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In this thesis, we will explore the minimum energy and time- optimal trajectory planning in periodic gaits of the quadrupedal walking machine. In general, the legged walking machines are more suitable than wheeled or tracked vehiclesto walk on a rough/soft terrain, and the energy efficiency and the speed are crucial issues for the researches of walking machines. Therefore, researches inthese areas would be significant and important. Firstly, we will present an efficient algorithm, the Compact QP method, to solve a constrained quadratic-optimization problem in order to make thiswalking machine walk with minimum energy consumption in real time. Then, a comparison of the proposed method with the traditional pseudo-inverse methodwill be given to show the superiority.Moreover, a minimum time algorithm will also be proposed and improved to implement the time-optimal path planning of the leg in the transfer phase. Furthermore, the derived results can be employedto the time- optimal trajectory planning of the whole quadrupedal walking machinein different periodic gaits. Simulation results show that the proposed methods are valid and efficient forthis walking machine.
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