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	   	 Footstep planning on the 3D fieldThis paper proposes a model-based 3D footstep planning method. A discrete-time kinematic model, in which vertical motions are independent of horizontal motions, describes the biped walking of the humanoid robot. The 3D field environment is represented by geographical features divided into the meshes, determined from measurements obtained by a sensor, where the inclinations in each mesh are assumed. The optimal plan is obtained by solving a constrained optimization problem based on the foot placements of the model. A goal-tracking evaluation of the problem on horizontal foot placements is carried out to reach the goal, while vertical motions are adopted to meet constraints consisting of the foot workspace and contact with the 3D field surface. A quadratic programming method is implemented to solve the problem based on the humanoid robot NAO in real time.    	

Model-Based Footstep Planning Method for Biped Walking on 3D Field