Nonlinear optimization of Step Duration and Step Location The modulation of step location and duration plays an important role in realizing robust bipedal walking. This paper formulates it as a nonlinear programming problem (NLP) and proposes a novel optimization approach to adjust step location and duration in real time. Based on state feedback, the Linear Inverted Pendulum dynamics is exploited to determine the optimal step parameters. Different from previous works, this work presents three main characteristics: i) the hyperbolic functions of step duration rather than the step duration itself are chosen to be optimization variables; ii) the approach can be switched from baseline twostepsprediction optimization to onestepprediction optimization through merely adding several equality constraints in problem formulation; iii) the approach can deal with relative step location tracking (velocity tracking) or absolute step location tracking (position tracking) via changing the reference step parameters. As a result, the first characteristic enables the NLP to be solved in a computationalefficient manner and the latter two endow the approach with versatility under different control modes. The effectiveness has been demonstrated by simulation experiments.

Normalized Neural Network for Energy Efficient Bipedal Walking Using Nonlinear Inverted Pendulum Model In this paper, we present a novel approach for bipedal walking pattern generation. The proposed method is designed based on 2D inverted pendulum model. All control variables are optimized for an energy efficient gait. To obviate the need of solving nonlinear dynamics online, a deep neural network is adopted for fast nonlinear mapping from desired states to control variables. Normalized dimensionless data is generated to train the neural network, therefore, the trained neural network can be applied to bipedal robots of any size, without any specific modification. The proposed method is later verified through numerical simulations. Simulation results demonstrated that the proposed approach can generate feasible walking motions, and regulate robotxe2x80x99s walking velocity successfully. Its disturbance rejection capability was also validated.