Gait Generation Research Articles

Research on the Spiral Rolling Gait of High-Voltage Power Line Serpentine Robots Based on Improved Hopf-CPGs Model

The efficiency of helical locomotion in snake-like robots along high-voltage transmission lines is often hindered by low motion efficiency, high joint signal noise, and challenges in traversing obstacles. This study aims to address these issues by proposing a gait generation method that leverages a standardized Central Pattern Generator (CPG). We modify the traditional Hopf-CPG model by incorporating constraint functions and a frequency-tuning mechanism to regulate the oscillator, which allows for the generation of asymmetric waveform signals for deflection joints and facilitates rapid convergence. The method begins by determining initial and obstacle-crossing state parameters, such as deflection angles and helical radii of the snake-like robot, using the backbone curve method and the Frenet–Serret framework. Subsequently, a CPG neural network is constructed based on Hopf oscillators, with a limit cycle convergent speed adjustment factor and amplitude bias signals to establish a fully connected matrix model for calculating multi-joint output signals. Simulation analysis using Simulink–CoppeliaSim evaluates the robot’s obstacle-crossing ability and the optimization of deflection joint signal noise. The results indicate a 55.70% increase in the robot’s average speed during cable traversal, a 57.53% reduction in deflection joint noise disturbance, and successful crossing of the vibration damper. This gait generation method significantly enhances locomotion efficiency and noise suppression in snake-like robots, offering substantial advantages over traditional approaches.

Flexible Model Predictive Control for Bounded Gait Generation in Humanoid Robots.

With advancements in bipedal locomotion for humanoid robots, a critical challenge lies in generating gaits that are bounded to ensure stable operation in complex environments. Traditional Model Predictive Control (MPC) methods based on Linear Inverted Pendulum (LIP) or Cart-Table (C-T) methods are straightforward and linear but inadequate for robots with flexible joints and linkages. To overcome this limitation, we propose a Flexible MPC (FMPC) framework that incorporates joint dynamics modeling and emphasizes bounded gait control to enable humanoid robots to achieve stable motion in various conditions. The FMPC is based on an enhanced flexible C-T model as the motion model, featuring an elastic layer and an auxiliary second center of mass (CoM) to simulate joint systems. The flexible C-T model's inversion derivation allows it to be effectively transformed into the predictive equation for the FMPC, therefore enriching its flexible dynamic behavior representation. We further use the Zero Moment Point (ZMP) velocity as a control variable and integrate multiple constraints that emphasize CoM constraint, embed explicit bounded constraint, and integrate ZMP constraint, therefore enabling the control of model flexibility and enhancement of stability. Since all the above constraints are shown to be linear in the control variables, a quadratic programming (QP) problem is established that guarantees that the CoM trajectory is bounded. Lastly, simulations validate the effectiveness of the proposed method, emphasizing its capacity to generate bounded CoM/ZMP trajectories across diverse conditions, underscoring its potential to enhance gait control. In addition, the validation of the simulation of real robot motion on the robots CASBOT and Openloong, in turn, demonstrates the effectiveness and robustness of our approach.

Footstep reward for energy-efficient quadruped gait generation and transition through deep reinforcement learning

The generation of quadruped robot gait through deep reinforcement learning (DRL) has emerged as a prominent topic in recent years. However, DRL methods face challenges in generating specific and energy-efficient gait patterns, as well as in achieving gait transition. These methods often require imposing restrictions on movement or on the learning process to achieve proper gait specification and generation, thereby limiting the quadruped model movement achievable with DRL training. In this paper, we propose a new DRL reward design method, called FootStep Reward, to successfully generate specific gait patterns that exhibit animal-like energetic properties. Our method is capable of generating Walk, Trot, and Gallop gait patterns at any velocity while demonstrating better energy efficiency compared to similar gait specification methods. Additionally, we employ our method to analyze the impact of two body parameters: model mass and joint stiffness, increasing our understanding of how these parameters influence Walk, Trot and Gallop gait efficiency. Finally, we implement the FootStep Reward method to generate gait transitions and successfully achieve the transition from Walk to Trot gait, optimizing locomotion at low and medium velocities.

Caterpillar-Inspired Multi-Gait Generation Method for Series-Parallel Hybrid Segmented Robot.

The body structures and motion stability of worm-like and snake-like robots have garnered significant research interest. Recently, innovative serial-parallel hybrid segmented robots have emerged as a fundamental platform for a wide range of motion modes. To address the hyper-redundancy characteristics of these hybrid structures, we propose a novel caterpillar-inspired Stable Segment Update (SSU) gait generation approach, establishing a unified framework for multi-segment robot gait generation. Drawing inspiration from the locomotion of natural caterpillars, the segments are modeled as rigid bodies with six degrees of freedom (DOF). The SSU gait generation method is specifically designed to parameterize caterpillar-like gaits. An inverse kinematics solution is derived by analyzing the forward kinematics and identifying the minimum lifting segment, framing the problem as a single-segment end-effector tracking task. Three distinct parameter sets are introduced within the SSU method to account for the stability of robot motion. These parameters, represented as discrete hump waves, are intended to improve motion efficiency during locomotion. Furthermore, the trajectories for each swinging segment are determined through kinematic analysis. Experimental results validate the effectiveness of the proposed SSU multi-gait generation method, demonstrating the successful traversal of gaps and rough terrain.

A Reinforcement Learning Path Following Strategy for Snake Robots Based on Transferable Constrained-Residual Gait Generator

A Reinforcement Learning Path Following Strategy for Snake Robots Based on Transferable Constrained-Residual Gait Generator

Simulation of autonomous rhythm and gait generation in quadrupedal locomotion with hindlegs

Intending to further simplify motion planning and control of quadrupedal locomotion through emergence, we propose a legged locomotion controller inspired by the sensorimotor functions observed in the spinal cord of cats. In simulations using a hind-legged biped robot, we demonstrate the emergence of a rhythm and gait closely resembling the belt-driven locomotion observed in spinal cats. We also show the self-propulsive locomotion of this hind-legged biped, based on the hypothesis that the brainstem output directs the intensity of muscle contraction (locomotion power) to the spinal cord. Furthermore, we meticulously examine the dynamic interaction with the environment, considering the fixture's presence, and document the entire process in detail. We show that the mechanisms underlying the emergence of legged locomotion are the interactions between leg phase switching, self-excited oscillations of the body or trunk, and leg load spatiotemporal pattern. In regard to the last parameter, the temporal pattern of the leg load determines the rhythm, and the spatial pattern determines the gait.

Gait Generation of a 10-DOF Humanoid Robot on Deformable Terrain Based on Spherical Inverted Pendulum Model

Abstract Gait generation of a humanoid robot on deformable terrain is a complex problem as the foot and terrain interaction and terrain deformation has to be included in the dynamics. In order to simplify the dynamics of walk on deformable terrain, we used a spherical inverted pendulum (SIP) to represent the single support phase, in which the effect of terrain deformation is represented by a spring and damper contact model. The impact model for leg transition is derived from angular momentum conservation. In order to minimize the energy loss due to impact, the double support phase is modeled as a suspended pendulum. Based on the motion of the SIP model, the hip and leg trajectories of a 10 DOF humanoid robot are generated. The joint angles of the humanoid are obtained from inverse kinematics. The motion of the center of mass is analyzed by inverse dynamics of a floating-base robot. The proposed gait generation method has been experimentally validated using a Kondo KHR-3HV humanoid robot on deformable terrain. The results show that the humanoid can effectively track the trajectories of the SIP model.

Embodying rather than encoding: Towards developing a source-filter theory for undulation gait generation

Biological undulation enables legless creatures to move naturally, and robustly in various environments. Consequently, many kinds of undulating robots have been developed. However, the fundamental mechanism of biological undulation gait generation has not yet been well explained, which hinders deepening the investigation and optimization of these robots. Towards developing a theory for explaining this biological behavior, which will further guide the design of artificial undulation systems, we propose a hypothesis based on both biological findings and previous robotics studies. To verify the hypothesis, we investigate embodied intelligence of undulation locomotion via a mechanical system. Through experimental study, we observe the phenomenon that undulation gait is a production of the source, which is the torque inputs, and the filter, which is the natural dynamics of the system. We further derive a general mathematical model and conduct morphological computation accordingly. From a simple model to a complicated system, our work explores the principles of undulation gait generation. Our findings significantly simplify the control system design of artificial undulating systems.

Optimal reorientation of planar floating snake robots with collision avoidance

In this paper, a motion planning algorithm for floating planar under-actuated hyper-redundant snake robots is proposed. The presented algorithm generates locally optimal shape trajectories, i.e., continuous trajectories in the base space of the robot. Such shape trajectories produce a desired rotation of the snake robot, i.e., change in the uncontrolled orientation fiber variable. The proposed method formulates the motion planning problem as an optimization problem where the objective function could be defined to minimize various metrics, such as energy-based cost functions. Additionally, the proposed motion planning algorithm uses a heuristic to generate shape trajectories that avoid self-intersections and obstacle collision. Hence, the motion planning method generates shape trajectories that locally minimize user-defined cost functions and eliminate self-intersections or obstacle collision. The proposed gait generation method is validated using numerical simulations of five-link and seven-link snake robots.

An Underwater Biomimetic Robot that can Swim, Bipedal Walk and Grasp

In developing and exploring extreme and harsh underwater environments, underwater robots can effectively replace humans to complete tasks. To meet the requirements of underwater flexible motion and comprehensive subsea operation, a novel octopus-inspired robot with eight soft limbs was designed and developed. This robot possesses the capabilities of underwater bipedal walking, multi-arm swimming, and grasping objects. To closely interact with the underwater seabed environment and minimize disturbance, the robot employs a cable-driven flexible arm for its walking in underwater floor through a bipedal walking mode. The multi-arm swimming offers a means of three-dimensional spatial movement, allowing the robot to swiftly explore and navigate over large areas, thereby enhancing its flexibility. Furthermore, the robot’s walking arm enables it to grasp and transport objects underwater, thereby enhancing its practicality in underwater environments. A simplified motion models and gait generation strategies were proposed for two modes of robot locomotion: swimming and walking, inspired by the movement characteristics of octopus-inspired multi-arm swimming and bipedal walking. Through experimental verification, the robot’s average speed of underwater bipedal walking reaches 7.26 cm/s, while the horizontal movement speed for multi-arm swimming is 8.6 cm/s.

Bipedal Robot Gait Generation Using Bessel Interpolation.

This paper introduces a novel approach to bipedal robot gait generation by proposing a higher-order form through the parameter equation of first-order Bessel interpolation. The trajectory planning for the bipedal robot, specifically for stepping up or down stairs, is established based on a three-dimensional interpolation equation. The experimental prototype, Roban, is utilized for the study, and the structural sketch of a single leg is presented. The inverse kinematics expression for the leg is derived using kinematic methods. Employing a position control method, the angle information is transmitted to the robot's joints, enabling the completion of both downstairs simulation experiments and physical experiments with the Roban prototype. The analysis of the experimental process reveals a noticeable phenomenon of hip and ankle joint tilting in the robot. This observation suggests that low-cost bipedal robots driven by servo motors exhibit low stiffness characteristics in their joints.

Enhancing undulation of soft robots in granular media: A numerical and experimental study on the effect of anisotropic scales

Generating efficient locomotion in granular media is important, although it is difficult for robots. Inspired by the fact that sand vipers usually have saw-like scales, in this study, we design a soft undulation robot with tangential anisotropic friction to enhance the undulation performance of soft robots in granular media. A mathematical model was derived and numerical simulations were conducted accordingly to investigate the effectiveness of tangential friction anisotropy for undulation gait generation in granular media. In particular, we introduce a pseudo-rigid-body dynamics model consisting of links and joints while simulating the pneumatic actuation method to more closely approximate the response of soft robots. Moreover, a soft snake-like robot was fabricated, and its forward and reverse undulations were compared in two sets of controlled experiments. The consistency between the experimental results and the numerical simulations confirms that tangential anisotropic friction induces a propulsive effect in undulation, thereby increasing the robot’s locomotion speed. This discovery provides new insights into the design of undulation robots in granular environments.

Robot motor learning shows emergence of frequency-modulated, robust swimming with an invariant Strouhal number.

Fish locomotion emerges from diverse interactions among deformable structures, surrounding fluids and neuromuscular activations, i.e. fluid-structure interactions (FSI) controlled by fish's motor systems. Previous studies suggested that such motor-controlled FSI may possess embodied traits. However, their implications in motor learning, neuromuscular control, gait generation, and swimming performance remain to be uncovered. Using robot models, we studied the embodied traits in fish-inspired swimming. We developed modular robots with various designs and used central pattern generators (CPGs) to control the torque acting on robot body. We used reinforcement learning to learn CPG parameters for maximizing the swimming speed. The results showed that motor frequency converged faster than other parameters, and the emergent swimming gaits were robust against disruptions applied to motor control. For all robots and frequencies tested, swimming speed was proportional to the mean undulation velocity of body and caudal-fin combined, yielding an invariant, undulation-based Strouhal number. The Strouhal number also revealed two fundamental classes of undulatory swimming in both biological and robotic fishes. The robot actuators were also demonstrated to function as motors, virtual springs and virtual masses. These results provide novel insights in understanding fish-inspired locomotion.

Free Gait Generation of Quadruped Robots via Impulse-Based Feasibility Analysis

Online gait adaptation is crucial for improving the dynamic performance of quadruped locomotion systems, while current approaches often adopt the predefined periodic gait pattern. This article proposes a free gait generation algorithm that only takes the robot state as input. Specifically, we introduce the feasible impulse polytope, which takes into account both linear and angular momentum impulses acting on the body in a prediction horizon. This naturally leads us to formulate a leg capability metric related to the effect of take-off and touch-down on the body motion. Then, gait sequence, take-off timing, and touch-down location can be automatically adjusted online as long as a metric threshold is given. To cope with rough terrain, a series of quadratic programming problems are established for online pose optimization under mild assumptions. Furthermore, we fully integrate the proposed algorithms with the robot control and estimation framework for real-time implementation. We first validate our approach with the quadruped robot SCIT-Dog through locomotion with speed changes, on stairs and slopes, and under lateral disturbances. Besides, a push-recovery experiment is established to show the superiority of the proposed approach over the baseline method with prespecified gait patterns. Experiment results verify the ability of the proposed algorithms to achieve autonomous gait transitions in response to various emergencies.

C-SQG: Cosine-Law-Based Spatially Quantized Gait Generation for Knee-stretched Biped Walking

Knee-stretched walking is desirable for biped robot because it is a characteristic of human walking as well as lower energy consumption. In this paper, we proposed a new knee-stretched bipedal walking pattern generation approach named Cosine-law-based Spatially Quantized Gait (C-SQG). C-SQG includes two parts, the first one is the Cosine law-based kinematic joint angles generation for knee-stretched biped walking with the hip horizontal displacement; the second one is combining with the concept of Spatially Quantized Dynamics (SQD) and the optimization-based methods. Based on these two approaches, the balanced human-like walking patterns with fully extended knee joints for humanoid robots can be generated. The proposed approach was tested on the CoppeliaSim simulation platform, and the experimental results indicate that the knee-stretched walking patterns for different walking speeds and foot locations can be generated. Compared to the existing knee-stretched gait generation approach, the C-SQG is more robust and adaptive to different desired foot locations appropriately.

Development of quadruped robot system mounting integrated circuits of pulse-type hardware neuron models for gait generation

Development of quadruped robot system mounting integrated circuits of pulse-type hardware neuron models for gait generation

Research on gait generation and gait conversion of (2UPS-U) +R series-parallel hybrid wheel-legged quadruped robot

This paper proposes a gait control method considering lateral stability for a four-wheeled foot robot that can realize wheel-foot transformation to achieve foot-stable walking, uses the CPG gait generator to study the generation methods of different gait patterns of the robot, selects the Hopf oscillator to establish the whole CPG control network, and analyzes the relevant parameters in its mathematical model; To analyze the CPG output signal and gait generation strategy in terms of joint swing angle and foot-end coordinates, to model the CPG gait generator model using Simulink, to verify the Walk gait and Tort gait by numerical simulation; The lateral adjustment of the body is introduced into the motion control of the robot, the Walk gait, the Tort gait, and the transition strategy between gaits are simulated and verified. The trajectory of the foot end of the robot is analyzed during in situ rotation and turn-turn walking, and the CPG control network for in situ rotation and turn-turn walking is established and simulated to verify the correctness of gait generation. The gait generation and conversion strategy studied in this paper can meet the stability of the robot’s walking, and at the same time, can be converted between gait according to the road conditions and the demand for travel speed, and also provides a high reference significance for the research of multiple gait control methods for quadruped robots.

Compliant gait control method based on CVSLIP-FF model for biped robot walking over uneven terrain

Bipedal walking over uneven terrain remains a challenging task due to the environmental complexity and unavoidable landing impact. To realize the stable and robust walking of biped robots, this paper proposes a compliant gait control method, which focuses on walking compliance and conducts research on two levels. In the gait generation level, a Continuous-Variable Spring-Loaded Inverted Pendulum with Finite-sized Foot (CVSLIP-FF) model is provided with the consideration of the ankle joint and compliant spring-loaded leg. Then, a CVSLIP-FF based gait generation pattern with relevant walking strategies is provided to enhance the mobility of biped robots. In the joint control level, an ankle joint admittance control strategy is applied to achieve compliant robot-environment interaction. Experimental results indicate that compared with the traditional SLIP model, the proposed method performs better adaptability to uneven terrain with a 217.77% improvement, and enables biped robots to cope with slight unknown disturbance.

Analysis of the Relationship between Gait Generation with Improved Traction and Energy Dissipation

Analysis of the Relationship between Gait Generation with Improved Traction and Energy Dissipation

Optimization of Biped Robot Walking Based on the Improved Particle Swarm Algorithm

The central pattern generator (CPG) is widely applied in biped gait generation, and the particle swarm optimization (PSO) algorithm is commonly used to solve optimization problems for CPG network controllers. However, the canonical PSO algorithms fail to balance exploration and exploitation, resulting in reduced optimization accuracy and stability, decreasing the control effectiveness of CPG controllers. In order to address this issue, a balanced PSO (BPSO) algorithm is proposed, which achieves better performance by balancing the algorithm’s exploration and exploitation capabilities. The BPSO algorithm’s solving process consists of two phases: the free exploration phase (FEP), which emphasizes exploration, and the attention exploration phase (AEP), which emphasizes exploitation. The proportion of each phase during optimization is controlled by an adjustable parameter. The BPSO algorithm is subjected to qualitative, numerical, convergence, and statistical analyses based on 13 benchmark functions. The experimental results from the benchmark functions demonstrate that the BPSO algorithm outperforms other comparison algorithms. Finally, a linear walking optimization method for humanoid robots based on the BPSO algorithm is established and tested in the Webots simulator. Comparative results with two other optimization methods show that the BPSO‐based optimization method enables the robot to achieve greater walking distance and smaller lateral deviation within a fixed number of iterations. Compared to the other two methods, walking distance increases by at least 60.98% and lateral deviation decreases by at least 1.96%. This research contributes to enhancing the locomotion capabilities of CPG‐controlled humanoid robots, enriching biped gait optimization theory and promoting the application of CPG gait control methods in humanoid robots.