Zero Moment Point Criterion Research Articles

Hybrid CPG–FRI dynamic walking algorithm balancing agility and stability control of biped robot

Dynamic walking fulfill agility and stability simultaneously is one of the most difficulty for biped robot control. The traditional zero moment point (ZMP) is the most commonly used reference point for biped robot static and quasi dynamic walking control. However, human walking experimental results indicate that during walking process of human beings, the ZMP trajectory is not always conformed to the requirement of stability, such as giant strides, acceleration walking or fast walking. In order to reveal the mechanism of the biped dynamic walking, this paper proposed a novel stability criterion for the biped walking by tuning the conventional fixed support polygon area to an adjustable one. This method includes the tiptoe underactuated phase of the support foot during the biped walking. A new algorithm for the real-time biped walking generation by combining central pattern generation (CPG) with foot rotation indicator (FRI) is presented. The FRI monitor establishes the mapping function between the center of mass of the biped robot with the boundary of the elastic support polygon. By introducing FRI information, the CPG parameters can be adjusted in real time to generate a rhythmic and stable walking pattern. Numerical simulation results show that the proposed algorithm extends the application area of the ZMP criterion and improves the walking velocity of the biped robot. Moreover, the algorithm builds a bridge for the dynamic biped walking from the robot agility to motor parameters. This means that the agility of the biped robot can be quantitative controlled by modulating the motor parameters.

Walking Engine Using ZMP Criterion and Feedback Control for Child-Sized Humanoid Robot

In this paper, a walking engine that achieves dynamic stable walking using zero moment point (ZMP) criterion and feedback control from a gyro sensor is proposed. The ZMP criterion is used for the dynamic walking, and the feedback control from a gyro sensor is adopted for stabilization. The proposed walking engine consists of ZMP controller and the gait generator. The three-dimensional linear inverted pendulum model (3D-LIPM) is adopted for a simplified model of the humanoid robot. The ZMP equations are derived based on the 3D-LIPM and are applied to the gait generator. The walking engine is tested on a child-sized, 21-degree-of-freedom (DOF) humanoid robot cognitive humanoid autonomous robot with learning and evolutionary system (CHARLES) which stands 110[Formula: see text]cm tall and weighs only 8[Formula: see text]kg. The design concept of CHARLES is low development cost, lightweight, and simple design, which all match well with the proposed walking engine. The results of the experiments present the efficacy of the proposed walking engine.

Optimal trajectory planning for increased stability of mobile flexible manipulators undergoing large deflection

In this article, a path planning algorithm for nonholonomic mobile flexible manipulators is presented that computes the robot trajectory by maximizing pose stability measures. Zero moment point criterion is used as a performance index for the system stability, which regards the mass moment of inertia of the mobile base. In dynamic analysis, an efficient model is employed to describe the treatment of flexible structure, in which both the geometric elastic nonlinearity and the foreshortening effects are considered. The optimization strategy is based on the indirect solution of the open-loop optimal control problem. Necessary optimality conditions in the form of Pontryagin’s minimum principle are established, which leads to a standard form of a two-point boundary value problem. A new objective function is proposed to improve stability for mobile flexible robot. In order to initially check the validity of the dynamic equations, the proposed model has been implemented and tested on a fixed-base flexible arm undergoing large deflection. A simulation study has been carried out to investigate further the validity and effectiveness of the mobile flexible manipulators on finding the optimal path between two points with stability consideration. The results clearly show the effect of flexibility and tip over stability on the mobile manipulators.

Bipedal walking with dynamic balance that involves three-dimensional upper body motion

This paper presents a method of designing a more human-like walking pattern for a bipedal humanoid robot. Motivated by biomechanical studies on human walking, we model the walking pattern with continuous and differentiable mathematical functions. For dynamic balance of the robot, we design a pattern generator based on the ZMP (Zero-Moment Point) criterion. In comparison to the conventional bent-knee walking pattern, the proposed walking pattern involves three-dimensional motion of the upper body. With the proposed walking pattern the robot can walk with almost stretched knees at low and medium walking speeds. This paper also presents a body posture control method. The controller is based on sensory feedback and modifies the reference walking pattern in real time in order to stabilize the robot.We have implemented the proposed walking pattern and control method on the humanoid robot NAO. Walking experiments have verified that the proposed scheme improves the dynamic balance of the robot. Besides, we have investigated the energy consumption at the knee joint actuators and the overall energy consumption at all the joints of both legs, by using NAO that fulfills the conventional walking pattern and the proposed walking pattern respectively. Experiments have proved that (i) knee-stretched motion can improve the walking efficiency of a humanoid robot; and (ii) the proposed walking pattern is more efficient.

Real-time Walking Pattern Generation for a Biped Robot with Hybrid CPG-ZMP Algorithm

Biped robots have better mobility than conventional wheeled robots. The bio-inspired method based on a central pattern generator (CPG) can be used to control biped robot walking in a manner like human beings. However, to achieve stable locomotion, it is difficult to modulate the parameters for the neural networks to coordinate every degree of freedom of the walking robot. The zero moment point (ZMP) method is very popular for the stability control of biped robot walking. However, the reference trajectories have low energy efficiency, lack naturalness and need significant offline calculation. This paper presents a new method for biped real-time walking generation using a hybrid CPG-ZMP control algorithm. The method can realize a stable walking pattern by combining the ZMP criterion with rhythmic motion control. The CPG component is designed to generate the desired motion for each robot joint, which is modulated by phase resetting according to foot contact information. By introducing the ZMP location, the activity of the CPG output signal is adjusted to coordinate the limbs’ motion and allow the robot to maintain balance during the process of locomotion. The numerical simulation results show that, compared with the CPG method, the new hybrid CPG-ZMP algorithm can enhance the robustness of the CPG parameters and improve the stability of the robot. In addition, the proposed algorithm is more energy efficient than the ZMP method. The results also demonstrate that the control system can generate an adaptive walking pattern through interactions between the robot, the CPG and the environment.

An Open Loop Walking on Different Slopes for NAO Humanoid Robot

Dynamic gait planning for humanoid robots encounters difficulties such as stability, speed, and smoothness. In most of previous studies, joints’ trajectories are calculated in 3D Cartesian space, then, introducing boundary conditions and using polynomials, the first and second derivatives of the motion are ensured to be continuous. Then, the stability of the motion is guaranteed using Zero Moment Point (ZMP) stability criterion. In this study, a trajectory planner is presented using the semi-ellipse equations of the motion; the continuity of the derivatives is preserved. Stabilization of motion is attained through using ZMP criterion and 3d inverted pendulum equations in three slope conditions. The effectiveness of the proposed approach is investigated using Webots software. Implementing proposed approach, smoothness, stability, and convenient speed (rather than 17cm/s in flat condition) are achieved

Balancing Control of AIT Leg Exoskeleton Using ZMP based FLC

This paper is focused on the use of Zero Moment Point (ZMP) concept for balancing control of the Asian Institute of Technology Leg EXoskeleton-I (ALEX-I). ALEX-I has been developed to assist patients who suffer from paraplegia or immobility due to the loss of power on lower limbs. The balanced posture set-points (joint trajectories) under ZMP criterion are generated offline. The ZMP based set points are provided as the desired postures to ALEX-I. Fuzzy Logic Controller (FLC) determines the modified set points based on postures balancing sensed by loadcells. Ground Contact Point (GCP) is used to find the “ZMP-like in real time”. GCP data is obtained by placing 4 loadcells forming a force plate on each foot of ALEX-I. This GCP data is then compared with the reference ZMP. Uncertainties of the model parameters, backlash, and joint tolerance are considered as disturbance. The differences of ZMP and GCP on x-z plane are used as the inputs to the FLC. The 4 outputs from FLC are the compensated angles of left and right ankles joints in roll and pitch axes that make the actual ZMP locate in the convex hull of the supporting area.

Stable Walking Pattern for an SMA-Actuated Biped

In this paper, a walking pattern filter for shape-memory-alloy (SMA)-actuated biped robots is presented. SMAs are known for their high power-to-mass ratio as well as slow response. When used as actuators, the SMA speed limitation can potentially lead to stability problems for biped robots. The presented filter adapts the human motion such that an SMA biped robot maintains a stable walking pattern. The zero moment point (ZMP) is used as the main criterion of the filter to guarantee the stability of the motion. The SMA actuators are designed based on the dynamics and kinematics of the motion. The response time of each SMA actuator is modeled in order to estimate the behavior of the actuator in realizing the given trajectory. After applying the delay times to the motion, the new trajectories are generated and evaluated by the filter for the ZMP criterion. Using simulations, it is shown that the filter can generate smooth trajectories for the SMA-actuated biped robots. The filter furthermore guarantees the stability of a robot mimicking the human walking motion.

Recurrent neural network approaches for biped walking robot based on zero-moment point criterion

The main objective of this paper is to use a recurrent neural network (RNN) to determine the trunk motion for a biped-walking machine, based on the zero-moment point (ZMP) criterion. ZMP criterion can be used to plan a stable gait for a biped-walking machine that has a trunk (inverted pendulum). So, a RNN is trained to determine a compensative trunk motion that makes the actual ZMP get closer to the planned ZMP. In this context, an identification scheme is presented to obtain the vector of parameters of the RNN. A first order standard back-propagation with momentum (BPM) is used to adjust free parameters for the network. Artificial neural network brings up important features for function approximation. This was the main reason to use an RNN to determine the trunk motion. The proposed scheme is simulated on a 10-degree-of-freedom biped robot. The results confirm the convergence of the proposed scheme, proving this is a new way to solve this classical problem in the biped-walking machine area.

抗力規範による移動マニピュレータの安定化制御 第１報 モデルの導出，ＺＭＰ規範との比較および安定化運動の効果

This research is concerned with a stability control method with a criterion based on reaction for motion control of a mobile manipulator. Mobile manipulators can propel themselves around a work area and can operate over a wide area. Then, a stability evaluation and a stability control method must be required for mobile manipulators that are not fixed on a floor. The evaluation method based on ZMP (Zero Moment Point) criterion, in which the model is regarded as a particle system, is not satisfactory for evaluating stability of a mobile manipulator that consists of solid links. In addition, transient state during tipping over has not been discussed. In this paper, we propose a stability evaluation criterion based on reaction for the solid model of a dynamic mobile manipulator. First, equations of motion of the mobile manipulator for stable and unstable states of motion are formulated based on constraint conditions. Second, a stability criterion based on reaction is proposed by referring the formulated model. Third, the relationships between changes in reaction and changes in ZMP during tipping over are discussed through simulations. Finally, it is shown that a mobile manipulator can return from unstable transient state to stable state by performing stability compensation motion.