Zero Moment Point Research Articles

Stability Control and Turning Algorithm of an Alpine Skiing Robot.

This paper proposes a general stability control method that uses the concept of zero-moment-point (ZMP) and a turning algorithm with a light detection and ranging (LiDAR) sensor for a bipedal alpine skiing robot. There is no elaborate simulator for skiing robots since the snow has complicated characteristics, such as compression and melting. However, real experiments are laborious because of the many varied skiing conditions. The proposed skiing simulator could be used, so that a humanoid robot can track its desired turning radius by modeled forces that are similar to real ones in the snow. Subsequently, the robot will be able to pass through gates with LiDAR sensors. By using ZMP control, the robot can avoid falling down while tracking its desired path. The performance of the proposed stabilization method and autonomous turning algorithm are verified by a dynamics simulation software, Webots, and the simulation results are obtained while using the small humanoid robot platform DARwIn-OP.

Dynamic Walking of a Legged Robot in Underwater Environments.

In this research, the dynamic walking of a legged robot in underwater environments is proposed. For this goal, the underwater zero moment point (Uzmp) is proposed in order to generate the trajectory of the centre of the mass of the robot. Also, the underwater zero moment point auxiliary (Uzmp aux.) is employed to stabilize the balance of the robot before it undergoes any external perturbations. The concept demonstration of a legged robot with hydraulic actuators is developed. Moreover, the control that was used is described and the hydrodynamic variables of the robot are determined. The results demonstrate the validity of the concepts that are proposed in this article, and the dynamic walking of the legged robot in an underwater environment is successfully demonstrated.

Capture Point-Based Controller Using Real-Time Zero Moment Point Manipulation for Stable Bipedal Walking in Human Environment.

For collaboration of humans and bipedal robots in human environments, this paper proposes a stability control method for dynamically modifiable bipedal walking using a capture point (CP) tracking controller. A reasonable reference CP trajectory for the CP tracking control is generated using the real-time zero moment point (ZMP) manipulation without information on future footstep commands. This trajectory can be modified at any time during the single support phase according to a given footstep command. Accordingly, this makes it possible for the robot to walk stably with dynamically modifiable walking patterns, including sudden changes in navigational commands during the single support phase. A reference CP trajectory during the double support phase is also generated for continuity. The CP of the robot is controlled to track the reference trajectory using a ZMP-based CP tracking controller. The ZMP while walking is measured by the force-sensing resistor sensors mounted on the sole of each foot. A handling method for infeasible footstep commands is utilized so that the manipulated ZMP satisfies the allowable ZMP region for stability. The validity of the proposed method is verified through simulations and experiments.

Portable Gait Lab: Zero Moment Point for Minimal Sensing of Gait.

Ambulatory sensing of gait kinematics using inertial measurement units (IMUs) usually uses sensor fusion filters. These algorithms require measurement updates to reduce drift between segments. A full body IMU suit can use biomechanical relations between body segments to solve this. However, when minimising the sensor set, we lose a lot of this information. In this study, we explore the assumptions of zero moment point (ZMP) as a possible source of measurement updates for the sensor fusion filters. ZMP is otherwise utilised for humanoid gait in robots. In this study, first, the relation between the ZMP and centre of pressure (CoP) is studied using a GRAIL system, consisting of opto-kinetic measurements. We find that the mean distance over the gait cycle between ZMP and CoP is 10.5±1.2% of the foot length. Following this, we show how these results could be used to improve measurements in a minimal IMU based sensing setup.

Motion design and Stability study of Biped Robot

Biped robot is one of many kinds of humanoid robot, with upper and lower limb structure of multiple degrees of freedom, humanoid appearance and friendly human-computer interaction interface. Robobasic programming language is used to set the rotation angle and direction of each steering gear, so as to carry out motion design and flexibly control the robot. Then, through the theoretical analysis of zero moment point (ZMP), the ideal motion trajectory of the robot in different environments can be determined to ensure that the robot can realize simple machine movements similar to those of human beings on the basis of stable motion.

Anti-Slip Gait Planning for a Humanoid Robot in Fast Walking

Humanoid robots are expected to have broad applications due to their biped mobility and human-like shape. To increase the walking speed, it is necessary to increase the power for driving the joints of legs. However, the resulting mass increasing of the legs leads to a rotational slip when a robot is walking fast. In this paper, a 3D three-mass model is proposed, in which both the trunk and thighs are regarded as an inverted pendulum, and the shanks and feet are considered as mass-points under no constraints with the trunk. Then based on the model, a friction constraint method is proposed to plan the trajectory of the swing leg in order to achieve the fastest walking speed without any rotational slip. Furthermore, the compensation for zero-moment point (ZMP) is calculated based on the 3D three-mass model, and the hip trajectory is obtained based on the compensated ZMP trajectory by using the preview control method, thus improving the robot’s overall ZMP follow-up effect. This planning method involves simple calculations but reliable results. Finally, simulations confirm that the rotational slip is avoided while stable and fast walking is realized, with free joints of the waist and arms, which then could be planned for other tasks.

A Control Strategy for Maintaining Gait Stability and Reducing Body-Exoskeleton Interference Force in Load-Carrying Exoskeleton

A key issue of load-carrying exoskeleton is to maintain the stability of gait during walking and prevent the wearer from falling over. Some of current strategies were to maintain ZMP (zero-moment point) in the support area, which had been widely used in humanoid robot. However, this method would cause serious interference between body and exoskeleton. because the body often gets energy-saving and rapid walking through unstable conditions during human walking. A control strategy for load-carrying exoskeleton was presented in this paper, which maintained the consistency of body ZMP and exoskeleton ZMP. This control strategy could reduce body-exoskeleton interference while maintaining the stability of walking. In this paper, we firstly introduced the experimental environment and the ZMP detection method, and then designed a computational model of the body-exoskeleton interaction force and evaluation criterion for gait stability. Then, a control strategy based on ZMP was designed. Finally, experiments showed that the control strategy could effectively reduce the body-exoskeleton interference, and maintained the stability of wearer’s walking.

DMP-Based Motion Generation for a Walking Exoskeleton Robot Using Reinforcement Learning

For the purpose of the assistance for human walking, this paper describes a novel coupled movement sequences planning and motion adaption based on dynamic movement primitives (DMPs) for a walking exoskeleton robot. The developed exoskeleton robot has eight degrees of freedom (DOFs). The hip and knee of each artificial leg can provide two electric-powered DOFs to flexion or extension, two passive-installed DOFs of the ankle are to achieve the motion of inversion/eversion and plantarflexion/dorsiflexion, and two passive DOFs of the hip are to achieve the motion of roll or yaw. A novel trajectory-learning scheme based on reinforcement learning (RL) combined with DMPs is presented for a lower limb exoskeleton robot, aiming to give assistance to human walking. In the proposed strategy, a two-level planning is designed. In the first level, the inverted pendulum approximation under the consideration of the locomotion parameters is utilized to guarantee the zero-moment point within the ankle joint of the support leg in the phase of single support. In the second level, the joint trajectories are modeled and learned by DMPs. Meanwhile, the RL is adopted to learn the trajectories for eliminating the effects of uncertainties in joint space. The experiment involving four subjects based on a lower limb exoskeleton robot demonstrates that the proposed scheme can effectively suppress the disturbances and uncertainties.

MODELING AND CONTROL OF HUMAN AND WHEELED ROBOTIC WALKER COUPLED DYNAMICS

The control of assistive robotic walkers are usually designed without considering the coupled dynamics of the user and the walker. This paper proposes a coupled dynamic modeling for human walking with a wheeled robotic walker and then control of this model. The 2D linear inverted pendulum mode (LIPM) is used to model human walking. The wheeled robotic walker is modeled as a simple wheeled subsystem moving on an even ground. To simulate the human arm, a parallel linear spring and damper set is then used to indicate the interaction forces. An optimal fixed final-state controller is used to control the walking model and to keep it balanced. To check whether the LIPM model walking is balanced, the zero-moment point position is calculated and checked to be in the support polygon. The results are validated with the experimental data of human walking along with a wheeled walker for three healthy subjects. The relative positions of center of mass, the absolute positions of the human and the walker, and the velocities are considered for comparison and discussion. The results for each subject is compared with the experiments through [Formula: see text] norm of the error between human and walker positions in simulation and experiments. The proposed model can be utilized in developing controllers for robotic walkers that consider the user’s dynamics.

Planning Trajectory of Anthropomorphic Walking Robot (Biped Robot)

Humanoid robots have been a topic of great interest for a long time. Among the various motions of a humanoid robot, the most basic and important motion is bipedal walking. Bipedal walking is probably the most appropriate way for robots to move around in a real environment. However Building trajectories for biped robot walking is a complex task considering all degrees of freedom (DOFs) commonly bound within the mechanical structure. To study the stable motion of any bipedal robot we should study the Kinematics, Dynamics, design a control system and of most important the trajectories. This work deals with planning trajectory of humanoid robots (AK Biped robot), especially for planning trajectory of center of mass (CoM), zero moment point (ZMP)a and planning trajectory of swing foot. diffident method used in planning trajectory like 3D linear inverted pendulum (LIMP), polynomial interpolation. The object of study is the process of automatic control walking of an anthropomorphic walking robot (AK biped robot), for that this paper proposes an approach of joint trajectory generation for the biped robot using the three Three-dimensional linear inverted pendulum for planning trajectory of CoM which keep the ZMP to be inside the support polygon which and guarantee stable dynamic walking of AK biped robot, then trajectory of swing foot derived using the polynomial interpolation function for smooth motion. The aim of this paper is to present a full 3D walking strategy using dynamic model of 3D inverted pendulum for generation references joint trajectories with simulation also design a control system that granites a stable walking of Biped Robot. This is done by first reviewing the literature about different walking strategies. During this literature review the 3D-Linear Inverted Pendulum Model appeared to be the most interesting strategy for further research. The idea of the strategy is simple. It models the human as a linear inverted pendulum with massless rods, which represent the legs, and a point mass at the end of the rods representing the total mass of the body. During walking, there is always at least one foot on the ground which can be seen as stance leg. This stance leg is then modeled as an inverted pendulum. The general closed form solution of the dynamics of the linear inverted pendulum are used to design a trajectory for the center of mass (CoM ) for stance leg. In the trajectory generator, the general solution of the 3D-LIPM is used to prescribe a trajectory. for the CoM of the biped robot AK. The trajectory of the swing leg is designed by a cosine velocity profile interpolation function. The joint trajectories are used as the input for a dynamic model of biped robot in SimMechanics. The proposed control system in simulation are carried out to tune the trajectory such that the dynamic model is able to walk balanced and the robustness of the gait was verified by adding of disturbances. For example, the position of the CoM was increased or decreased and the steps were simulated with different ground levels. These simulations showed that the trajectory is relatively robust. Ref. 10, fig. 4.

Design of compact switchable magnetic grippers for the HyReCRo structure-climbing robot

Steel structures require inspection and maintenance tasks which are too dangerous for human workers, due to the risk of falling from heights. These tasks can be safely performed with the help of inchworm-like climbing robots, which use magnetic grippers to adhere, climb, and explore steel structures. This paper presents the design and implementation of novel magnetic grippers for the HyReCRo robot, which is a biped robot to climb and explore steel structures. Each gripper carries three switchable magnets and three rubber pads to increase friction and prevent slippage, and they are designed in two steps. Firstly, the notion of the Zero Moment Point is applied to guarantee that the grippers will not detach from the structure. Secondly, a static friction analysis is performed, determining the impending motion of the robot on the onset of slippage and the minimum friction coefficient necessary to prevent it. The developed grippers are very compact and offer an adhesion force of 33 kg on 3 mm-thick steel plates, which ensures a firm and stable adhesion to steel structures in all postures, as the experiments demonstrate.

Disturbance Rejection for Biped Walking Using Zero-Moment Point Variation Based on Body Acceleration

For real-world applications, a biped robot should maintain stable walking when subjected to sudden external disturbances. Typically, unexpected changes to body acceleration indicate that a robot is experiencing an external disturbance. This paper presents a biped walking controller for rapid response to large external disturbances. First, a novel adjustment algorithm for foot placement is proposed. Here, zero-moment point variations are mapped onto the new foothold based on calculations from changes in body acceleration. Second, a novel impact reduction control for foot landing is presented based on abating body vibrations. To avoid false detection triggers and excessive foothold adjustment, a rapid disturbance detection method is established using the body acceleration derivative. Finally, the effectiveness of the proposed methods is validated under simulations and in experiments with an actual biped robot.

Bipedal walking and push recovery with a stepping strategy based on time-projection control

In this paper, we present a simple control framework for online push recovery on biped robots with dynamic stepping properties. Owing to relatively heavy legs in our humanoid robot COMAN, we use a linear model called 3LP, which is composed of three pendulums to take swing and torso dynamics into account. Based on 3LP equations, we formulate discrete linear quadratic regulator (LQR) controllers and use a particular time-projection method to adjust footstep locations during the motion continuously. This process, which is based on pelvis and swing foot tracking errors, naturally considers swing dynamics and leads to leg-retraction properties. Suggested adjustments are added to the Cartesian 3LP gaits and converted into joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies are also used to ensure enough ground clearance in perturbed walking conditions. The proposed control architecture is robust, yet uses very simple state estimation and basic position tracking. We rely on series elastic actuators to absorb impacts while introducing simple laws to compensate for spring compressions. Extensive experiments on COMAN (real) and Atlas (simulated) robots demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness with minimal reliance on the ankles and avoiding any active zero moment point (ZMP) control. The proposed architecture is therefore generic, computationally very fast and yet with no critical parameter to tune.

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.

Gate Planning and Control of a Nine-Link Biped Robot with Toe Joints via Impact Effects

The adaptation of a biped’s foot motion to the ground conditions and maintaining stability of the robot is an undeniable necessity that is the focus of this research. In this research, dynamics equations will be obtained for single support phase (SSP), double support phase (DSP), and impact. The results of impact dynamics have been used to correlate the gait parameters with the contact event following impact. In this study, in addition to explaining impact equations for a nine-link biped robot with toe and heel in first and second impact phases, a clear response for the external impulses is obtained in a compact form for the first time. In this paper, the trajectory of the foot and toe is done by determining the constraints of motion parameters with and without impact effect. Then, a method based on smooth hip motion with the largest stability margin using only two parameters, is implemented through iterative calculations, to ensure stability of the robot in accordance with the criterion of zero-moment point (ZMP). Finally, the response of a model-based controller, called feed-forward algorithm (FA), and a non-model-based controller, called the transposes Jacobian algorithm (TJ), will be used to control the robot.

Estimation of Ground Reaction Force for Quadruped Robot Control Using a High-Gain Observer

Ground reaction force is one of the most important information for legged-locomotion control. This paper presents a novel design of an observer for estimating the ground reaction force of a quadruped robot without force sensors. Simple dynamics model of a general quadruped robot is derived by assuming that the robot’s fore and hind legs can be treated separately, and they can support force provided by opposite legs and the ground reaction force are considered as external disturbance force to be estimated by a disturbance observer. Simulation results show that the proposed observer can successfully estimate the ground reaction force even though the leg is in its swing phase. The estimation of the ground reaction force by the proposed observer may be applied to the controller design using the ground reaction force such as Zero-Moment Point and Central Pattern Generator modulated by the ground reaction force.

Trajectory Optimization for Wheeled-Legged Quadrupedal Robots Using Linearized ZMP Constraints

We present a trajectory optimizer for quadrupedal robots with actuated wheels. By solving for angular, vertical, and planar components of the base and feet trajectories in a cascaded fashion and by introducing a novel linear formulation of the zero-moment point balance criterion, we rely on quadratic programming only, thereby eliminating the need for nonlinear optimization routines. Yet, even for gaits containing full flight phases, we are able to generate trajectories for executing complex motions that involve simultaneous driving, walking, and turning. We verified our approach in simulations of the quadrupedal robot ANYmal equipped with wheels, where we are able to run the proposed trajectory optimizer at 50 Hz. To the best of our knowledge, this is the first time that such dynamic motions are demonstrated for wheeled-legged quadrupedal robots using an online motion planner.

Stability Control for Dynamic Walking of Bipedal Robot with Real-time Capture Point Trajectory Optimization

This paper proposes a stabilization method for dynamic walking of a bipedal robot with real-time optimization of capture point trajectories. We used the capture point trajectories to generate the control input, which is the desired zero moment point (ZMP) with a sliding-mode ZMP controller to follow the desired ZMP. This method enables the robot to implement various dynamic walking commands, such as forward stride, lateral stride, walking direction, single support time, and double support time. We also adopted enhanced dynamics with the three mass linear inverted pendulum model (3M-LIPM). First, the compensated ZMP is calculated by both walking commands and kinematic configuration of the robot in closed form. Then, the walking pattern is obtained by using initial and boundary conditions of the 3M-LIPM, which satisfies the walking commands. The capture point (CP) trajectory is optimized in real time to control the walking stability and a capture point tracking controller is used for tracking the optimized CP trajectory, which generates an optimal control input that is near the center of the support polygon. The performance of the proposed stabilization method was verified by a dynamics simulator, Webots, and comparison with the original capture point controller-based walking algorithm is presented.

Locomotion Stability Analysis of Lower Extremity Augmentation Device

Stability is of great significance in the theoretical framework of biped locomotion. Real-time control and walking patterns planning are on the premise that the robot works in the stable condition. In this paper, we address the crucial issue of the locomotion stability based on the modified Poincare return map and the hybrid automata. Not akin to the traditional stability criteria, i.e., the Zero Moment Point (ZMP) and the Center of Mass (CoM), the modified Poincare return map is more appropriate for both dynamic walking and non-periodic walking. Moreover, a novel high-level reinforcement learning methodology, so-called active PI2 CMA-ES, is proposed in this paper to plan the exoskeleton locomotion. The proposed learning methodology demonstrates that the locomotion of the exoskeleton is asymptotically stable according to the modified Poincare return map criterion. Finally, the proposed learning methodology is tested by the Lower Extremity Augmentation Device (LEAD) and its effectiveness is verified by the experiments.

The Effects of Walking Speed and Hardness of Terrain on the Foot-Terrain Interaction and Driving Torque for Planar Human Walking

The foot-terrain interaction mechanics of human is important in understanding the biped locomotion mechanism. This paper aims to investigate the effect of walking speed and the hardness of the terrain on foot-terrain interaction mechanics. In the experiments, mobile portable plantar mechanical measuring insoles with 107 sensor elements were used to gauge the plantar force and contact area in real-time. Seven subjects with healthy feet have participated in typical experiments. The statistical methods including correlation analysis, univariance analysis, and systematic identification are primarily used to obtain several main results. Bimodal functions in describing the total pressure-time relations were performed at slow and regular speeds but only one hump is left if walking at fast paces; they can be unified and summed by three subsections’ unimodal functions. The forefoot produces a large peak impact force in slow and regular quasi-static walking on both hard ground and deformable terrains, while the heel absorbs more dynamic impact shocks in fast walking on hard ground. The torques generated by the ankle joints are calculated based on plantar force or its derived information such as zero moment point. Some implications are drawn, for example, the dynamically changed positions of zero moment point (ZMP) for humans are similar to that generated by reptiles wiggling through the flowable terrains; increasing the stride length on the hard ground produces more impact vibrations than quickening paces but more effective in accelerating walks on deformable terrains.