Smaldone Filippo M, Scianca Nicola, Lanari Leonardo, Oriolo Giuseppe
Dipartimento di Ingegneria Informatica, Automatica e Gestionale, Sapienza University of Rome, Rome, Italy.
Front Robot AI. 2022 Aug 16;9:876613. doi: 10.3389/frobt.2022.876613. eCollection 2022.
We present a real time algorithm for humanoid 3D walking and/or running based on a Model Predictive Control (MPC) approach. The objective is to generate a stable gait that replicates a footstep plan as closely as possible, that is, a sequence of candidate footstep positions and orientations with associated timings. For each footstep, the plan also specifies an associated reference height for the Center of Mass (CoM) and whether the robot should reach the footstep by walking or running. The scheme makes use of the Variable-Height Inverted Pendulum (VH-IP) as a prediction model, generating in real time both a CoM trajectory and adapted footsteps. The VH-IP model relates the position of the CoM to that of the Zero Moment Point (ZMP); to avoid falling, the ZMP must be inside a properly defined support region (a 3D extension of the 2D support polygon) whenever the robot is in contact with the ground. The nonlinearity of the VH-IP is handled by splitting the gait generation into two consecutive stages, both requiring to solve a quadratic program. Thanks to a particular triangular structure of the VH-IP dynamics, the first stage deals with the vertical dynamics using the Ground Reaction Force (GRF) as a decision variable. Using the prediction given by the first stage, the horizontal dynamics become linear time-varying. During the flight phases, the VH-IP collapses to a free-falling mass model. The proposed formulation incorporates constraints in order to maintain physically meaningful values of the GRF, keep the ZMP in the support region during contact phases, and ensure that the adapted footsteps are kinematically realizable. Most importantly, a stability constraint is enforced on the time-varying horizontal dynamics to guarantee a bounded evolution of the CoM with respect to the ZMP. Furthermore, we show how to extend the technique in order to perform running on tilted surfaces. We also describe a simple technique that receives input high-level velocity commands and generates a footstep plan in the form required by the proposed MPC scheme. The algorithm is validated via dynamic simulations on the full-scale humanoid robot HRP-4, as well as experiments on the small-sized robot OP3.
我们提出了一种基于模型预测控制（MPC）方法的人形机器人三维行走和/或跑步实时算法。目标是生成一种稳定的步态，尽可能紧密地复制脚步计划，即一系列带有相关时间的候选脚步位置和方向。对于每一步，该计划还指定了质心（CoM）的相关参考高度以及机器人应通过行走还是跑步到达该脚步。该方案利用变高度倒立摆（VH-IP）作为预测模型，实时生成质心轨迹和适配的脚步。VH-IP模型将质心的位置与零力矩点（ZMP）的位置相关联；为避免跌倒，每当机器人与地面接触时，ZMP必须位于适当定义的支撑区域内（二维支撑多边形的三维扩展）。通过将步态生成分为两个连续阶段来处理VH-IP的非线性，这两个阶段都需要求解一个二次规划问题。由于VH-IP动力学的特殊三角结构，第一阶段使用地面反作用力（GRF）作为决策变量来处理垂直动力学。利用第一阶段给出的预测，水平动力学变为线性时变。在飞行阶段，VH-IP退化为自由落体质量模型。所提出的公式纳入了约束条件，以保持GRF的物理有意义的值，在接触阶段将ZMP保持在支撑区域内，并确保适配的脚步在运动学上是可实现的。最重要的是，对时变水平动力学施加稳定性约束，以保证质心相对于ZMP的有界演化。此外，我们展示了如何扩展该技术以在倾斜表面上运行。我们还描述了一种简单的技术，该技术接收输入的高级速度命令，并生成所提出的MPC方案所需形式的脚步计划。该算法通过在全尺寸人形机器人HRP-4上的动态模拟以及在小型机器人OP3上的实验进行了验证。
