Novel design algorithm for low complexity programmable FIR filters based on extended double base number system. IEEE transactions on circuits and systems I : regular papers, 62(1), 224-233.
Stable walking in real-world environments is a challenging task for humanoid robots, especially when considering the dynamic disturbances, e.g., caused by external perturbations that may be encountered during locomotion. The varying nature of disturbance necessitates high adaptability.In this paper, we propose an enhanced Nonlinear Model Predictive Control (NMPC) approach for robust and adaptable walking -we term it versatile locomotion, by limiting both the Center of Pressure (CoP) and Divergent Component of Motion (DCM) movements. Due to utilization of the Nonlinear Inverted Pendulum plus Flywheel model, the robot is endowed with the capabilities of CoP manipulation (if equipped with finitesized feet), step location adjustment, upper body rotation, and vertical height variation. Considering the feasibility constraints, especially the usage of relaxed CoP constraints, the NMPC scheme is established as a Quadratically Constrained Quadratic Programming problem, which is solved efficiently by Sequential Quadratic Programming with enhanced solvability. Simulation experiments demonstrate the effectiveness of our method to recruit optimal hybrid strategies in order to realize versatile locomotion, for the robot with finite-sized or point feet.
Energy consumption for bipedal walking plays a central role for a humanoid robot with limited battery capacity. Studies have revealed that exploiting the allowable Zero Moment Point region (AZR) and Center of Mass (CoM) height variation (CoMHV) are strategies capable of improving energy performance. In general, energetic cost is evaluated by integrating the electric power of multi joints. However, this Joint-Power-based Index requires computing joint torques and velocities in advance, which usually requires time-consuming iterative procedures, especially for multi-joints robots. In this work, we propose a CoM-Acceleration-based Optimal Index (CAOI) to synthesize an energetically efficient CoM trajectory. The proposed method is based on the Linear Inverted Pendulum Model, whose energetic cost can be easily measured by the input energy required for driving the point mass to track a reference trajectory. We characterize the CoM motion for a single walking cycle and define its energetic cost as Unit Energy Consumption. Based on the CAOI, an analytic solution for CoM trajectory generation is provided. Hardware experiments demonstrated the computational efficiency of the proposed approach and the energetic benefits of exploiting AZR and CoMHV strategies.
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