A 'sidewinding' locomotion gait for hyper-redundant robots

This paper considers a novel form of hyper-redundant mobile robot locomotion which is analogous to the 'sidewinding' locomotion gait employed by several species of snake. It is shown that this gait can be generated by a repetitive traveling wave of mechanism deformation. This paper considers primarily the kinematics of the sidewinding gait. The kinematic analysis is based on a continuous 'backbone curve' model which captures the robot's important macroscopic features. Using this continuous model, we first develop algorithms which enable travel in a uniform direction. We subsequently extend this basic gait pattern to enable changes in the direction of travel.     

Snake Robot Obstacle-Aided Locomotion: Modeling, Simulations, and Experiments

Snakes utilize irregularities in the terrain, such as rocks and vegetation, for faster and more efficient locomotion. This motivates the development of snake robots that actively use the terrain for locomotion, i.e., obstacle-aided locomotion. In order to accurately model and understand this phenomenon, this paper presents a novel nonsmooth (hybrid) mathematical model for wheel-less snake robots, which allows the snake robot to push against external obstacles apart from a flat ground. The framework of nonsmooth dynamics and convex analysis allows us to systematically and accurately incorporate both unilateral contact forces (from the obstacles) and isotropic friction forces based on Coulomb's law using set-valued force laws. The mathematical model is verified through experiments. In particular, a back-to-back comparison between numerical simulations and experimental results is presented. It is, furthermore, shown that the snake robot is able to move forward faster and more robustly by exploiting obstacles.     

Development of a new spinning gait for a planar snake robot using central pattern generators

In this paper, we first present dynamic equation of n-link snake robot using Lagrange’s method in a simplified matrix form and verify them experimentally. Next, we introduce a new locomotion mode called spinning gait. Central pattern generators (CPGs) are used for online gait generation. To realize spinning gait, genetic algorithm is used to find optimal CPG network parameters. We illustrate both theoretically, using derived robot dynamics and experimentally that the CPG-based online gait generation method allows continuous and rather smooth transitions between gaits. Lastly, we present an application where the snake robot is guided from an initial to final position while avoiding obstacles by changing CPG parameters.     

Control of snake robots with switching constraints: trajectory tracking with moving obstacle

We propose control of a snake robot that can switch lifting parts dynamically according to kinematics. Snakes lift parts of their body and dynamically switch lifting parts during locomotion: e.g. sinus-lifting and sidewinding motions. These characteristic types of snake locomotion are used for rapid and efficient movement across a sandy surface. However, optimal motion of a robot would not necessarily be the same as that of a real snake as the features of a robot’s body are different from those of a real snake. We derived a mathematical model and designed a controller for the three-dimensional motion of a snake robot on a two-dimensional plane. Our aim was to accomplish effective locomotion by selecting parts of the body to be lifted and parts to remain in contact with the ground. We derived the kinematic model with switching constraints by introducing a discrete mode number. Next, we proposed a control strategy for trajectory tracking with switching constraints to decrease cost function, and to satisfy the conditions of static stability. In this paper, we introduced a cost function related to avoidance of the singularity and the moving obstacle. Simulations and experiments demonstrated the effectiveness of the proposed controller and switching constraints.     

3-D Snake Robot Motion: Nonsmooth Modeling, Simulations, and Experiments

A nonsmooth (hybrid) 3-D mathematical model of a snake robot (without wheels) is developed and experimentally validated in this paper. The model is based on the framework of nonsmooth dynamics and convex analysis that allows us to easily and systematically incorporate unilateral contact forces (i.e., between the snake robot and the ground surface) and friction forces based on Coulomb's law of dry friction. Conventional numerical solvers cannot be employed directly due to set-valued force laws and possible instantaneous velocity changes. Therefore, we show how to implement the model for numerical treatment with a numerical integrator called the time-stepping method. This method helps to avoid explicit changes between equations during simulation even though the system is hybrid. Simulation results for the serpentine motion pattern lateral undulation and sidewinding are presented. In addition, experiments are performed with the snake robot ldquoAikordquo for locomotion by lateral undulation and sidewinding, both with isotropic friction. For these cases, back-to-back comparisons between numerical results and experimental results are given.     

Ground adaptive and optimized locomotion of snake robot moving with a novel gait

In this paper, we present a novel gait, forward head serpentine (FHS), for a two dimensional snake robot. The advantage of this new gait is that the head link remains in the forward direction during motion. This feature significantly improves snake robot potential applications. Genetic Algorithm (GA) is used to find FHS gait parameters. Relationship between FHS gait parameters and friction coefficients of the ground are developed. Next, robot speed is considered in the optimization. A fitness function covering robot speed and head link angular changes is defined. A general sinusoidal wave form is applied for each joint. GA is used to find gait parameters resulting in maximum speed while head link angular changes remain in an acceptable range. Optimal gait parameters are also calculated for different friction coefficients and relationships between them are developed. Experiments are also performed using a 5-link snake robot. It is shown that experimental and theoretical results closely agree.     

Minimalistic control of biped walking in rough terrain

Toward our comprehensive understanding of legged locomotion in animals and machines, the compass gait model has been intensively studied for a systematic investigation of complex biped locomotion dynamics. While most of the previous studies focused only on the locomotion on flat surfaces, in this article, we tackle with the problem of bipedal locomotion in rough terrains by using a minimalistic control architecture for the compass gait walking model. This controller utilizes an open-loop sinusoidal oscillation of hip motor, which induces basic walking stability without sensory feedback. A set of simulation analyses show that the underlying mechanism lies in the “phase locking” mechanism that compensates phase delays between mechanical dynamics and the open-loop motor oscillation resulting in a relatively large basin of attraction in dynamic bipedal walking. By exploiting this mechanism, we also explain how the basin of attraction can be controlled by manipulating the parameters of oscillator not only on a flat terrain but also in various inclined slopes. Based on the simulation analysis, the proposed controller is implemented in a real-world robotic platform to confirm the plausibility of the approach. In addition, by using these basic principles of self-stability and gait variability, we demonstrate how the proposed controller can be extended with a simple sensory feedback such that the robot is able to control gait patterns autonomously for traversing a rough terrain.     

Formation control of underactuated bio-inspired snake robots

This paper considers formation control of snake robots. In particular, based on a simplified locomotion model, and using the method of virtual holonomic constraints, we control the body shape of the robot to a desired gait pattern defined by some pre-specified constraint functions. These functions are dynamic in that they depend on the state variables of two compensators which are used to control the orientation and planar position of the robot, making this a dynamic maneuvering control strategy. Furthermore, using a formation control strategy we make the multi-agent system converge to and keep a desired geometric formation, and enforce the formation follow a desired straight line path with a given speed profile. Specifically, we use the proposed maneuvering controller to solve the formation control problem for a group of snake robots by synchronizing the commanded velocities of the robots. Simulation results are presented which illustrate the successful performance of the theoretical approach.     

Analysis of creeping locomotion of a snake-like robot

Snakes perform many kinds of movement adapted to the environment. Utilizing the snake (its forms and motion) as a model to develop a snake-like robot, that performs the snake's function, is important for generating a new type of locomotion and expanding the possible uses of robots. In this study, we developed a simulator to simulate the creeping locomotion of the snake-like robot, in which the robot dynamics is modeled and the interaction with the environment is considered through Coulomb friction. This simulator makes it possible to analyze creeping locomotion with normaldirection slip, adding to the glide along the tangential direction. Through the developed simulator, we investigate the snake-like robot creeping locomotion which is generated only by swinging each of the joints from side to side and discuss the optimal creeping locomotion of the snake-like robot that is adapted to the environment.     

Computer simulation and dynamic modeling of a quadrupedal pronking gait robot with SLIP model

In this study, a quadrupedal pronking gait robot modeling was carried out with Spring Loaded Inverted Pendulum model in stance phase. This is achieved by solving a natural problem in which the main goal is to enable the robot to walk and run in a stable condition regardless of the environmental conditions. In order to solve this problem, dynamic model and control of a quadrupedal robot were realized for a pronking gait. The stance and flight phase dynamic structures were solved in a sequential closed loop to obtain the equation of motion for pronking gait. Spring Loaded Inverted Pendulum model was used as a dynamic model to simplify the simulation, dynamic locomotion and experimental works of the system, and also to simplify the pronking gait concept. The quadrupedal robot with pronking gait was controlled by proportional-derivative control algorithm. As a result, all computer simulations have shown that the proposed control actions and methods are more effective and make the system control quite easy and successful.     

Exploiting natural dynamics for gait generation in undulatory locomotion

ABSTRACT

Robotic vehicles inspired by animal locomotion operate via periodic body movements. The pattern of body oscillation (gait) can be mimicked from animals, but understanding the principles underlying gait generation would allow for broad, flexible applications beyond nature's design. We hypothesise that travelling-wave oscillations observed in undulatory locomotion can be characterised as a natural oscillation of the locomotion dynamics and propose a formal definition of the natural gait for locomotion systems. We identify the essential dynamics and define the mode shape of natural oscillation by the free response of an idealised system. We then use body-environment resonance to define the amplitude and frequency. Explicit formulas for the natural gait are derived to provide insight into the mechanisms underlying undulatory locomotion. Examples of a swimming leech and a fictitious swimmer illustrate how undulatory gaits similar to those observed can be produced as the natural gait and modulated to achieve different swim speeds.     

Multi-objective optimization for efficient motion of underwater snake robots

Underwater snake robots constitute a bio-inspired solution within underwater robotics. Increasing the motion efficiency in terms of the forward speed by improving the locomotion methods is a key issue for underwater robots. Furthermore, the energy efficiency is one of the main challenges for long-term autonomy of these systems. In this study, we will consider both these aspects of efficiency, which in some cases can be conflicting. To this end, we formulate a multi-objective optimization problem to minimize power consumption and maximize forward velocity. In particular, the optimal values of the gait parameters for different motion patterns are calculated in the presence of trade-offs between power consumption and velocity. As is the case with all multi-objective optimization problems, the solution is not a single point but rather a set of points. We present a weighted-sum method to combine power consumption and forward velocity optimization problems. Particle swarm optimization is applied to obtain optimal gait parameters for different weighting factors. Trade-off curves or Pareto fronts are illustrated in a power consumption–forward velocity plane for both lateral and eel-like motion pattern. They give information on objective trade-offs and can show how improving power consumption is related to deteriorating the forward velocity along the trade-off curve. Therefore, decision makers can specify the preferred Pareto optimal point along the trade-off curve. Moreover, we address some interesting questions regarding the optimal gait parameters, which is a significant issue for the control of underwater snake robots in the future.     

Four-leg independent mechanism for MEMS microrobot

In this paper, the development of a quadruped micro-electro mechanical system (MEMS) microrobot with a four-leg independent mechanism is described. As the actuator mechanism inside small robot bodies is difficult to realize, many microrobots use external field forces such as magnetism and vibration. In this paper, artificial muscle wires that are family of shape memory alloy are used for the force of the actuator. The artificial muscle wire shows the large displacement by passing the electrical current through the material itself. The double four-link mechanism is adopted for the leg system. The link mechanism transforms the linear motion of the artificial muscle wire to the foot step-like pedaling motion. The location of the backward swing motion is lower than that of forward swing motion. This motion generates the locomotion force. As a result, the total length of the constructed quadruped MEMS microrobot was 6 mm. The microrobot could perform similar gait pattern changes as the quadruped animal.     

A review on modelling, implementation, and control of snake robots

This paper provides an overview of previous literature on snake robot locomotion. In particular, the paper considers previous research efforts related to modelling of snake robots, physical development of these mechanisms, and finally control design efforts for snake locomotion. The review shows that the majority of literature on snake robots so far has focused on locomotion over flat surfaces, but that there is a growing trend towards locomotion in environments that are more challenging, i.e. environments that are more in line with realistic applications of these mechanisms.     

Adaptive Robot Biped Locomotion with Dynamic Motion Primitives and Coupled Phase Oscillators

In order to properly function in real-world environments, the gait of a humanoid robot must be able to adapt to new situations as well as to deal with unexpected perturbations. A promising research direction is the modular generation of movements that results from the combination of a set of basic primitives. In this paper, we present a robot control framework that provides adaptive biped locomotion by combining the modulation of dynamic movement primitives (DMPs) with rhythm and phase coordination. The first objective is to explore the use of rhythmic movement primitives for generating biped locomotion from human demonstrations. The second objective is to evaluate how the proposed framework can be used to generalize and adapt the human demonstrations by adjusting a few open control parameters of the learned model. This paper contributes with a particular view into the problem of adaptive locomotion by addressing three aspects that, in the specific context of biped robots, have not received much attention. First, the demonstrations examples are extracted from human gaits in which the human stance foot will be constrained to remain in flat contact with the ground, forcing the “bent-knee” at all times in contrast with the typical straight-legged style. Second, this paper addresses the important concept of generalization from a single demonstration. Third, a clear departure is assumed from the classical control that forces the robot’s motion to follow a predefined fixed timing into a more event-based controller. The applicability of the proposed control architecture is demonstrated by numerical simulations, focusing on the adaptation of the robot’s gait pattern to irregularities on the ground surface, stepping over obstacles and, at the same time, on the tolerance to external disturbances.     

A Novel Method of Gait Synthesis for Bipedal Fast Locomotion

Common methods of gait generation of bipedal locomotion based on experimental results, can successfully synthesize biped joints’ profiles for a simple walking. However, most of these methods lack sufficient physical backgrounds which can cause major problems for bipeds when performing fast locomotion such as running and jumping. In order to develop a more accurate gait generation method, a thorough study of human running and jumping seems to be necessary. Most biomechanics researchers observed that human dynamics, during fast locomotion, can be modeled by a simple spring loaded inverted pendulum system. Considering this observation, a simple approach for bipedal gait generation in fast locomotion is introduced in this paper. This approach applies a nonlinear control method to synchronize the biped link-segmental dynamics with the spring-mass dynamics. This is done such that while the biped center of mass follows the trajectory of the mass-spring model, the whole biped performs the desired running/jumping process. A computer simulation is done on a three-link under-actuated biped model in order to obtain the robot joints’ profiles which ensure repeatable hopping. The initial results are found to be satisfactory, and improvements are currently underway to explore and enhance the capabilities of the proposed method.     

Comments on “Sidewinding with Minimal Slip: Snake and Robot Ascent of Sandy Slopes”

Marvi et al(Science,2014,vol.346,p.224)concluded a sidewinder rattlesnake increases the body contact length with the sand when granular incline angle increases.They also claimed the same principle should work on robotic snake too.We have evidence to prove that this conclusion is only partial in describing the snake body-sand interaction.There should be three phases that fully represent the snake locomotion behaviors during ascent of sandy slopes,namely lifting,descending,and ceasing.The snake body-sand interaction during the descending and ceasing phases helps with the climbing while such interaction during the lifting phase in fact contributes resistance.     

Passivity-Based Control of Bipedal Locomotion

In this article, we have shown how to design energy-based and passivity-based control laws that exploit the existence of passive walking gaits to achieve walking on different ground slopes, to increase the size of the basin of attraction and robustness properties of stable limit cycles, and to regulate walking speed. Many of the results presented in this are the compass gait are equally applicable to bipeds with knees and a torso. Practical considerations such as actuator saturation, ground reaction forces, and ground friction need to be addressed. The problem of foot rotation introduces an underactuated phase into the walking gait, which greatly challenges the application of energy shaping ideas. For walking in 3D, finding purely passive limit cycles, which is the first step in applying our energy control results, may be difficult. It was shown how ideas of geometric reduction can be used to generate 3D stable gaits given only 2D passive limit cycles.     

Terrain Classification Using Weakly-Structured Vehicle/Terrain Interaction

We present a new terrain classification technique both for effective, autonomous locomotion over rough, unknown terrains and for the qualitative analysis of terrains for exploration and mapping. Our approach requires a single camera with little processing of visual information. Specifically, we derived a gait bounce measure from visual servoing errors that results from vehicle-terrain interactions during normal locomotion. Characteristics of the terrain, such as roughness and compliance, manifest themselves in the spatial patterns of this signal and can be extracted using pattern classification techniques. This vision-based approach is particularly beneficial for resource-constrained robots with limited sensor capability. In this paper, we present the gait bounce derivation. We demonstrate the viability of terrain classification for legged vehicles using gait bounce with a rigorous study of more than 700 trials, obtaining an 83% accuracy on a set of laboratory terrains. We describe how terrain classification may be used for gait adaptation, particularly in relation to an efficiency metric. We also demonstrate that our technique may be generally applicable to other locomotion mechanisms such as wheels and treads.