Trajectory Generation for Stair Ascent Walking using Rayleigh Oscillator

This paper describes a trajectory generation technique for stair-ascent walking. The knee, hip and ankle joint trajectory during stair ascent are generated using mutually coupled, nonlinear oscillators. The parameters of the oscillators are tuned using the harmonic balance method, which converts the nonlinear differential equations to a set of algebraic equations. Fourier analysis of data generated by stair-ascent walking is performed to extract the amplitude and the phase of the dominant frequency components for each joint trajectory. The solution for the oscillator is assumed to be a sinusoidal wave and then by harmonic balance method the parameters of the oscillator are found. Each oscillator is responsible for generating a single frequency component with a specific phase and amplitude. The complete trajectory is obtained by summing the output of the oscillators that are relevant to one joint and the coupling maintains the phase relationship between the oscillators

Experimental comparison of the van der Pol and Rayleigh nonlinear oscillators for a robotic swinging task

In this paper, the effects of different lower-level building blocks of a robotic swinging system are explored, from the perspective of motor skill acquisition. The van der Pol and Rayleigh oscillators are used to entrain to the system’s natural dynamics, with two different network topologies being used: a symmetric and a hierarchical one. Rayleigh outperformed van der Pol regarding maximum oscillation amplitudes for every morphological configuration examined. However, van der Pol started large amplitude relaxation oscillations faster, attaining better performance during the first half of the transient period. Hence, even though there are great similarities between the oscillators, differences in their resultant behaviours are more pronounced than originally expected

Analisis Kestabilan Model Robot Bipedal Menggunakan Metode Keseimbangan Harmonis

Penerapan matematika dalam bidang teknologi telah banyak dikembangkan. Contohnya robot bipedal yang merupakan robot berkaki dua. Teknologi ini dapat melakukan tugas - tugas manusia dan memiliki kemampuan seperti manusia serta beberapa keuntungan bila dibandingkan model robot yang lain. Robot bipedal merupakan rangkaian rumit karena menggunakan sistem dinamik non linier. Banyaknya jumlah degrees of freedom atau derajat kebebasan yang digunakan pada permodelan juga dapat mempengaruhi hasil dari simulasi. Studi tentang robot bipedal telah menarik minat karena masalah seperti stabilitas buruk yang melekat dan kerjasama dengan tingkat kebebasan yang besar. Berdasarkan teknologi maju terkini, termasuk perangkat  keras dan perangkat lunak, memungkinkan masalah ini ditangani dengan cepat. Sehingga kemampuan sistem ini untuk berjalan benar – benar mandiri di medan yang tidak rata dan berbagai cara yang kuat yaitu di kehidupan sehari-hari, masih harus dibuktikan. Model robot bipedal yang akan dipelajari terbentuk oleh kumpulan rangkaian osilator Rayleigh. Tujuan dari penelitian ini agar dapat merekonstruksi, menganalisis kestabilan dan melakukan simulasi tentang model robot bipedal menggunakan metode keseimbangan harmonis. Hal ini bermanfaat untuk mengetahui kestabilan dari model robot bipedal. Dengan demikian, hasilnya dapat dijadikan suatu pertimbangan untuk pembuatan robot bipedal yang lebih baik lagi. Rekonstruksi model robot bipedal menggunakan tiga derajat kebebasan saja, yaitu : sudut lutut kiri, sudut pinggul, dan sudut lutut kanan. Dari analisis kestabilan menggunakan metode keseimbangan harmonis diperoleh bahwa dari persamaan (4.7) - (4.9) akan berupa solusi periodik jika nilai parameter sesuai persamaan (4.33) – (4.38) dengan parameter yang ada. Selain itu, dari hasil simulasi diperoleh bahwa sistem persamaan model robot bipedal stabil di tiga solusi periodik yaitu kurva berwarna biru adalah sudut lutut kanan, kurva berwarna merah adalah sudut pinggul, dan kurva berwarna hijau adalah sudut lutut kiri.   Kata kunci: Robot Bipedal, Osilator Rayleigh, Metode Keseimbangan Harmoni

ANALISIS KESTABILAN MODEL ROBOT BIPEDAL MENGGUNAKAN METODE KESEIMBANGAN HARMONIS

Penerapan matematika dalam bidang teknologi telah banyak dikembangkan. Contohnya robot bipedal yang merupakan robot berkaki dua. Teknologi ini dapat melakukan tugas - tugas manusia dan memiliki kemampuan seperti manusia serta beberapa keuntungan bila dibandingkan model robot yang lain. Robot bipedal merupakan rangkaian rumit karena menggunakan sistem dinamik non linier. Banyaknya jumlah degrees of freedom atau derajat kebebasan yang digunakan pada permodelan juga dapat mempengaruhi hasil dari simulasi. Studi tentang robot bipedal telah menarik minat karena masalah seperti stabilitas buruk yang melekat dan kerjasama dengan tingkat kebebasan yang besar. Berdasarkan teknologi maju terkini, termasuk perangkat  keras dan perangkat lunak, memungkinkan masalah ini ditangani dengan cepat. Sehingga kemampuan sistem ini untuk berjalan benar – benar mandiri di medan yang tidak rata dan berbagai cara yang kuat yaitu di kehidupan sehari-hari, masih harus dibuktikan. Model robot bipedal yang akan dipelajari terbentuk oleh kumpulan rangkaian osilator Rayleigh. Tujuan dari penelitian ini agar dapat merekonstruksi, menganalisis kestabilan dan melakukan simulasi tentang model robot bipedal menggunakan metode keseimbangan harmonis. Hal ini bermanfaat untuk mengetahui kestabilan dari model robot bipedal. Dengan demikian, hasilnya dapat dijadikan suatu pertimbangan untuk pembuatan robot bipedal yang lebih baik lagi. Rekonstruksi model robot bipedal menggunakan tiga derajat kebebasan saja, yaitu : sudut lutut kiri, sudut pinggul, dan sudut lutut kanan. Dari analisis kestabilan menggunakan metode keseimbangan harmonis diperoleh bahwa dari persamaan (4.7) - (4.9) akan berupa solusi periodik jika nilai parameter sesuai persamaan (4.33) – (4.38) dengan parameter yang ada. Selain itu, dari hasil simulasi diperoleh bahwa sistem persamaan model robot bipedal stabil di tiga solusi periodik yaitu kurva berwarna biru adalah sudut lutut kanan, kurva berwarna merah adalah sudut pinggul, dan kurva berwarna hijau adalah sudut lutut kiri.   Kata kunci: Robot Bipedal, Osilator Rayleigh, Metode Keseimbangan Harmoni

Evolution of central pattern generators for the control of a five-link bipedal walking mechanism

Central pattern generators (CPGs), with a basis is neurophysiological studies, are a type of neural network for the generation of rhythmic motion. While CPGs are being increasingly used in robot control, most applications are hand-tuned for a specific task and it is acknowledged in the field that generic methods and design principles for creating individual networks for a given task are lacking. This study presents an approach where the connectivity and oscillatory parameters of a CPG network are determined by an evolutionary algorithm with fitness evaluations in a realistic simulation with accurate physics. We apply this technique to a five-link planar walking mechanism to demonstrate its feasibility and performance. In addition, to see whether results from simulation can be acceptably transferred to real robot hardware, the best evolved CPG network is also tested on a real mechanism. Our results also confirm that the biologically inspired CPG model is well suited for legged locomotion, since a diverse manifestation of networks have been observed to succeed in fitness simulations during evolution.Comment: 11 pages, 9 figures; substantial revision of content, organization, and quantitative result

On the Role of Sensory Feedbacks in Rowat–Selverston CPG to Improve Robot Legged Locomotion

This paper presents the use of Rowat and Selverston-type of central pattern generator (CPG) to control locomotion. It focuses on the role of afferent exteroceptive and proprioceptive signals in the dynamic phase synchronization in CPG legged robots. The sensori-motor neural network architecture is evaluated to control a two-joint planar robot leg that slips on a rail. Then, the closed loop between the CPG and the mechanical system allows to study the modulation of rhythmic patterns and the effect of the sensing loop via sensory neurons during the locomotion task. Firstly simulations show that the proposed architecture easily allows to modulate rhythmic patterns of the leg, and therefore the velocity of the robot. Secondly, simulations show that sensori-feedbacks from foot/ground contact of the leg make the hip velocity smoother and larger. The results show that the Rowat–Selverston-type CPG with sensory feedbacks is an effective choice for building adaptive neural CPGs for legged robots

Quadruped locomotion reference synthesis wıth central pattern generators tuned by evolutionary algorithms

With the recent advances in sensing, actuating and communication tecnologies and in theory for control and navigation; mobile robotic platforms are seen more promising than ever. This is so for many fields ranging from search and rescue in earthquake sites to military applications. Autonomous or teleoperated land vehicles make a major class of these mobile platforms. Legged robots, with their potential virtues in obstacle avoidance and cross-country capabilities stand out for applications on rugged terrain. In the nature, there are a lot of examples where four-legged anatomy embraces both speed and climbing characteristics. This thesis is on the locomotion reference generation of quadruped robots. Reference generation plays a vital role for the success of the locomotion controller. It involves the timing of the steps and the selection of various spatial parameters. The generated references should be suitable to be followed. They should not be over-demanding to cause the robot fall by loosing its balance. Nature tells that the pattern of the steps, that is, the gait, also changes with the speed of locomotion. A well-planned reference generation algorithm should take gait transitions into account. Central Pattern Generators (CPG) are biologically-inspired tools for legged-robot locomotion reference generation. They represent one of the main stream quadruped robot locomotion synthesis approaches, along with Zero Moment Point (ZMP) based techniques and trial–and–error methods. CPGs stand out with their natural convenience for gait transitions. This is so because of the stable limit cycle behavior inhertent in their structure. However, the parameter selection and tuning of this type of reference generators is difficult. Often, trial–and–error iterations are employed to obtain suitable parameters. The background of complicated dynamics and difficulties in reference generation makes automatic tuning of CPGs an interesting area of research. A natural command for a legged robot is the speed of its locomotion. When considered from kinematics point of view, there is no unique set of walking parameters which yield a given desired speed. However, some of the solutions can be more suitable for a stable walk, whereas others may lead to instability and cause robot to fall. This thesis proposes a quadruped gait tuning method based on evolutionary methods. A velocity command is given as the input to the system. A CPG based reference generation method is employed. 3D full-dynamics locomotion simulations with a 16-degrees-of-freedom (DOF) quadruped robot model are performed to assess the fitness of artificial populations. The fitness is measured by three different cost functions. The first cost function measures the amount of support the simulated quadruped receives from torsional virtual springs and dampers opposing the changes in body orientation, whereas the second one is a measure of energy efficiency in the locomotion. The third cost function is a combination of the firs two. Tuning results with the three cost functions are obtained and compared. Cross-over and mutation mechanisms generate new populations. Simulation results verify the merits of the proposed reference generation and tuning method