Walking Pattern Generation Research Articles

将来にわたるZMP許容領域を考慮したオンライン2足歩行軌道生成法

将来にわたるZMP許容領域を考慮したオンライン2足歩行軌道生成法

Online Walking Pattern Generation for a Humanoid that uses Estimated Actual Velocity of the Robot

This paper presents a method of utilizing estimated actual velocity of robot links for online walking pattern generation. Repetitive generation of the dynamically-feasible trajectories that start from the actual motion status of the robot is carried out, so that the balance of the actual walking will be maintained by the generation. A method of estimating the absolute velocity of the torso and feet based on the gyroscopic-sensor information is discussed. Then we present a method of designing a trajectory that satisfies estimated position and velocity as initial conditions and converges to a trajectory that realizes given walking parameters. Those 2 methods were implemented in the online walking controller of full-size humanoid HRP-2. The validity of the proposed methods is confirmed through the walking experiments of HRP-2.

1A2-O02 予見制御によるオンライン歩行パターン生成アルゴリズム(ヒューマノイド(2))

This paper describes an online walking pattern generation using preview control. Before a robot starts walking, the first 3-step walking pattern is generated by using the pattern generation method. If a generated 3-step pattern is created, it will be connected with the previous step using linear interpolation. The first walking pattern is connected with the second walking pattern when the ZMP (Zero Moment Point) is in the center of the support polygon formed by both feet. When the robot stops, the last 3-step pattern is performed. In order to verify the effectiveness of the online walking pattern generation method, various walking experiments using a biped humanoid robot are conducted.

Command State-Based Modifiable Walking Pattern Generation on an Inclined Plane in Pitch and Roll Directions for Humanoid Robots

Previous research related to walking on an inclined plane for humanoid robots, including the 3-D linear inverted pendulum model (3D-LIPM) approach, were unable to modify walking period, step length, and walking direction independently without any additional step for adjusting the center of mass (CoM) motion. Moreover, the inclination along the pitch direction was only considered for walking. To solve these problems, a novel command state (CS)-based modifiable walking pattern generator for humanoid robots is proposed for modifiable walking on an inclined plane in both pitch and roll directions. The dynamic equation of the 3D-LIPM on the inclined plane in both pitch and roll directions is derived to obtain the CoM motion. Using the CoM motion, a method for modifiable walking pattern generation on the inclined plane is developed to follow a given CS composed of walking periods, step lengths, and walking directions for both legs. The effectiveness of the proposed walking pattern generator is demonstrated through both simulation and experiment for the small-sized humanoid robot, HanSaRam-IX (HSR-IX).

Evolutionary Multiobjective Footstep Planning for Humanoid Robots

This paper proposes a novel evolutionary multiobjective footstep planner for humanoid robots. First, a footstep planner using a univector field navigation method is proposed to provide a command state (CS), which is to be an input of a modifiable walking pattern generator (MWPG) at each footstep. Then, the MWPG generates corresponding trajectories for every leg joint of the humanoid robot at each footstep to follow the CS. Second, a multiobjective evolutionary algorithm (MOEA) is employed to optimize the univector fields satisfying multiple objectives in navigation. Finally, a preference-based selection algorithm based on a fuzzy measure and fuzzy integral is proposed to select the preferred one out of various nondominated solutions obtained by the MOEA. The effectiveness of the proposed evolutionary multiobjective footstep planner is demonstrated through computer simulations for a simulation model of a small-sized humanoid robot, HanSaRam-VIII.

Adaptive walking pattern generation and balance control of the passenger-carrying biped robot, HUBO FX-1, for variable passenger weights

A passenger-carrying biped robot is a practical robot capable of carrying a passenger for both entertainment purposes and disabled transport by means of biped walking. In the walking controls of the biped walking robot, changes in the payload are not generally considered. However, in the case of a passenger-carrying biped robot, the range of possible payloads for passenger weight is relatively wide, from zero to approximately one hundred kgf. In the authors' previous research pertaining to passenger-carrying biped robots, the robot was modeled using a specific passenger weight; hence, the control parameters were tuned for it and kept to be constant. However, the previous method's weakness was a decrease in the walking performance and walking stability of the robot when the passenger's weight was much heavier or lighter than the predefined passenger weight. Therefore, in this paper, the walking pattern generation and balance control methods are developed to adaptively cope with variable passenger weights. These methods are then experimentally verified to ensure that the walking performance could be preserved uniformly for a variation of passenger weights.

推定絶対運動状態を始点とする短周期軌道生成を用いたヒューマノイドの不整地適応歩行制御

This paper presents a novel robust framework for online walking control that can handle unknown terrain. The actual motion of the robot in the absolute coordinate system is estimated and used as the initial conditions of short cycle online walking pattern generation in the framework so that the walking pattern generation is put into the feedback loop of the balance maintenance of the actual walking. We used attitude sensor system for estimating the absolute motion, and the walking patterns are generated at 20[ms] cycle by using full body dynamic model. Since the initial conditions are decided from the estimated actual posture, the pattern generated in each cycle is discontinuous to the one generated in the previous cycle. Therefore, a local sensor feedback controller is developed that can execute discontinuous segments of the trajectory and control the ground reaction force. Damping control of the foot position by using position-controlled leg joints is adopted to attain the desired ground reaction force. In addition, damping control of the torso inclination is implemented in the local sensor feedback to suppress the divergence of the torso motion from that commanded in the absolute coordinate system. The proposed framework is implemented on the full-size humanoid HRP-2, and validated through the experiments including walking on many types of unknown terrain with up to 10 degrees slope uncertainty and over 20[mm] in height uncertainty.

Enhancing Zero Moment Point-Based Control Model: System Identification Approach

The approximation of a humanoid robot by an inverted pendulum is one of the most frequently used models to generate a stable walking pattern using a planned zero moment point (ZMP) trajectory. However, on account of the difference between the multibody model of the humanoid robot and the simple inverted pendulum model, the ZMP error might be bigger than the polygon of support and the robot falls down. To overcome this limitation, we propose to improve the accuracy of the inverted pendulum model using system identification techniques. The candidate model is a quadratic in the state space representation. To identify this system, we propose an identification method that is the result of the comprehensive application of system identification to dynamic systems. Based on the quadratic system, we also propose controlling algorithms for on-line and off-line walking pattern generation for humanoid robots. The efficiency of the quadratic system and the walking pattern generation methods has been successfully shown using dynamical simulation and conducting real experiments on the cybernetic human HRP-4C.

Walking Pattern Generation for a Biped Walking Robot Using Convolution Sum

This paper describes a novel walking pattern generation method for a biped humanoid robot using a convolution sum. For a biped walking model, a single mass inverted pendulum model is generally used and the zero moment point (ZMP) equation is described by a decoupled linear differential equation. As a walking pattern generation method for the robot model, a novel method using a convolution sum is proposed in this paper. From the viewpoint of the linear system response, walking pattern generation can be regarded as a convolution of an arbitrary reference ZMP and the walking pattern for an impulse reference ZMP. For the calculation of convolution, the walking pattern for an impulse reference ZMP is first derived from the analytic walking pattern for a step reference ZMP. The convolution sum is then derived in two recursive forms, which can be applied online and offline, respectively. The proposed algorithm requires low computation power, since the walking pattern equation is composed of a recursive form. As the algorithm is expressed in analytic form, it is not necessary to solve optimization problems or calculate the fast Fourier transform, contrary to previous approaches. A computer simulation of walking demonstrates that the proposed algorithm yields excellent accuracy compared to the preview control method — one of the most highly regarded walking pattern generation methods. In addition, the application on the multi-point mass model is shown with the computer simulation.

209205 二次元神経筋骨格モデルに基づくニホンザル二足歩行の生成(OS05 生体の計測とモデリング2,オーガナイズド・セッション)

We constructed a two-dimensional musculoskeletal model of the Japanese macaque for simulation of bipedal walking based on forward dynamic simulation. The musculoskeletal system was constructed as 9 rigid links with 10 principal muscles. To generate locomotion, phase oscillators were used as a model of the spinal central pattern generator and motor commands sent to each muscle was modeled as a combination of square waves. By determining the parameters defining the shape of motor commands using genetic algorithm such as to maximize walking distance and to minimize energy expenditure, bipedal locomotion was generated. Although the generated walking pattern did not coincide with that of actually measured, we found that incorporating restricted joint motions due to muscle's passive resistive property is important for simulating monkey-like bent-hip, bent-knee bipedal walking.

2P2-J02 推定した絶対速度情報を用いるヒューマノイドの短周期歩行軌道生成(ヒューマノイド)

This paper presents a method of utilizing estimated actual velocity of robot links for online walking pattern generation. The aim of the method is repetitively generating dynamically feasible trajectories that start from the actual motion status of the robot so that the balance of the robot will be maintained. A method of estimating the absolute velocity of the torso and feet based on gyroscopic sensor information is discussed. Then a method of designing a trajectory that satisfies estimated position and velocity as initial conditions and converges to a trajectory that realizes given walking parameters. Those 2 methods were implemented in the online walking controller of full-size humanoid HRP-2. The validity of the proposed methods is confirmed through the walking experiments of HRP-2.

Subject-oriented overground walking pattern generation on a rehabilitation robot based on foot and pelvic trajectories

Robotic devices have been designed to enhance motor recovery by replicating clinical motion pattern training. A rehabilitation gait system has been developed to assist the subject-centric gait rehabilitation on overground walking. Environment constraints are presented such as intermittent ground contact, impact between foot and ground, and foot clearance requirement. A subject-oriented gait pattern generation is proposed with respect to the pelvic and foot trajectory of the human gait. For simplicity, ten designated points over one gait cycle are defined to express an individual walking pattern with specific stride height and length. Gait and posture on these points are studied in terms of the trajectory of ankle and metatarsal. Furthermore, the pelvic motion serves as compensation to fulfill those predescribed foot trajectory, while the joint angles for the robotic orthosis attached to the lower limb are calculated based on the solving of inverse kinematics. Results of the initial testing indicate the effectiveness and smoothness of the desired motion generated by the gait system. The labor saving of using the developed gait system is highlighted and the performance of the gait system is evaluated by the EMG analysis of selected lower limb muscles.

HUMAN-LIKE GAIT GENERATION FOR BIPED ANDROID ROBOT USING MOTION CAPTURE AND ZMP MEASUREMENT SYSTEM

This article proposes a novel strategy to generate both a human-like walking pattern and a human-like zero moment point (ZMP) trajectory for a biped android robot. In general, the motion-capture technique has been widely utilized to obtain a walking pattern that is kinematically similar to the walking of a human. However, in addition to kinematic considerations, a suitable ZMP shaping technique is necessary to apply the human gait derived by motion capturing to biped robots more effectively. In previous research by the authors, a walking pattern generation strategy was developed considering the kinematics using motion capturing and Fourier fitting. However, it was found that there were differences between the calculated ZMP trajectory of the earlier research and the measured ZMP trajectory directly derived from the sensor in this research. Therefore, the differences and their factors are analyzed and a new strategy is proposed that effectively reduces the differences between them. Finally, the proposed strategy is shown to be effective for generating human-like walking pattern and ZMP trajectory for biped android robots through stick figure simulations.

Two-Stage Time-Parametrized Gait Planning for Humanoid Robots

In this paper, we propose a framework on planning collision-free walking motion for biped humanoid robots. Our proposed planner is composed of two phases. In the first phase, the constraint condition is generated as a function of time by using the walking pattern generator. In the second phase, the collision-free walking motion is planned. To generate the collision-free motion, we add a time parameter to each milestone of the single-query, bidirectional, lazy collision checking planner in order to explicitly consider the time-parametrized constraint conditions. Further, we smoothen the generated path by using B-spline interpolation. Through experimental results, we show that our planner is effective in realizing collision-free walking motion by real humanoid robots.

Energy-efficient gait generation for biped robot based on the passive inverted pendulum model

SUMMARYFrom the viewpoint of the system's mechanical energy, the passive inverted pendulum model (PIPM) is proposed for the generation of more energy-efficient biped gait pattern. The generated walking pattern, based on the PIPM, enables the fully actuated biped robots to closely mimic the behavior of stable passive walking, so that it can have good energy-efficiency, which is the inherent advantage of the passive system. Furthermore, the pattern generation method is extended to any desired terrain as well. As for SHR-1, the first-generation biped robot of Shanghai Jiao Tong University, gait synthesis is clarified in detail. Finally, the walking experiments are carried out on SHR-1, and the effectiveness of the proposed pattern generation method is confirmed.

REAL-TIME BIPEDAL WALKING GAIT ADJUSTMENT MODES BASED ON A TRUNCATED FOURIER SERIES MODEL

This paper presents three basic bipedal walking gait adjustment modes: step-frequency, step-length and biped lower extremities' pattern adjustments. All the adjustment modes are based on a simple Fourier Series formulation named the Truncated Fourier Series (TFS) model which is newly proposed as a walking pattern generator. Making use of these three gait adjustment modes, bipedal walking can be modified in real-time according to the environment changes. In this paper, the developed gait adjustment modes have been studied by dynamic simulations. The results obtained show that stable walking on uneven terrains as well as human-like walking behaviors can be achieved.

WALKING PATTERN MAPPING FROM IMPERFECT MOTION CAPTURE DATA ONTO BIPED HUMANOID ROBOTS

This paper proposes an efficient walking pattern mapping algorithm from motion capture data onto biped humanoid robots. Currently, the technology known as human motion capture is widely utilized to generate various humanlike motions in many applications, including robotics. An important thing is that several difficulties are associated with motion capture data. These include a data offset issue, noise, and drift problems due to measurement errors caused by imperfect camera calibration, and marker position. If a biped robot uses motion capture data without suitable post-processes, the walking motion of the robot will differ from an actual walking motion, and the Zero Moment Point (ZMP) will be asymmetrical and noisy, leading to unstable walking. A further difficulty exists in the walking pattern mapping process due to the different joint numbers, link sizes, and weights between a human and a robot. Although walking pattern mapping is suitable after addressing the above difficulties, a slip problem between the feet and the ground can continue to cause problems. To solve these difficulties efficiently, a Fourier fitting method is proposed in this research. Improvements of walking pattern and the ZMP trajectory are confirmed using the proposed method. Furthermore, a geometric mapping method is introduced to generate walking patterns for various biped robots while maintaining a degree of similarity to humans. By applying a no-slip constraint to the feet and modifying the joint angles through inverse kinematics, the slip problem is also solved. The effectiveness of the proposed algorithm is verified through computer simulations of two different biped robots that have different sizes, weights, walking cycles, and step lengths.

2A2-F10 扁平足を有した歩行モデルのリミットサイクル規範三次元歩行制御法の構築

Our ultimate goal is introducing energy-efficient walking patterns to actual humanoid robots. It is known that Limit Cycle based walking methods, e.g. Passive Dynamic Walking, have such a desired property. Unfortunately, the methods have been limited to simple planar biped models. In this paper, we propose a way of extending Limit Cycle based walking pattern generation to apply it to a 7DOF 3D biped with ankles, knees, an upper body and with flat feet. Our approach decouples roll and pitch motions in the frontal/sagittal planes, respectively. We derive the limit-cycle based walking pattern with the help of an extended planar model including ankles, knees and the upper body. Robustness of the motion is ensured via a feedback control method based on mechanical energy. The performance of the walking pattern generator in 3D and the controller is confirmed via numerical simulations.

ヒューマノイドロボットの全身動作と足の着地位置の同時計画(機械力学,計測,自動制御)

This paper proposes a method for simultaneously planning the whole-body-motion and the foot-place for a humanoid robot dynamically walking on the flat ground. As constraint conditions imposed on the planner, we consider the differential equation of the robot's motion. To solve this constraint, we use the real-time walking pattern generator. We randomly sample the configuration space to search for the path connecting the start and the goal configurations. When sampling the configuration space, a few milestones are sequentially connected to the parent milestone. To show the effectiveness of the proposed method, we show an experimental result where the humanoid robot HRP-2 avoids the obstacle dynamically walking on the ground.

Simulation of bipedal walking based on CPG for Clogs-type Sole Shape

In our research, we use GETA, Japanese traditional wooden-clogs. The simulator we developed can simulate human walking with GETA. The simulator employs Central Pattern Generator (CPG) for bipedal walking pattern generation. The CPG based walking pattern is one of the candidates for simulating human walking. The average Japanese body dimensions data are applied to the bipedal model so that human walking efficiency is evaluated on the simulator. The proposed simulator is compared with real human walking, by analyzing the swing leg trajectory and the data from the pressure sensor on the GETA. The data show the effectiveness of the simulator, and point out that efficiency of walking with GETA is better than normal walking without GETA.