. Given the cost function and constraints, a sparse sequential quadratic programming optimisation algorithm was used to determine the parameters of the model. Using these techniques, asymptotically stable walking (returns back to the gait after being perturbed) was produced. Instead of synthesising the DoF trajectories, an alternative is to track supplied reference trajectories. In  , a trajectory control law was developed to be resilient to perturbation. The authors identified a lack of resilience as a problem of previous tracking methods. Using human motion capture data was investigated in BIB004 , and methods for interpreting the data automatically, for use by a humanoid robot, were developed. Analytical approaches have occasionally been compared to other control methods. A ZMP inverted pendulum method (IMP) was used in BIB032 but, although successful, the approach produced slower walking speeds than an oscillator based control system. Instead of an inverted pendulum model, a static balance equation was used for the hip angle in BIB033 . This was implemented for a ditch crossing walk, and the foot placements were determined as a function of the distance from the ditch. The dynamic stability and energy efficiency of the analytical approach were compared to an optimized neural network, and fuzzy logic approaches. It was found to be the least stable and least efficient of the three approaches.