High-level motion planning for CPG-driven modular robots

Modular robots may become candidates for search and rescue operations or even for future space missions, as they can change their structure to adapt to terrain conditions and to better fulfill a given task. A core problem in such missions is the ability to visit distant places in rough terrain. Traditionally, the motion of modular robots is modeled using locomotion generators that can provide various gaits, e.g. crawling or walking. However, pure locomotion generation cannot ensure that desired places in a complex environment with obstacles will in fact be reached. These cases require several locomotion generators providing motion primitives that are switched using a planning process that takes the obstacles into account. In this paper, we present a novel motion planning method for modular robots equipped with elementary motion primitives. The utilization of primitives significantly reduces the complexity of the motion planning which enables plans to be created for robots of arbitrary shapes. The primitives used here do not need to cope with environmental changes, which can therefore be realized using simple locomotion generators that are scalable, i.e., the primitives can provide motion for robots with many modules. As the motion primitives are realized using locomotion generators, no reconfiguration is required and the proposed approach can thus be used even for modular robots without self-reconfiguration capabilities. The performance of the proposed algorithm has been experimentally verified in various environments, in physical simulations and also in hardware experiments.     

六足步行机横向行走最佳步态及其运动特性初探

本文分别以纵向稳定裕量和一般稳定裕量为准则,通过对六足步行机横向行走几何模型的分析和计算机优化计算,得出六足步行机横向运动时的最佳步态为广义三角步态.此外,文中对广义三角步态的运动特性(包括静态稳定性、爬坡能力、越沟能力等)进行了初步研究,阐明了这些运动特性与步行机若干几何参数间的内在联系,为六足步行机的总体尺寸设计提供了理论依据。     

Bayesian optimization for learning gaits under uncertainty

Designing gaits and corresponding control policies is a key challenge in robot locomotion. Even with a viable controller parametrization, finding near-optimal parameters can be daunting. Typically, this kind of parameter optimization requires specific expert knowledge and extensive robot experiments. Automatic black-box gait optimization methods greatly reduce the need for human expertise and time-consuming design processes. Many different approaches for automatic gait optimization have been suggested to date. However, no extensive comparison among them has yet been performed. In this article, we thoroughly discuss multiple automatic optimization methods in the context of gait optimization. We extensively evaluate Bayesian optimization, a model-based approach to black-box optimization under uncertainty, on both simulated problems and real robots. This evaluation demonstrates that Bayesian optimization is particularly suited for robotic applications, where it is crucial to find a good set of gait parameters in a small number of experiments.     

A lattice-type reconfigurable robotic system for achieving gaits of chain-type robots

Traditional lattice-type reconfigurable robots can only achieve the flow-style locomotion with low efficiency. Since gaits of chain-type robots are proved to be efficient and practical, this paper presents a novel lattice distortion approach for lattice-type reconfigurable robots to achieve locomotion gaits of chain-type robots. Using this approach, the robotic system can be actuated by local lattice distortion to move as an ensemble. In this paper, a rule that makes the lattice distortion equivalent to joint rotation is presented firstly. Then, a kind of module structure is designed according to requirements of the lattice distortion. Finally, a motion planning for achieving locomotion is developed, which works well in physics-based simulations of completing a serpentine locomotion gait of a snake-like robot and a tripod gait of a hexapod robot.     

Policy gradient learning for a humanoid soccer robot

In humanoid robotic soccer, many factors, both at low-level (e.g., vision and motion control) and at high-level (e.g., behaviors and game strategies), determine the quality of the robot performance. In particular, the speed of individual robots, the precision of the trajectory, and the stability of the walking gaits, have a high impact on the success of a team. Consequently, humanoid soccer robots require fine tuning, especially for the basic behaviors. In recent years, machine learning techniques have been used to find optimal parameter sets for various humanoid robot behaviors. However, a drawback of learning techniques is time consumption: a practical learning method for robotic applications must be effective with a small amount of data. In this article, we compare two learning methods for humanoid walking gaits based on the Policy Gradient algorithm. We demonstrate that an extension of the classic Policy Gradient algorithm that takes into account parameter relevance allows for better solutions when only a few experiments are available. The results of our experimental work show the effectiveness of the policy gradient learning method, as well as its higher convergence rate, when the relevance of parameters is taken into account during learning.     

面向仿人机器人自然步态规划的人体步行实验分析

自然步态规划方法是实现仿人机器人步态柔顺和能量优化的可行方法,该方法要求对人体步行及其平衡策略进行定量研究．本文分析自然步态规划方法的原理,建立了一套快捷有效的人体步态测试系统,并通过实验建立了人体步行的参数化数据库．实验结果揭示了人体步行的参数化特征及其平衡策略,对于仿人机器人的自然步态规划及控制提供了理论指导．结论特别指出,仅仅通过规划的方式实现仿人机器人的自然步态是不完备的,自然步态的实现必须同仿生控制策略相结合．同时实验结论对于仿人机器人的本体优化设计也提供了参考．     

Controlling swimming and crawling in a fish robot using a central pattern generator

Online trajectory generation for robots with multiple degrees of freedom is still a difficult and unsolved problem, in particular for non-steady state locomotion, that is, when the robot has to move in a complex environment with continuous variations of the speed, direction, and type of locomotor behavior. In this article we address the problem of controlling the non-steady state swimming and crawling of a novel fish robot. For this, we have designed a control architecture based on a central pattern generator (CPG) implemented as a system of coupled nonlinear oscillators. The CPG, like its biological counterpart, can produce coordinated patterns of rhythmic activity while being modulated by simple control parameters. To test our controller, we designed BoxyBot, a simple fish robot with three actuated fins capable of swimming in water and crawling on firm ground. Using the CPG model, the robot is capable of performing and switching between a variety of different locomotor behaviors such as swimming forwards, swimming backwards, turning, rolling, moving upwards/downwards, and crawling. These behaviors are triggered and modulated by sensory input provided by light, water, and touch sensors. Results are presented demonstrating the agility of the robot and interesting properties of a CPG-based control approach such as stability of the rhythmic patterns due to limit cycle behavior, and the production of smooth trajectories despite abrupt changes of control parameters. The robot is currently used in a temporary 20-month long exhibition at the EPFL. We present the hardware setup that was designed for the exhibition, and the type of interactions with the control system that allow visitors to influence the behavior of the robot. The exhibition is useful to test the robustness of the robot for long term use, and to demonstrate the suitability of the CPG-based approach for interactive control with a human in the loop. This article is an extended version of an article presented at BioRob2006 the first IEEE/RAS-EMBS International Conference on Biomedical Robotics and Biomechatronics.     

CONRO: Towards Deployable Robots with Inter-Robots Metamorphic Capabilities

Metamorphic robots are modular robots that can reconfigure their shape. Such capability is desirable in tasks such as earthquake search and rescue and battlefield surveillance and scouting, where robots must go through unexpected situations and obstacles and perform tasks that are difficult for fixed-shape robots. The capabilities of the robots are determined by the design specification of their modules. In this paper, we present the design specification of a CONRO module, a small, self-sufficient and relatively homogeneous module that can be connected to other modules to form complex robots. These robots have not only the capability of changing their shape (intra-robot metamorphing) but also can split into smaller robots or merge with other robots to create a single larger robot (inter-robot metamorphing), i.e., CONRO robots can alter their shape and their size. Thus, heterogeneous robot teams can be built with homogeneous components. Furthermore, the CONRO robots can separate the reconfiguration stage from the locomotion stage, allowing the selection of configuration-dependent gaits. The locomotion and automatic inter-module docking capabilities of such robots were tested using tethered prototypes that can be reconfigured manually. We conclude the paper discussing the future work needed to fully realize the construction of these robots.     

An adaptive locomotion controller for a hexapod robot: CPG,kinematics and force feedback

Insects can perform versatile locomotion behaviors such as multiple gaits, adapting to different terrains, fast escaping, etc. However, most of the existing bio-inspired legged robots do not possess such walking ability, especially when they walk on irregular terrains. To tackle this challenge, a central pattern generator （CPG）-based locomotion control methodology is proposed, integrated with a contact force feedback function. In this approach, multiple gaits are produced by the CFG module. After passing through a post-processing circuit and a delay-line, the control signal is fed into six trajectory generators to generate predefined feet trajectories for the six legs. Then, force feedback is employed to adjust these trajectories so as to adapt the robot to rough terrains. Finally the regulated trajectories are sent to inverse kinematics modules such that the position control instructions are generated to control the actuators. In both simulations and real robot experiments, we consistently show that the robot can perform sophisticated walking patterns. What is more, the robot can use the force feedback mechanism to deal with the irregularity in rough terrain. With this mechanism, the stability and adaptability of the robot are enhanced. In conclusion, the CPG-base control is an effective approach for legged robots and the force feedback approach is able to improve walking ability of the robots, especially when they walk on irregular terrains.     

Piecewise linear spine for speed–energy efficiency trade-off in quadruped robots

We compare the effects of linear and piecewise linear compliant spines on locomotion performance of quadruped robots in terms of energy efficiency and locomotion speed through a set of simulations and experiments. We first present a simple locomotion system that behaviorally resembles a bounding quadruped with flexible spine. Then, we show that robots with linear compliant spines have higher locomotion speed and lower cost of transportation in comparison with those with rigid spine. However, in linear case, optimal speed and minimum cost of transportation are attained at very different spine compliance values. Moreover, it is verified that fast and energy efficient locomotion can be achieved together when the spine flexibility is piecewise linear. Furthermore, it is shown that the robot with piecewise linear spine is more robust against changes in the load it carries. Superiority of piecewise linear spines over linear and rigid ones is additionally confirmed by simulating a quadruped robot in Webots and experiments on a crawling two-parts robot with flexible connection.     

六边形对称分布六腿机器人的典型步态及其运动性能分析

为了便于在不同地理条件下合理地选择较优的步态,实现稳定高效的智能行走,本文针对一种六边形 对称分布的六腿机器人研究其不同步态的优劣．主要从行走能力、稳定性和能耗3 个角度对六边形对称结构的六腿 机器人在同样占空比下的3 种静态稳定周期步态进行了比较研究,此外还简要分析了其越障能力和穿越窄道的能 力．研究分析结果表明3 种步态（横向昆虫式摆动步态、哺乳动物式踢腿步态和混合步态）在不同条件下各有优劣： 横向昆虫式摆动步态在能耗和越障能力方面较其他两种步态有优势;而混合步态在稳定性上最具优势,其它能力处 于中间;哺乳动物式踢腿步态则可穿越窄道,步长上较昆虫摆动步态略好．本文的研究工作为六边形对称结构的六 腿机器人在未知复杂地貌环境下的智能行走提供了重要参考．     

From human to humanoid locomotion—an inverse optimal control approach

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control problems is to determine—for a given dynamic process and an observed solution—the optimization criterion that has produced the solution. Inverse optimal control problems are difficult from a mathematical point of view, since they require to solve a parameter identification problem inside an optimal control problem. We propose a pragmatic new bilevel approach to solve inverse optimal control problems which rests on two pillars: an efficient direct multiple shooting technique to handle optimal control problems, and a state-of-the art derivative free trust region optimization technique to guarantee a match between optimal control problem solution and measurements. In this paper, we apply inverse optimal control to establish a model of human overall locomotion path generation to given target positions and orientations, based on newly collected motion capture data. It is shown how the optimal control model can be implemented on the humanoid robot HRP-2 and thus enable it to autonomously generate natural locomotion paths.     

Optimal fault tolerant gait sequence of the hexapod robot withoverlapping reachable areas and crab walking

This paper extends the authors' previous results on fault tolerant locomotion of the hexapod robot on even terrain by relaxing nonoverlap of redefined reachable cells of legs and considering crab walking. It is shown that in fault tolerant locomotion two adjacent legs of the hexapod robot can have overlapping redefined reachable cells with each other and consequently the stride length of the gaits is increased. Also, the optimal fault tolerant periodic gaits for hexapod robots to have the maximum stride length in one cycle in crab walking on even terrain are derived with distinct reachable cells. The derived sequence for crab walking has different orders of leg swing according to the relative values of the crab angle and some design parameters of the robot     

Development of wheel-less snake robot with two distinct gaits and gait transition capability

Snake robots are mostly designed based on single mode locomotion. However, single mode gait most likely could not work effectively when the robot is subject to an unstructured working environment with different measures of terrain complexity. As a solution, mixed mode locomotion is proposed in this paper by synchronizing two types of gaits known as serpentine and wriggler gaits used for non-constricted and narrow space environments, respectively, but for straight line locomotion only. A gait transition algorithm is developed to efficiently change the gait from one to another. This study includes the investigation on kinematics analysis followed by dynamics analysis while considering related structural constraints for both gaits. The approach utilizes the speed of the serpentine gait for open area locomotion and exploits the narrow space access capability of the wriggler gait. Hence, it can increase motion flexibility in view of the fact that the robot is able to change its mode of locomotion according to the working environment.     

Gait optimization of step climbing for a hexapod robot

RHex-style hexapod robot is a type of legged robot which can perform multiple moving gaits according to different applications, due to its simple structure and strong mobility. However, traversing high obstacles has always been a big challenge for legged robots. In this paper, gait optimization of a hexapod robot is proposed for climbing steps at different heights, which even enables the robot to climb the step 3.9 times of the leg length. First, a previous step-climbing gait is optimized by adjusting body inclination when placing front legs on top of the step, which enables RHex with different sizes to perform the rising stage of the gait. Second, to improve the climbing heights, a novel quasi-static climbing gait is proposed by using the reversed claw-shape legs to reach the higher step. The nondeformable legs are used to raise the center of mass (COM) of the body by lifting the front and rear legs alternately so that the front legs can reach the top of the step, then the front and middle legs are lifted alternately to maneuver COM up onto the step. The simulations and dynamic analysis of climbing steps are utilized to verify the feasibility of the improved gait. Finally, the step-climbing experiments at different heights are performed with the optimized gaits to compare with the existing gaits. The results of simulations and experiments show the superiority of the proposed gaits due to climbing higher steps.     

Evolving gaits for hexapod robots using cyclic genetic algorithms

A major facet of multi-legged robot control is locomotion. Each leg must move in such a manner that it efficiently produces thrust and provides maximum support. The motion of all the legs must be coordinated so that they are working together to provide constant stability while propelling the robot forward. In this paper, we discuss the use of a cyclic genetic algorithm (CGA) to evolve control programs that produce gaits for actual hexapod robots. Tests done in simulation and verified on the actual robot show that the CGA successfully produces gaits for both fully capable and disabled robots.     

通信距离约束下异构水下爬游机器人任务分配

为了保证执行任务的水下爬游机器人之间时刻保持信息交互,提出了一种带通信距离约束的异构水下爬游机器人集群任务分配方法;首先,建立了异构水下爬游机器人集群的任务分配数学模型;其次,分析了多水下爬游机器人通信距离、航程等约束条件;最后,采用蚁群优化算法对异构水下爬游机器人集群的任务分配问题进行求解,在满足约束条件情况下实现了多爬游机器人总航行距离最短;仿真验证了该方法在通信距离约束下实现多水下爬游机器人任务分配的有效性.     

AmphiBot I: an amphibious snake-like robot

This article presents a project that aims at constructing a biologically inspired amphibious snake-like robot. The robot is designed to be capable of anguilliform swimming like sea-snakes and lampreys in water and lateral undulatory locomotion like a snake on ground. Both the structure and the controller of the robot are inspired by elongate vertebrates. In particular, the locomotion of the robot is controlled by a central pattern generator (a system of coupled oscillators) that produces travelling waves of oscillations as limit cycle behavior. We present the design considerations behind the robot and its controller. Experiments are carried out to identify the types of travelling waves that optimize speed during lateral undulatory locomotion on ground. In particular, the optimal frequency, amplitude and wavelength are thus identified when the robot is crawling on a particular surface.     

Genetic programming incorporating biased mutation for evolution and adaptation of Snakebot

In this work we propose an approach for incorporating learning probabilistic context-sensitive grammar (LPCSG) in genetic programming (GP), employed for evolution and adaptation of locomotion gaits of a simulated snake-like robot (Snakebot). Our approach is derived from the original context-free grammar which usually expresses the syntax of genetic programs in canonical GP. Empirically obtained results verify that employing LPCSG contributes to the improvement of computational effort of both (i) the evolution of the fastest possible locomotion gaits for various fitness conditions and (ii) adaptation of these locomotion gaits to challenging environment and degraded mechanical abilities of the Snakebot.