Biped Walking Robot Research Articles

Exponential Stabilization of Fully Actuated Planar Bipedal Robotic Walking With Global Position Tracking Capabilities

This paper focuses on the development of a model-based feedback controller to realize high versatility of fully actuated planar bipedal robotic walking. To conveniently define both symmetric and asymmetric walking patterns, we propose to use the left and the right legs for gait characterization. In addition to walking pattern tracking error, a biped's position tracking error in Cartesian space is included in the output function in order to enable high-level task planning and control such as multi-agent coordination. A feedback controller based on input–output linearization and proportional–derivative control is then synthesized to realize exponential tracking of the desired walking pattern as well as the desired global position trajectory. Sufficient stability conditions of the hybrid time-varying closed-loop system are developed based on the construction of multiple Lyapunov functions. In motion planning, a new method of walking pattern design is introduced, which decouples the planning of global motion and walking pattern. Finally, simulation results on a fully actuated planar biped show the effectiveness of the proposed walking strategy.

Modeling and Designing of Bipedal Walking Robot

Modeling and Designing of Bipedal Walking Robot

A neural network with central pattern generators entrained by sensory feedback controls walking of a bipedal model

A neuromechanical simulation of a planar, bipedal walking robot has been developed. It is constructed as a simplified, planar musculoskeletal model of the biomechanics of the human lower body. The controller consists of a dynamic neural network with central pattern generators (CPGs) entrained by force and movement sensory feedback to generate appropriate muscle forces for walking. The CPG model is a two-level architecture, which consists of separate rhythm generator and pattern formation networks. The biped model walks stably in the sagittal plane without inertial sensors or a centralized posture controller or a ‘baby walker’ to help overcome gravity. Its gait is similar to humans’ and it walks at speeds from 0.850 m s−1 up to 1.289 m s−1 with leg length of 0.84 m. The model walks over small unknown steps (6% of leg length) and up and down 5° slopes without any additional higher level control actions.

A novel projected Fletcher‐Reeves conjugate gradient approach for finite‐time optimal robust controller of linear constraints optimization problem: Application to bipedal walking robots

SummaryFor finite‐time optimal robust control problem of bipedal walking robot, a class of global and feasible projected Fletcher‐Reeves conjugate gradient approach is proposed based on an online convex optimization algorithm. The optimal robust controllers are solved by projected Fletcher‐Reeves conjugate gradient approach. The approach can rapidly converge to a stable gait cycle by selecting an initial gait. Under some suitable conditions, we provide a rigorous proof of global convergence and well‐defined properties for projected Fletcher‐Reeves conjugate gradient approach. To demonstrate the effectiveness of the bipedal walking robot, we will conduct numerical simulations on the model of 3‐link robot with nonlinear, impulsive, and underactuated dynamics. Furthermore, to indicate the availability of high‐dimensional robotic system, the main result is illustrated on a nonlinear impulsive model of a bipedal walking robot through simulations via finite‐time optimal robust controller. Numerical results show that the projected Fletcher‐Reeves conjugate gradient approach is feasible and effective for bipedal walking robots. Therefore, it is reasonable to infer that the optimal robust control approach can be used in practical systems.

Evaluation of physical damage associated with action selection strategies in reinforcement learning

Reinforcement learning techniques enable robots to deal with their own dynamics and with unknown environments without using explicit models or preprogrammed behaviors. However, reinforcement learning relies on intrinsically risky exploration, which is often damaging for physical systems. In the case of the bipedal walking robot Leo, which is studied in this paper, two sources of damage can be identified: fatigue of gearboxes due to backlash re-engagements, and the overall system damage due to falls of the robot. We investigate several exploration techniques and compare them in terms of gearbox fatigue, cumulative number of falls and undiscounted return. The results show that exploration with the Ornstein-Uhlenbeck (OU) process noise leads to the highest return, but at the same time it causes the largest number of falls. The Previous Action-Dependent Action (PADA) method results in drastically reduced fatigue, but also a large number of falls. The results reveal a previously unknown trade-off between the two sources of damage. Inspired by the OU and PADA methods, we propose four new action-selection methods in a systematic way. One of the proposed methods with a time-correlated noise outperforms the well-known e-greedy method in all three benchmarks. We provide guidance towards the choice of exploration strategy for reinforcement learning applications on real physical systems.

Sliding Passive Dynamic Walking of Compass-Like Biped Robot: Collision Modeling, Necessary Conditions, and Complexity

[abstFig src='/00290003/06.jpg' width='300' text='Short- and long-period sliding passive compass gaits' ] This paper investigates the modeling and analysis of the sliding passive dynamic walking of a compass-like biped robot with pointed feet. First, we present the passive compass-like biped model and redevelop the inelastic collision equation for stance-leg exchange, taking the impulsive frictional effect into account. Second, we numerically show that two different steady motions, the short- and long-period sliding passive compass gaits, can be generated according to the initial conditions in the presence of the effects of the hip damper and impulsive frictional force. Furthermore, we numerically analyze the change characteristics of the gait descriptors with respect to the system parameters, and we discuss the relationship between the short- and long-period gaits.

Asymmetric Swing-Leg Motions for Speed-Up of Biped Walking

[abstFig src='/00290003/04.jpg' width='120' text='Stick diagram of limit cycle walking with asymmetric swing-leg motion' ] This study presents a novel swing-leg control strategy for speed-up of biped robot walking. The trajectory of tip of the swing-leg is asymmetric at the center line of the torso in the sagittal plane for this process. A methodology is proposed that enables robots to achieve the synchronized asymmetric swing-leg motions with the stance-leg angle to accelerate their walking speed. The effectiveness of the proposed method was simulated using numerical methods.

3D stable biped walking control and implementation on real robot

A combination of walking control methods was proposed and implemented on a biped robot. The LIPM-based model predictive control (MPC) was adopted to generate a basic stable walking pattern. The stability of pitch and yaw rotation was improved through pitch and yaw momentum control as a supplementation of MPC. It is found that biped robot walking tends to deviate from the planned walking direction if not considering the rotation friction torque in yaw axis under the support foot. There are basically two methods to control yaw momentum, waist and swing arms rotation control. However, the upper body is often needed to accomplish other tasks. Therefore, a yaw momentum control method based on swing leg dynamics was proposed. This idea does not depend on upper body’s motion and is highlighted in this paper. Through experiments, the feasibility of the combination of the control methods proved to be practical in keeping biped robot walking stable both in linear and rotation motion. The pros and cons of the yaw momentum control method were also tested and discussed through comparison experiments, such as walking on flat and uneven terrain, walking with different payloads.

Parallel Elastic Elements Improve Energy Efficiency on the STEPPR Bipedal Walking Robot

This paper describes how parallel elastic elements can be used to reduce energy consumption in the electric-motor-driven, fully actuated, Sandia Transmission-Efficient Prototype Promoting Research (STEPPR) bipedal walking robot without compromising or significantly limiting locomotive behaviors. A physically motivated approach is used to illustrate how selectively engaging springs for hip adduction and ankle flexion predict benefits for three different flat-ground walking gaits: human walking, human-like robot walking, and crouched robot walking. Based on locomotion data, springs are designed and substantial reductions in power consumption are demonstrated using a bench dynamometer. These lessons are then applied to STEPPR, a fully actuated bipedal robot designed to explore the impact of tailored joint mechanisms on walking efficiency. Featuring high-torque brushless DC motors, efficient low-ratio transmissions, and high-fidelity torque control, STEPPR provides the ability to incorporate novel joint-level mechanisms without dramatically altering high-level control. Unique parallel elastic designs are incorporated into STEPPR, and walking data show that hip adduction and ankle flexion springs significantly reduce the required actuator energy at those joints for several gaits. These results suggest that parallel joint springs offer a promising means of supporting quasi-static joint torques due to body mass during walking, relieving motors of the need to support these torques and substantially improving locomotive energy efficiency.

A functional electrical stimulation system for human walking inspired by reflexive control principles.

This study presents an innovative multichannel functional electrical stimulation gait-assist system which employs a well-established purely reflexive control algorithm, previously tested in a series of bipedal walking robots. In these robots, ground contact information was used to activate motors in the legs, generating a gait cycle similar to that of humans. Rather than developing a sophisticated closed-loop functional electrical stimulation control strategy for stepping, we have instead utilised our simple reflexive model where muscle activation is induced through transfer functions which translate sensory signals, predominantly ground contact information, into motor actions. The functionality of the functional electrical stimulation system was tested by analysis of the gait function of seven healthy volunteers during functional electrical stimulation–assisted treadmill walking compared to unassisted walking. The results demonstrated that the system was successful in synchronising muscle activation throughout the gait cycle and was able to promote functional hip and ankle movements. Overall, the study demonstrates the potential of human-inspired robotic systems in the design of assistive devices for bipedal walking.

Development of Biped Robot and Pose stabilization and Based on Passive Dynamic Walking

Walking method based zero moment position algorithms that can guarantee the stability of the biped walking robot while walking, but it moves the legs for the stability of the walking in a way that is not related to energy conservation. Walking method using ZMP can cause low battery efficiency and load on leg joints. The walking method using the passive walking, which is a natural and efficient method of walking, can reduce the load on the joints of the robot by using the method without using the inertia that occurs when walking and reduced control elements and efficient use of battery. In this paper, a biped robot with an actuator based on the principle of passive dynamic walker mechanism is applied to a passive walking algorithm. In order to solve the problem of stabilization of the posture during walking, the posture was stabilized by using the swing motion of the arm. and the walking movement of the robot was observed using the AHRS sensor applied to the robot .It was confirmed that the posture can be stabilized based on measured values using AHRS.

非対称CPGを用いた空圧式除振装置の流量外乱抑制

Pneumatic anti-vibration apparatus (AVA) has been used for suppressing the vibration from the floor. Compressed air produced by the air compressor is supplied to air spring, which is used as an actuator in AVA. This paper considers the suppression of flow disturbance, which is caused by pressure variation of compressed air. Based on the internal model principle, the suppression of vibration of AVA due to flow disturbance has been confirmed by using Central Pattern Generator (CPG) in parallel with a displacement controller. In biological study, CPG in bodies playing a significant role in the walking have been learned. Moreover, mathematical models of CPG have been reported, and some researchers have been studying about walking of biped-robots by using CPG to generate desired value. On the other hand, this paper proposes asymmetric CPG as new model for further vibration suppression, compared with the symmetric CPG which is the conventional model. This new model introduces asymmetry by changing its parameters into different values in order to improve reproducibility of waveform which shows the variation of supplied air pressure. Validity of the proposed model is presented by experimental result of AVA. The effectiveness is shown by analyzing and comparing the results of experiment and simulation of symmetric and asymmetric CPGs.

Constrained Quadratic Programming and Neurodynamics-Based Solver for Energy Optimization of Biped Walking Robots

The application of biped robots is always trapped by their high energy consumption. This paper makes a contribution by optimizing the joint torques to decrease the energy consumption without changing the biped gaits. In this work, a constrained quadratic programming (QP) problem for energy optimization is formulated. A neurodynamics-based solver is presented to solve the QP problem. Differing from the existing literatures, the proposed neurodynamics-based energy optimization (NEO) strategy minimizes the energy consumption and guarantees the following three important constraints simultaneously: (i) the force-moment equilibrium equation of biped robots, (ii) frictions applied by each leg on the ground to hold the biped robot without slippage and tipping over, and (iii) physical limits of the motors. Simulations demonstrate that the proposed strategy is effective for energy-efficient biped walking.

An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation

This paper is an introductory tutorial for numerical trajectory optimization with a focus on direct collocation methods. These methods are relatively simple to understand and effectively solve a wide variety of trajectory optimization problems. Throughout the paper we illustrate each new set of concepts by working through a sequence of four example problems. We start by using trapezoidal collocation to solve a simple one-dimensional toy problem and work up to using Hermite--Simpson collocation to compute the optimal gait for a bipedal walking robot. Along the way, we cover basic debugging strategies and guidelines for posing well-behaved optimization problems. The paper concludes with a short overview of other methods for trajectory optimization. We also provide an electronic supplement that contains well-documented MATLAB code for all examples and methods presented. Our primary goal is to provide the reader with the resources necessary to understand and successfully implement their own direct collocation...

二脚歩行ロボットにおける柔軟体幹機構および腕振り運動の効果

二脚歩行ロボットにおける柔軟体幹機構および腕振り運動の効果

영상 처리를 이용한 소형 이족 보행 로봇의 임무 수행

영상 처리를 이용한 소형 이족 보행 로봇의 임무 수행

Design of a bioinspired tunable stiffness robotic foot

The human foot is capable of adapting to various diverse terrains, and this function is due, in part, to the foot's capacity of varying its stiffness in different anatomical regions. The purpose of this study is to develop an adaptable robotic foot by emulating the human foot's arch, horizontal tie (the plantar aponeurosis, midfoot ligaments, etc.), and its ability of varying its stiffness. The robotic foot is designed, analyzed, optimized and fabricated as a semi-circular arch with a horizontal tie consisting of a Tunable Stiffness Mechanism (TSM). The active number of coils in parallel/series configuration of concentric helical springs is changed to control the stiffness of the TSM. The arch stiffness and tunable stiffness range were optimized using the epsilon constraint method. Analytical and finite element modeling results closely match the experimental validation of both the tunable axial stiffness behavior of the TSM and tunable bending stiffness of the robotic foot assembly. The results also show that the TSM is capable of varying the potential energy storage at midstance depending on the load or displacement applied. In conclusion, a robotic foot was developed to adapt to various diverse terrains through varying stiffness and therefore potential energy stored at midstance; the potential energy is then available for an elastic rebound and propulsion in the terminal phase of gait. By implementing proper control algorithms, the proposed tunable stiffness robotic foot is capable of real-time adaptations to changing terrains, which may lead to the design and development of more adaptive industrial and bipedal walking robots.

Bifurcation gait suppression of a bipedal walking robot with a torso based on model predictive control

In our previous work, we have studied a bipedal walking model with a torso, in which the gait evolves from the stable period-1 pattern directly into the Neimark–Sacker bifurcation pattern. Using the Ott–Grebogi–Yorke method, the bifurcation gait could be suppressed into the period-1 gait with higher energy efficiency and walking speed. However, the disturbance rejection ability of the obtained period-1 gait was insufficient, i.e., the basin of attraction was small. In this paper, a new suppression method based on the idea of model predictive control is proposed. Because of the design of the new walking model, which has a time window for computation, and the ability to calculate the walking map quickly, the optimal parameter perturbation can be generated in real time during walking. As a result, the suppression of the bifurcation gait for our bipedal robot can be achieved on-line. This new method not only makes the gait of the controlled model converge to the target period-1 gait with desired high performance, but also guarantees that the obtained gait is better able to reject disturbances.

Analytical Energetic Approach for Predictive Generation of Dynamic Biped Walking - Use of Average Energies

This paper presents a control strategy for biped robot walking based on energetic approach. Our aim is to be able, in real time, to predict the length of the next step that the biped should execute to ensure its desired speed. According to known (measured) state in the previous step the proposed algorithm will establish the desired global parameters (i.e. the biped average velocity). The new approach presented in this paper benefits from a formulation of energy exchanges using the average values of all energies contributing during dynamic bipedal walking. We develop a model that takes into account kinetic and propulsion (provided by the rear leg) energies as well as the energy lost during the impact of the front leg. We introduce a recursive formulation in order to predict the energy behavior of the biped robot during its walk. Analytical and concise expression suitable for real-time application was developed. We show that the same formulation is convenient for both flat terrain and crossing over obstacles in the sagittal plane. Hence, we are able, in both cases, to determine the next step length required to ensure the desired average velocity. We validate the proposed approach through an ADAMS simulation of a planar robot in the sagittal plane. The obtained results show the efficiency of this promising approach.

Bipedal Locomotion Control Based on Simultaneous Trajectory and Foot Step Planning

[abstFig src='/00280004/11.jpg' width='300' text='Snapshots of a bipedal robot walking forward (upper figure) and walking sideways (lower figure)' ] This paper proposes a trajectory planner for bipedal locomotion that determines a center-of-mass (CoM) trajectory, footsteps, and step durations simultaneously. Trajectory planning based on a linear inverted pendulum model is formulated as a nonlinear constraint satisfaction problem. The proposed iterative constraint solving algorithm is able to solve this problem in a short amount of time so that trajectory replanning at every walking step is possible. Unlike existing planning methods that determine footsteps and a CoM trajectory sequentially under fixed walking period, the proposed planner can produce complex walking patterns that fully utilize the interdependency of these physical quantities. The proposed trajectory planner and a trajectory tracking controller is implemented on a real robot and their performance is evaluated.