Walking Pattern Generation Research Articles

Analytical solution to a time-varying LIP model for quadrupedal walking on a vertically oscillating surface

This paper introduces an analytically tractable and computationally efficient model for legged robot dynamics during locomotion on a dynamic rigid surface (DRS), along with an approximate analytical solution and a real-time walking pattern generator synthesized based on the model and solution. By relaxing the static-surface assumption, we extend the classical, time-invariant linear inverted pendulum (LIP) model for legged locomotion on a static surface to dynamic-surface locomotion, resulting in a time-varying LIP model termed as “DRS-LIP”. Sufficient and necessary stability conditions of the time-varying DRS-LIP model are obtained based on the Floquet theory. This model is also transformed into Mathieu’s equation to derive an approximate analytical solution that provides reasonable accuracy with a relatively low computational cost. Using the extended model and its solution, a walking pattern generator is developed to efficiently plan physically feasible trajectories for quadrupedal walking on a vertically oscillating surface. Finally, simulations and hardware experiments from a Laikago quadrupedal robot walking on a pitching treadmill (with a maximum vertical acceleration of 1 m/s2) confirm the accuracy and efficiency of the proposed analytical solution, as well as the efficiency, feasibility, and robustness of the pattern generator, under various surface motions and gait parameters.

Mechanical Design of a Biped Robot FORREST and an Extended Capture-Point-Based Walking Pattern Generator

In recent years, many studies have shown that soft robots with elastic actuators enable robust interaction with the environment. Compliant joints can protect mechanical systems and provide better dynamic performance, thus offering huge potential for further developments of humanoid robots. This paper proposes a new biped robot. The new robot combines a torque sensor-based active elastic hip and a spring-based passive elastic knee/ankle. In the first part, the mechanical design is introduced, and in the second part, the kinematics and dynamics capabilities are described. Furthermore, we introduce a new extended capture-point-based walking pattern generator that calculates footstep positions, which are used as input for the controller of our new biped robot. The main contribution of this article is the novel mechanical design and an extended walking pattern generator. The new design offers a unique solution for cable-driven bipeds to achieve both balancing and walking. Meanwhile, the new walking pattern generator can generate smooth desired curves, which is an improvement over traditional generators that use a constant zero-moment-point (ZMP). A simple cartesian controller is applied to test the performance of the walking pattern generator. Although the robot has been built, all experiments regarding the pattern generator are still simulated using MATLAB/Simulink. The focus of this work is to analyze the mechanical design and show the capabilities of the robot by applying a new pattern generator.

A Novel General Inverse Kinematics Optimization-Based Solution for Legged Robots in Dynamic Walking by a Heuristic Approach

This work presents a new optimization-based solution to the Inverse Kinematics Problem (IKP) of legged robots, including a modified Walking Pattern Generator that automatically avoids singularity configurations regarding position. The approach uses a numeric constrained problem solved with heuristic algorithms, where the joint vector is calculated to minimize the position errors, while orientation errors are handled as equality constraints, and threshold values are used to set the maximum error for each foot along the trajectories. The optimization model can generalize the IKP for robots with any number of legs and any number of poses within the physically consistent trajectories for the Center of Mass and the feet, considering the dynamics of the robot for a stable walking. The case study was a 12-DOF biped robot, and the resulting joint trajectories were validated by a dynamic simulation, using a Gazebo-ROS platform, where the walking was successfully performed without requiring a feedback control for correcting the torso tilt, showing the solution quality.

Stable Locomotion of Humanoid Robots on Uneven Terrain Employing Enhanced DAYANI Arc Contour Intelligent Algorithm

Abstract Humanoid robots must be capable of walking on complicated terrains and tackling a variety of obstacles leading to their wide range of possible implementations. To that aim, in this article, the issue of humanoid robots walking on uneven terrain and tackling static and dynamic obstacles is examined. It is inspected by implementing a novel Enhanced DAYANI Arc Contour Intelligent (EDACI) Algorithm that designs trajectory by searching feasible points in the environment. It provides an optimum steering angle, and step optimization is performed by Broyden–Fletcher–Goldfarb–Shanno (BFGS) Quasi-Newton method that leads to guide the humanoid robot stably to the target. The leg length policy has been presented, and a reward-based system has been implemented in the walking pattern generator that provides the optimum gait parameters. One humanoid robot act as a dynamic obstacle to others if they are navigating on a single terrain. It may generate a situation of deadlock, which needs to be solved. In this article, a dining philosopher controller (DPC) is employed to deal with and solve this issue. Simulations are used to evaluate the proposed approach in several uneven terrains having two humanoid NAOs. The findings indicate that it can precisely and efficiently produce optimal collision-free paths, demonstrating its efficacy. Experiments in similar terrain are performed that validate the results with a deviation under 6%. The energy efficiency of the developed controller is evaluated in reference to the inbuilt controller of NAO based on energy consumption. In order to check the feasibility and accuracy of the developed controller, a comparison with an established technique is provided.

Advanced biped gait generator using NARX-MLP neural model optimized by enhanced evolutionary algorithm

A novel biped walking pattern combining robust zero-moment-point ZMP technique and pre-determined foot-lifting value is proposed in this paper. The implementation of suggested approach contains following stages. Initially, a one-step ZMP curve for a small-sized humanoid is created using the 3rd-order interpolating equation, with pre-determined velocity responding the ZMP concept. The next step, biped gait planning is modeled as a non-linear MIMO plant including ten degree-of-freedom DOF. Then, the installation of a biped walking pattern generator (WPG) based on the new hybrid Neural-NARX model is completed. Eventually, the novel Enhanced Differential Evolution (EDE) technique is applied to optimally identify the weights of the hybrid Neural-NARX structure, for ensuring robust robot walking in terms of desired ZMP trajectories and pre-determined foot-lifting value. All case studies confirm that it is surely provide a biped WPG satisfying both of the effectiveness and high robustness. The verification of the newly proposed WPG is adequately tested via both simulation and experiment results.

A continuous-time walking pattern generator for realizing seamless transition between flat-contact and heel-to-toe walking

A planning algorithm that can generate continuous-time walking patterns including the seamless transition between flat-contact and heel-to-toe walking gaits is proposed. The planner makes use of the closed-form solution of a modified linear inverted pendulum mode which includes the ZMP and the weight ratio of each foot explicitly in its dynamics. The heel-to-toe movement of each foot is directly parameterized by the ZMP, and therefore consistency between the foot movement and the low-dimensional dynamics is ensured. In simulations with a 32 DoF model of a life-sized humanoid robot, fast human-like walking at the maximum speed of 4.6 km/h was achieved.

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.

Toward Reactive Walking: Control of Biped Robots Exploiting an Event-Based FSM

Reactivity to unforeseen disturbances is one of the most crucial characteristics for biped robots to walk robustly in the real world. Nevertheless, conventional walking methods generally have limited capability for generating rapid reactions to disturbances, because in these methods it is necessary to wait until the end of the preplanned time period to proceed to the next phase. In this study, to improve reactivity, we develop an event-based finite-state machine (E-FSM) for walking pattern generation. Reactivity is enhanced by determining the state transition conditions of the E-FSM only with time-independent events based on the present robot state. Moreover, in the E-FSM, the robot can walk robustly even when the center of mass and the swing foot motion are disturbed, by employing the capture point concept combined with a new swing foot position constraint. Finally, we propose to control the walking robot by incorporating the E-FSM with an inverse dynamics-based motion/force controller to achieve compliant behavior. This can provide safe responses to external disturbances. The developed method is verified by experiments on a 12-degrees-of-freedom torque-controlled biped robot while it locomotes under irregular external disturbances applied to the upper body or swing leg.

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.

Human Trajectory Prediction Model and Its Coupling With a Walking Pattern Generator of a Humanoid Robot

In order to smoothly perform interactions between a humanoid robot and a human, knowledge about the human locomotion can be efficiently used. Indeed, in a human-robot collaboration, a prediction model of the human behaviour allows the robot to act proactively. In this letter, an optimal control based model predicting the human Center of Mass (CoM) trajectory during gait is presented. A Walking Pattern Generator (WPG) based on non-linear model predictive control is, then, introduced in order to generate the robot CoM and footsteps along the predicted trajectory. The combination of the human trajectory prediction model and this new WPG aims to allow the robot to proactively walk along with a human instead of passively follow him. These models have been tested in simulation on Gazebo on a TALOS humanoid robot model using measured human trajectories. To perform the CoM and foot trajectories computed by the WPG, a real-time whole-body controller is used. This controller is a Quadratic Program which solves the inverse dynamics of the robot at torque level.

물리적 상호작용 기반의 이족 보행 패턴을 이용한 인간형 로봇의 이동 제어

This paper describes a biped walking pattern for physical interaction between a human and humanoid robot. The study of the physical interaction between robots and humans is an important research field when considering a future society where humans and robots must coexist. In this paper, to move the humanoid robot in the direction intended by the human, the previous method of generating a walking pattern is extended to a method of generating a walking pattern suitable for physical human-robot interaction. When the human applies disturbance to the robot, the robot naturally move in the direction of applied disturbance to recover balance. The applied disturbance is measured by the capture point. To stabilize the perturbed capture point, the desired Zero Moment Point (ZMP) is calculated by using the capture point control. This desired ZMP is tracked by the walking pattern generator. The walking pattern generator automatically calculate the center of mass trajectory, which satisfies the ZMP constraint, by model predictive control. The proposed method was applied to the humanoid robot DRC-HUBO+ and verified that it can be used for physical humanrobot interaction.

Closed‐form solution for real‐time optimal walking pattern generation constrained by the desired amount of capture point

AbstractI present a calculus variations problem for an optimal zero‐moment point (ZMP) pattern, and derive a closed‐form solution satisfying two‐boundary conditions of ZMP and an additional constraint, which is a difference between a current capture point and another. In addition, I present a closed‐form solution for the equation of motion of the linear inverted pendulum model, or a cart‐table model using the optimal ZMP pattern. Through the closed‐form solutions, a current walking pattern is generated with every step period, and is connected with a previous pattern without discontinuity. I demonstrate my optimal walking pattern generator with 13 forward steps, and compare power consumption with walking, using a linearly interpolated ZMP pattern for effectiveness. Moreover, I indicate the walking pattern changes in real‐time, depending on varying step lengths.

A performance comparison between closed form and numerical optimization solutions for humanoid robot walking pattern generation

This article presents the modeling process of the lower part of a humanoid biped robot in terms of kinematic/dynamic states and the creation of a full dynamic simulation environment for a walking robot using MATLAB/Simulink. This article presents two different approaches for offline walking pattern generation: one relying on a closed-form solution of the linear inverted pendulum model (LIPM) mathematical model and another that considers numerical optimization as means of desired output trajectory following for a cart table state-space model. This article then investigates the possibility of introducing solution-dependent modifications to both approaches that could increase the reliability of basic walking pattern generation models in terms of smooth single support–double support phase transitioning and power consumption optimization. The algorithms were coded into offline walking pattern generators for NAO humanoid robot as a valid example and the two approaches were compared against each other in terms of stability, power consumption, and computational effort as well as against their basic unmodified counterparts.

Omnidirectional Walking Pattern Generator Combining Virtual Constraints and Preview Control for Humanoid Robots.

This paper presents a novel omnidirectional walking pattern generator for bipedal locomotion combining two structurally different approaches based on the virtual constraints and the preview control theories to generate a flexible gait that can be modified on-line. The proposed strategy synchronizes the displacement of the robot along the two planes of walking: the zero moment point based preview control is responsible for the lateral component of the gait, while the sagittal motion is generated by a more dynamical approach based on virtual constraints. The resulting algorithm is characterized by a low computational complexity and high flexibility, requisite for a successful deployment to humanoid robots operating in real world scenarios. This solution is motivated by observations in biomechanics showing how during a nominal gait the dynamic motion of the human walk is mainly generated along the sagittal plane. We describe the implementation of the algorithm and we detail the strategy chosen to enable omnidirectionality and on-line gait tuning. Finally, we validate our strategy through simulation experiments using the COMAN + platform, an adult size humanoid robot developed at Istituto Italiano di Tecnologia. Finally, the hybrid walking pattern generator is implemented on real hardware, demonstrating promising results: the WPG trajectories results in open-loop stable walking in the absence of external disturbances.

Humanoid Gait Pattern Generation with Orbital Energy

A novel approach has been proposed to generate the gait pattern of the humanoid robot with use of orbital energy concept. As the bipedal robots can be modeled as Linear Inverted Pendulum Model (LIPM) and rolling sphere model, the detailed discussion is presented here to generate stable walking pattern with help of this model. The intensive uses and advantages of the orbital energy concept have also been presented compared to different traditional approach of walking pattern generation. In this context, a novel algorithm has been proposed to generate 3D walking pattern of the bipedal robots, and how the 3D walking pattern can be approximated as the 2D walking pattern. All the analytical results are provided and verified with NaO robot (Biped robot).

Simulation and Experimental Walking Pattern Generation for Two Types of Degrees of Freedom Bipedal Locomotion Robot

Humanoids or bipedal robots are other kinds of robots that have legs. The balance of humanoids is the general problem in these types when the other in the support phase and the leg in the swing phase. In this work, the walking pattern generation is studied by MATLAB for two types of degrees of freedom, 10 and 17 degrees of freedom. Besides, the KHR-2HV simulation model is used to simulate the experimental results by Webots. Similarly, Arduino and LOBOT LSC microcontrollers are used to program the bipedal robot. After the several methods for programming the bipedal robot by Arduino microcontroller, LOBOT LSC-32 driver model is the better than PCA 96685 Driver-16 channel servo driver for programming the bipedal walking robot. The results showed that this driver confirms the faster response than the Arduino microcontroller in walking the bipedal robot. The walking pattern generation results showed that the step height for 17 degrees of freedom bipedal robot increases approximately (20%) than 10 degrees of freedom bipedal robot, which decreases the step period by about (7%). Also, the time interval of the double support phase for 17 degrees of freedom bipedal robot increases approximately (11%) with decreases step length approximately (33% on X-axis) and (16% on Z-axis).

Generation of diverse insect-like gait patterns using networks of coupled Rössler systems.

The generation of walking patterns is central to bio-inspired robotics and has been attained using methods encompassing diverse numerical as well as analog implementations. Here, we demonstrate the possibility of synthesizing viable gaits using a paradigmatic low-dimensional non-linear entity, namely, the Rössler system, as a dynamical unit. Through a minimalistic network wherein each instance is univocally associated with one leg, it is possible to readily reproduce the canonical gaits as well as generate new ones via changing the coupling scheme and the associated delays. Varying levels of irregularity can be introduced by rendering individual systems or the entire network chaotic. Moreover, through tailored mapping of the state variables to physical angles, adequate leg trajectories can be accessed directly from the coupled systems. The functionality of the resulting generator was confirmed in laboratory experiments by means of an instrumented six-legged ant-like robot. Owing to their simple form, the 18 coupled equations could be rapidly integrated on a bare-metal microcontroller, leading to the demonstration of real-time robot control navigating an arena using a brain-machine interface.

A Simple Yet Effective Whole-Body Locomotion Framework for Quadruped Robots.

In the context of legged robotics, many criteria based on the control of the Center of Mass (CoM) have been developed to ensure a stable and safe robot locomotion. Defining a whole-body framework with the control of the CoM requires a planning strategy, often based on a specific type of gait and a reliable state-estimation. In a whole-body control approach, if the CoM task is not specified, the consequent redundancy can still be resolved by specifying a postural task that set references for all the joints. Therefore, the postural task can be exploited to keep a well-behaved, stable kinematic configuration. In this work, we propose a generic locomotion framework which is able to generate different kind of gaits, ranging from very dynamic gaits, such as the trot, to more static gaits like the crawl, without the need to plan the CoM trajectory. Consequently, the whole-body controller becomes planner-free and it does not require the estimation of the floating base state, which is often prone to drift. The framework is composed of a priority-based whole-body controller that works in synergy with a walking pattern generator. We show the effectiveness of the framework by presenting simulations on different types of simulated terrains, including rough terrain, using different quadruped platforms.

Optimized stable gait planning of biped robot using multi-objective evolutionary JAYA algorithm

This article proposes a new stable biped walking pattern generator with preset step-length value, optimized by multi-objective JAYA algorithm. The biped robot is modeled as a kinetic chain of 11 links connected by 10 joints. The inverse kinematics of the biped is applied to derive the specified biped hip and feet positions. The two objectives related to the biped walking stability and the biped to follow the preset step-length magnitude have been fully investigated and Pareto optimal front of solutions has been acquired. To demonstrate the effectiveness and superiority of proposed multi-objective JAYA, the results are compared to those of MO-PSO and MO-NSGA-2 optimization approaches. The simulation and experiment results investigated over the real small-scaled biped HUBOT-4 assert that the multi-objective JAYA technique ensures an outperforming effective and stable gait planning and walking for biped with accurate preset step-length value.

Terrain Identification for Humanoid Robots Applying Convolutional Neural Networks

Stable and efficient walking strategies for humanoid robots usually relies on assumptions regarding terrain characteristics. If the robot is able to classify the ground type at the footstep moment, it is possible to take preventive actions to avoid falls and to reduce energy consumption. In this article, a new terrain identification method that makes use of a convolutional neural network to classify the terrain type is proposed. The input of this network is a bidimensional matrix-a signature image of the impact-composed of raw data from inertial and torque sensors, sampled after the impact between the foot and ground. Six different terrains types were selected for testing the proposed approach: these terrains were tested both in simulation using the Gazebo 9.0 environment and with one real robot, designed to satisfy the requirements for the RoboCup Humanoid Competition. In both robots the ROS framework was used, and the LIPM was the selected approach for the biped walking pattern generation. Results showed that the proposed method was able to classify the terrain type with an accuracy greater than 98% for both real and virtual situations, surpassing current state-of-the-art terrain classification methods for legged robots.