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Title: A study of humanoid robot walking with variable step lengths in different pitch and roll inclinations
Authors: Yu, Hoi Fai
Degree: M.Phil.
Issue Date: 2015
Abstract: Extensive research works have been conducted on humanoid robot walking on horizontal plane in the last two decades. Not only horizontal plane, inclined plane also exists in our cities and natural environment. A number of studies on bipedal robot walking on an inclined plane have also been started recently. However, researches on bipedal robot walking with pitch and roll inclination were seldom reported. The mobility of bipedal robot is limited if it cannot achieve stable walking when encountering pitch and roll inclinations. This study aims to investigate stable humanoid robot walking considering pitch and roll inclinations, as well as variable step length.The development of an accurate mathematical model embracing the robot and the ground contact is the pre-requisite of effective simulation. The first goal is to establish an effective simulation environment for the interaction between robot and the ground. The forward kinematic model is established by Denavit-Hartenberg notation to check whether the feet of the robot contact the ground. In this study, humanoid robot kit KHR-3HV is purchased and modified for conducting simulations and experiments. A 3-D linear spring damper system is adopted as ground contact model to exhibit sticking and sliding effect between the feet and the ground. The second goal is to choose appropriate joint trajectory generator. The walking gait of robot is generated by Central Pattern Generator (CPG). The parameters of CPG model can be tuned through offline or online learning. Online learning requires installing a large number of sensors to evaluate the performance of given walking gait. The embedded controller cannot handle such a great number of sensors. Hence, offline optimization is adopted in this research. The optimization technique is chosen to be Self-Adaptive Differential Evolutionary algorithm (SaDE) which can self-tune the algorithm parameters and choose appropriate strategies. Walking gaits for 27 representative cases considering different combinations of pitch and roll inclinations as well as commanded step length are searched by SaDE. It is time consuming to optimize walking gaits for every combination of pitch and roll inclinations. The final goal is to choose an appropriate method to learn the relationship between 1) pitch, roll inclination and step length and 2) CPG model parameters. In this study, Network-based Fuzzy Inference System (NFIS) is adopted due to its fast learning speed. Since the size of training data is not large, solely consequent parameters are adjusted by least square regression for learning the above-mentioned relationship. To provide more training data for learning, walking gaits considering different combinations of pitch and roll inclinations as well as commanded step length are obtained through interpolation. Ultimately, 125 sets of training data are provided for training. There are 8 NFIS designed for 8 CPG model parameters. The inputs of NFIS are 1) pitch inclination (θpitch), 2) roll inclination (θroll) and 3) commanded step length while the output of NFIS is CPG model parameter.
Fine-tuned CPG model parameters are obtained from NFIS learning. Based on these parameters, CPG model can generate walking gait with more accurate step length for KHR-3HV. Simulation results confirm that over 60% of the 125 cases give a smaller error in step length when compared to the training sets. Then, 10 cases with arbitrary generated pitch and roll inclinations and commanded step length are tested. Here, the robot is commanded to walk two steps to evaluate its performance in terms of kinematic and dynamic aspects of the resulting walking gaits generated by CPG model and NFIS. Simulation results show that the maximum step length error is about 0.003m. From these ten cases, dynamic aspects of the resulting walking gaits are satisfactory. In some cases,ZMPx and ZMPy are observed to lie outside the area of support polygon after the landing of swing foot sole. However, they re-enter the area of support polygon in a short time. Also, orientation errors are observed since sliding is solely resisted by the ground without any external active control. The maximum orientation error is about 2.6° To further investigate the effectiveness of the proposed method, challenges of simulations are enhanced by 1) increasing number of steps, 2) considering random input errors and 3) changing step lengths in the trajectory. In Case 1, the test bed is commanded to walk ten steps with constant step length. In Case 2, the test bed walks ten steps again but adding random errors to the input 1 (θpitch) and input 2 (θroll) of NFIS simultaneously. In Case 3, the test bed walks ten steps with various step lengths and random errors are added to the input 1 (θpitch) and input 2 (θroll). These three cases have been studied in simulations and experiments. The main purpose is to evaluate the dynamic aspect of the resulting walking gaits. Both simulation and experimental results show that the robot can walk stably on different terrains. In experiments, backlash of R/C servo leads to slight oscillation in frontal plane. However, without feedback, backlash cannot be compensated. A comparison test has also been conducted to verify that asymmetric frontal plane motion is necessary to guarantee the dynamic stability in case of roll inclination.
Subjects: Robots
Hong Kong Polytechnic University -- Dissertations
Pages: xxiv, 240 leaves : illustrations ; 30 cm
Appears in Collections:Thesis

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