Zero Moment Point Research Articles

Trot Gait Stability Control of Small Quadruped Robot Based on MPC and ZMP Methods

The stability of a quadruped robot is mainly affected by the obstacles in the horizontal direction and the roughness in the vertical direction, which often leads to the robot unable to achieve the desired gait effect. In order to solve this problem, the Model Predictive Control (MPC) model and the Zero Moment Point (ZMP) method are combined, and applied to gait planning and the foot end landing control of a small quadruped robot. The tort gait of a small quadruped robot is the focus of research in this study, which simulated trajectory planning and gait stability. In addition, through comparative analysis with the corresponding experiments, the results show that the simulation results are similar to the experimental results, and the quadruped robot gait is stable. Meanwhile, it shows that the combination of the MPC model and ZMP method is feasible for gait stability control of a quadruped robot.

COM Shifter and Body Rotator for Step-by-Step Teleoperation of Bipedal Robots

This paper presents a controller for step-by-step teleoperation of bipedal robots, in which the user commands the robot’s foot motions in a step-by-step manner through a pair of handheld 3-dimensional pointing devices. The proposed controller is intended to allow users to precisely manipulate the swing foot motions to traverse rough terrains by avoiding obstacles. It aims to realize quick response to user commands and stable automatic balancing even under erroneous user commands. The main components of the proposed controller are a COM (center-of-mass) shifter and a body rotator, which are simple sensory feedback controllers that do not involve first-in first-output (FIFO) buffers, time-series generation, or online optimization. The COM shifter is a controller to produce a COM motion according to a reference zero moment point (ZMP). The body rotator complements the COM shifter to produce an appropriate angular momentum rate to enhance the regulation of ZMP. The proposed controller is validated in our interactive/realtime simulation environment.

Predictive control of zero moment point (ZMP) for terrain robot kinematics

Maintaining stability and completing the required trajectory are the most important motion control issues for a six-kinematic-degrees-of-freedom legged robot. Zero-moment point (ZMP) approaches have evolved into an indispensable tool for obtaining dynamic equilibrium in humanoid or bipod robots for walking and handling. It's point where momentary, applied, and reactive forces cancel out. Despite ZMP advancements, legged robots continue to struggle with a number of essential skills exhibited by primates, such as like the Atlas robot, which can walk but not jump, run, or sprint. In complex environments, it may be incapable of interception. Hence, in this study, the effect of center of mass (CoM) trajectory on biped robot stability has been explored to understand the secure walking behavior. The research investigates the predictive control technique of adjusting CoM trajectory to generate stable walking patterns, which pioneered the concept of altering the CoM in advance during human walking and reacting to changing path restrictions. This section explains how to fix continuous variation's ZMP tracking problem. This allows monitoring the necessary ZMP, expanding gait generation systems and their analysis. Predictive control can produce secure walking models by manipulating the COM and CoG pathline in bipod robots.

Strict Stealth Walking of Legged Robot Formed by Four Parallelogram Links and Equipped with Wobbling Mass and Reaction Wheel

This paper proposes a novel legged locomotion robot model formed by four parallelogram links and equipped with a wobbling mass and a reaction wheel, and investigates the method for generating a strict stealth walking gait on the frictionless road surface. First, we describe the robot equation of motion, and design an output-following control system for generating a walking motion by ignoring the condition of the vertical ground reaction forces. Second, we redesign the control system taking into consideration the distribution of the vertical reaction forces or the zero-moment point. Furthermore, we discuss the improvement of energy efficiency using elastic elements in terms of specific resistance.

Stability analysis of the food delivery robot with suspension damping structure

Aiming at the shock absorption and stability under complex terrain conditions, a six-wheeled food delivery robot with a suspension damping structure was designed. The food delivery robot is mainly composed of a take-out box, a chassis mobile structure and a suspension damping structure. The dynamic analysis of the suspension damping structure of the robot is carried out through the Lagrangian equation, and the offset of the wheels in different driving environments is obtained. Then, the zero-moment point method is used to analyze the stability of the food delivery robot in two non-horizontal movement environments of the left and right wheels and the front and rear wheels. Based on this, taking speed bumps and ramp terrain with different slopes as examples, the stability of the food delivery robot is analyzed by ADAMS simulation. The simulation and experiment results verify the rationality of the structure design of the food delivery robot with a suspension damping structure and the correctness of the theoretical analysis.

Motion analysis and stability optimization for metamorphic robot reconfiguration

AbstractMetamorphic robots are a new type of unmanned vehicle that can reconfigure and morph between a car mode and a biped walking machine mode. Such a vehicle is superior in trafficability because it can drive at high speeds on its wheels on structured pavement and walk on its legs on unstructured pavement. An engineering prototype of a metamorphic robot was proposed and designed based on the characteristics of wheeled–legged hybrid motion, and reconfiguration planning of the robot was conducted. A kinematics model of the reconfiguration process was established using the screw theory for metamorphic robots. To avoid component impact during the rapid global reconfiguration and achieve smoothness of the reconfiguration process, a rotation rule for each rotating joint was designed and the kinematics model was used to simulate and validate the motion of the system’s end mechanism (front frame) and the entire robot system. Based on the kinematics model and the rotation rules of the rotating joints, a zero-moment point (ZMP) calculation model of the entire robot mechanism in the reconfiguration process was established, and the stability of the reconfiguration motions was evaluated based on the ZMP motion trajectory. The foot landing position was optimized to improve the robot’s stability during the reconfiguration. Finally, the smoothness and stability of the reconfiguration motion were further validated by testing the prototype of the metamorphic robot.

Technical tips to optimize the surgical view during robotic-assisted pancreaticoduodenectomy

Maintaining stability and completing the required trajectory are the most important motion control issues for a six-kinematic-degrees-of-freedom legged robot. Zero-moment point (ZMP) approaches have evolved into an indispensable tool for obtaining dynamic equilibrium in humanoid or bipod robots for walking and handling. It's point where momentary, applied, and reactive forces cancel out. Despite ZMP advancements, legged robots continue to struggle with a number of essential skills exhibited by primates, such as like the Atlas robot, which can walk but not jump, run, or sprint. In complex environments, it may be incapable of interception. Hence, in this study, the effect of center of mass (CoM) trajectory on biped robot stability has been explored to understand the secure walking behavior. The research investigates the predictive control technique of adjusting CoM trajectory to generate stable walking patterns, which pioneered the concept of altering the CoM in advance during human walking and reacting to changing path restrictions. This section explains how to fix continuous variation's ZMP tracking problem. This allows monitoring the necessary ZMP, expanding gait generation systems and their analysis. Predictive control can produce secure walking models by manipulating the COM and CoG pathline in bipod robots.

A New Stability Framework for Trajectory Tracking Control of Biped Walking Robots

This article proposes a new stability criterion for biped walking systems on the linear inverted pendulum model, in which the dynamic relationship between the center of mass (CoM) and the zero moment point (ZMP) is dealt with. More precisely, based on the fact that a biped walking robot is stable if its ZMP is always located in the supporting region, we consider whether the ZMP error between its reference and real values stays inside a certain area to guarantee the stability condition. To this end, a norm-based new stability criterion is introduced, in which the temporal supremum of the ZMP error is concerned. Regarding the applicability of the stability criterion, we propose two control approaches to biped walking systems with the consideration of the norm-based stability criterion. In other words, full-state and observer-based feedback control approaches are analyzed in this article, and the initial CoM conditions with respect to the stability criterion are obtained for the two control approaches. We call the sets derived by such conditions the stability regions. Toward a more practical significance, we also deal with the effect of unknown disturbances and sensor noises on the stability of biped walking systems. More importantly, even though computing stability regions intrinsically involves an infinite number of linear inequalities, all the stability regions are shown to be explicitly obtained through only finite numbers of computations in this article. Finally, some simulation results are provided to demonstrate the validity as well as the practical applicability of the developed computation methods.

МОДЕЛИРОВАНИЕ ПОЛУАВТОМАТИЧЕСКОГО РЕЖИМА УПРАВЛЕНИЯ ДВИЖЕНИЕМ ДВУНОГИХ ШАГАЮЩИХ РОБОТОВ В СИСТЕМАХ ВИРТУАЛЬНОГО ОКРУЖЕНИЯ

The paper considers methods and approaches for semi-automatic motion control of bipedal walking robots in virtual environment systems. The proposed solutions include generating a walking pattern, calculating inverse kinematics, and synthesis of PD-controllers with feedback based on the angle sensor readings. To ensure the static and dynamic stability of the walking robot, generating its movement trajectories is implemented using the criterion of zero mo-ment point (ZMP) and the inverse pendulum model with virtual height. In this case, the walking pattern is generated by solving the problem of inverse kinematics using the Leven-berg-Marquardt method to calculate the rotation angles in the robot joints. To implement semi-automatic motion control of a walking robot in a virtual environment, an approach based on the technology of functional diagrams and virtual control panels is used. Testing the proposed methods and approaches is carried out in the VirSim virtual environment software package and shows their adequacy and efficiency for modelling a walking robot movement while maintaining its balance.

Stability analysis and design of an unmanned deformable vehicle during coupled reconfiguration motion

An unmanned deformable vehicle, which is a new type of robot combining a car and a robot, can drive at high speed with wheels and walk with steps. An unmanned deformable vehicle is prone to tipping instability when reconfigured between the automotive and humanoid states. The following work reported herein addresses these issues. The kinematic model of an unmanned deformed vehicle during the coupled reconfiguration process was established. The zero moment point (ZMP) theory was used as the stability criterion, and based on the requirement for stability during the reconstruction process, a genetic algorithm was used to find the optimal value of the support state foot landing position for the parking and driving coupled reconfiguration, and for the optimal value of the driving acceleration of the deformed vehicle during the driving coupled reconfiguration. On the basis of the optimal foot landing position, the total reconfiguration time threshold, deformed vehicle driving acceleration threshold, and support surface tilt angle threshold were analysed and calculated in accordance with stability requirements during the reconfiguration. Finally, the stability performance of the optimised system was verified through prototype testing.

Fault-tolerant motion planning for a hexapod robot with single-leg failure using a foot force control method

Hexapod robots are widely used for resource exploration, post-disaster rescue, and military equipment. They typically travel on rugged and complex roads. The robot itself has a high probability of failure owing to mechanical failure, driving motor failure, or external environmental interference. To improve the adaptability of the robot to a complex environment, a motion control method for fault-tolerant gait was designed. The trajectory generator based on zero-moment point information can generate a smooth desired trajectory for the body’s center of mass, thereby improving the robot’s zero-moment point trajectory tracking effect and motion stability. The force-distribution algorithm based on torque optimization selects the minimum square sum of the driving force as the objective function and reduces the number of constraint equations through QR decomposition to increase the speed at which the expected contact force at the foot is calculated. A CoppeliaSim and MATLAB/Gurobi joint simulation platform were built to simulate and verify the fault-tolerant motion planning of the hexapod robot and foot contact force control algorithm. The feasibility and effectiveness of the fault-tolerant motion planning and foot force control algorithm applied to a hexapod robot with a single-foot failure are verified.

Gait multi-objectives optimization of lower limb exoskeleton robot based on BSO-EOLLFF algorithm

AbstractAiming at problems of low optimization accuracy and slow convergence speed in the gait optimization algorithm of lower limb exoskeleton robot, a novel gait multi-objectives optimization strategy based on beetle swarm optimization (BSO)-elite opposition-based learning (EOL) levy flight foraging (LFF) algorithm was proposed. In order to avoid the algorithm from falling into the local optimum, the EOL strategy with global search capability, the LFF strategy with local search capability and the dynamic mutation strategy with high population diversity were introduced to improve optimization performance. The optimization was performed by establishing a multi-objectives optimization function with the robot’s gait zero moment point (ZMP) stability margin and driving energy consumption. The joint comparative tests were carried out in SolidWorks, ADAMS and MATLAB software. The simulation results showed that compared with the particle swarm optimization algorithm and the BSO algorithm, the ZMP stability margin obtained by the BSO-EOLLFF algorithm was increased, and the average driving energy consumption was reduced by 25.82% and 17.26%, respectively. The human-machine experiments were conducted to verify the effectiveness and superiority. The robot could realize stable and smooth walking with less energy consumption. This research will provide support for the application of exoskeleton robot.

From Walking to Running: 3D Humanoid Gait Generation via MPC.

We present a real time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates a footstep plan as closely as possible, that is, a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as a prediction model, generating in real time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation into two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as a decision variable. Using the prediction given by the first stage, the horizontal dynamics become linear time-varying. During the flight phases, the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.

Zero Moment Line-Universal Stability Parameter for Multi-Contact Systems in Three Dimensions.

The widely used stability parameter, the zero moment point (ZMP), which is usually defined on the ground, is redefined, in this paper, in two different ways to acquire a more general form that allows its application to systems that are not supported only on the ground, and therefore, their support polygon does not extend only on the floor. This way it allows to determine the stability of humanoid and other floating-based robots that are interacting with the environment at arbitrary heights. In the first redefinition, the ZMP is represented as a line containing all possible ZMPs, called the zero moment line (ZML), while in the second redefinition, the ZMP is represented as the ZMP angle, i.e., the angle between the ZML and the vertical line, passing through the center of mass (COM) of the investigated system. The first redefinition is useful in situations when the external forces and their acting locations are known, while the second redefinition can be applied in situations when the COM of the system under study is known and can be tracked. The first redefinition of the ZMP is also applied to two different measurements performed with two force plates, two force sensors, and the Optitrack system. In the first measurement, a subject stands up from a bench and sits down while being pulled by its hands, while in the second measurement, two subjects stand still, hold on to two double handles, and lean backward. In both cases, the stability of the subjects involved in the measurements is investigated and discussed.

Whole-body momentum control with linear quadratic state incremental walking pattern generation and a centroidal moment pivot balancing strategy for humanoid robots

ABSTRACT In this paper, a proposed momentum control framework adopts the quadratic programming method to handle the multi-task prioritized problem by assigning suitable constraints and the objective function, including desired end-effectors motions, the limitations of joints and the rate of change of linear and angular momentum of a robot. First, the centroidal momentum matrix is used to derive the relationship between the linear and angular momentum of the center of mass and the whole-body motion of the robot. Second, the linear quadratic state incremental walking pattern generator is used to regulate the rate of change of linear momentum of the robot for balanced walking. Then, according to the difference between the centroidal moment pivot and the zero moment point (ZMP), the compensatory rate of change of horizontal angular momentum can be calculated to keep the balance from unexpected larger disturbances. Finally, the performance of this control framework is verified effectively through the simulations and the experiments. In addition, the ZMP tracking performance is improved up to 50% in the simulations and 14% in the experiments.

Adaptability Control Towards Complex Ground Based on Fuzzy Logic for Humanoid Robots

Stability control for humanoid robots based on zero moment point (ZMP) control and impedance control are widespread. However, uncertain changes in the center of mass (CoM) height for ZMP control and specific regulation of the variable stiffness of impedance control have been challenging issues in previous studies. In this article, these two problems are solved by implementing fuzzy control-based regulations. First, the fuzzy ZMP controller, which regulates the feedback gains online based on the CoM height change and CoM tracking errors, is proposed. Second, we propose a fuzzy regulation law for variable stiffness, which is applied for uncertain contact situations and inspired by the pattern of human muscle stiffness. With these two methods, the ground adaptability for humanoid robots is enhanced. The proposed method is validated with experiments on a real robot platform, BHR-T.

Whole-body balance stability regions for multi-level momentum and stepping strategies

A unified framework is established for general balance stability criteria of biped systems. The stability regions of balanced and steppable states are partitions of the center-of-mass (COM) state space that is augmented for general biped systems and tasks. Their boundaries are the set of maximum allowable COM velocity perturbations, under which a specified contact can be maintained (balanced) or a desired step can be made (steppable). Whole-body models with full-order dynamics and system-specific kinematic and actuation limits are established to quantify the effects of momenta and stepping on the system's balance stability under contact interactions. The generality of the framework with respect to systems and tasks is verified with a humanoid robot and a human for walking and standing. Validity and implications of the computed stability regions are demonstrated in the sagittal plane through comparative analyses across strategies and against existing criteria (capturability and zero-moment point), reduced-order models, and simulations. Distinct stability characteristics of experimental walking for the robot (overly balanced) versus humans (unbalanced but steppable) are validated, and the walking principle is analyzed. The partitions also provide inter/intra-region analyses of multi-level momentum and stepping strategies for balancing. A partition-aware controller is implemented for the robot to monitor the stability of the current state and selectively exploit stabilizing actions during simulated standing push recovery.

ANALYSIS ON ANTI-OVERTURNING STABILITY OF A TRUCK CRANE BASED ON ZERO MOMENT POINT THEORY

Truck crane stability has been a hot research issue. It is a conventional method used to calculate the moments equilibrium when analyzing stability. However, errors can occur because of the lack of dynamic simulation in conventional methods. Hence, to minimize errors, this study utilized the zero moment point (ZMP) theory to calculate the maximum lifting capacity of the truck crane considering the dynamic load, and proposed an anti-overturning detection method based on the theory. First, the model of the truck crane was established and the solution formula of ZMP was obtained. From the Lagrange equation, the dynamic model of payload oscillations was analyzed during crane operations. Second, the ZMP theory was used to analyze the stability of the truck crane and derive the maximum payload. Next, the experiment was conducted to measure the pressure of the four outriggers and their center of pressure (CoP) during hoisting, luffing, and slewing operations were calculated. Compared to stable movement, the CoP would vibrate irregularly, consequently reducing the lifting capacity of unstable motion. Finally, the anti-overturning detection method is proposed based on ZMP and CoP. Results demonstrate that the reduction of lifting capacity is caused by the dynamic load. The payload swing has a larger effect on the maximum lifting capacity than hoisting, luffing, and slewing motions. The maximum payload can decrease with the increase of the swing angle. The proposed method provides a correct judgment on the stability of the truck crane, which can accurately predict the overturning state of the crane and reduce the risk in the operation. Keywords: truck crane, overturning, zero moment point, center of pressure, stability

Identification of a Step-And-Brake Controller of a Human Based on Prediction of Capturability.

An explicit mathematical form of a human’s step-and-brake controller is identified through motion measurement of the human subject. The controller was originally designed for biped robots based on the reduced-order dynamics and the model predictive control scheme with the terminal capturability condition, and is compatible with both stand-still and stepping motions. The minimal number of parameters facilitates the identification from measured trajectories of the center of mass and the zero-moment point of the human subject. In spite of the minimality, the result only suited the human’s behaviors well with slight modifications of the model by taking direction-dependency of the natural falling speed and the inertial torque about the center of mass into account. Furthermore, the parameters are successfully identified even from the first half of motion sequence, which means that the proposed method is available in designing on-the-fly systems to evaluate balancing abilities of humans and to assist balances of humans in walking.

Real-Time Footprint Planning and Model Predictive Control Based Method for Stable Biped Walking.

In order to walk in a physical environment, the biped will encounter various external disturbances, and walking under persistent conditions is still challenging. This paper tries to improve the push recovery performance based on capture point (CP) and model predictive control. The trajectory of zero moment point (ZMP) and center of mass are solved and predicted in a limited time horizon. Online footprint generator is combined with MPC walking pattern generation, which can keep biped stable in the next few steps, and projection of ZMP is used to calculate the next footprint and reach the target CP in an incremental way. Verification of the proposed stable biped walking method is conducted by simulation and experiments.