Online footstep planning is essential for bipedal walking robots, allowing them to walk in the presence of disturbances and sensory noise. Most of the literature on the topic has focused on optimizing the footstep placement while keeping the step timing constant. In this work, we introduce a footstep planner capable of optimizing footstep placement and step time online. The proposed planner, consisting of an Interior Point Optimizer (IPOPT) and an optimizer based on Augmented Lagrangian (AL) method with analytical gradient descent, solves the full dynamics of the Linear Inverted Pendulum (LIP) model in real time to optimize for footstep location as well as step timing at the rate of 200~Hz. We show that such asynchronous real-time optimization with the AL method (ARTO-AL) provides the required robustness and speed for successful online footstep planning. Furthermore, ARTO-AL can be extended to plan footsteps in 3D, allowing terrain-aware footstep planning on uneven terrains. Compared to an algorithm with no footstep time adaptation, our proposed ARTO-AL demonstrates increased stability in simulated walking experiments as it can resist pushes on flat ground and on a $10^{\circ}$ ramp up to 120 N and 100 N respectively. For the video, see https://youtu.be/ABdnvPqCUu4. For code, see https://github.com/WangKeAlchemist/ARTO-AL/tree/master.

翻译：在线落脚点规划对双足步行机器人至关重要，使其能在存在干扰和传感器噪声的环境中行走。现有文献大多关注在保持步态时序恒定前提下优化落脚点位置。本文提出了一种能够在线优化落脚点位置和步态时序的规划器。该规划器由内点优化器（IPOPT）和基于增广拉格朗日（AL）方法（含解析梯度下降）的优化器组成，可实时求解线性倒立摆（LIP）模型的完整动力学方程，以200赫兹的频率优化落脚点位置和步态时序。我们证明，这种基于AL方法的异步实时优化（ARTO-AL）具有在线落脚点规划所需的鲁棒性和速度。此外，ARTO-AL可扩展至三维落脚点规划，支持在非平坦地形上实现地形感知的落脚点规划。与无步态时序自适应算法相比，我们提出的ARTO-AL在仿真行走实验中表现出更强的稳定性，在平坦地面和10度斜坡上可分别抵抗高达120牛和100牛的推力。视频见https://youtu.be/ABdnvPqCUu4，代码见https://github.com/WangKeAlchemist/ARTO-AL/tree/master。