Yang Tianbo, Tong Yuchuang, Zhang Zhengtao
Institute of Automation, Chinese Academy of Sciences, Beijing 100089, China.
Biomimetics (Basel). 2025 Jan 6;10(1):30. doi: 10.3390/biomimetics10010030.
With advancements in bipedal locomotion for humanoid robots, a critical challenge lies in generating gaits that are bounded to ensure stable operation in complex environments. Traditional Model Predictive Control (MPC) methods based on Linear Inverted Pendulum (LIP) or Cart-Table (C-T) methods are straightforward and linear but inadequate for robots with flexible joints and linkages. To overcome this limitation, we propose a Flexible MPC (FMPC) framework that incorporates joint dynamics modeling and emphasizes bounded gait control to enable humanoid robots to achieve stable motion in various conditions. The FMPC is based on an enhanced flexible C-T model as the motion model, featuring an elastic layer and an auxiliary second center of mass (CoM) to simulate joint systems. The flexible C-T model's inversion derivation allows it to be effectively transformed into the predictive equation for the FMPC, therefore enriching its flexible dynamic behavior representation. We further use the Zero Moment Point (ZMP) velocity as a control variable and integrate multiple constraints that emphasize CoM constraint, embed explicit bounded constraint, and integrate ZMP constraint, therefore enabling the control of model flexibility and enhancement of stability. Since all the above constraints are shown to be linear in the control variables, a quadratic programming (QP) problem is established that guarantees that the CoM trajectory is bounded. Lastly, simulations validate the effectiveness of the proposed method, emphasizing its capacity to generate bounded CoM/ZMP trajectories across diverse conditions, underscoring its potential to enhance gait control. In addition, the validation of the simulation of real robot motion on the robots CASBOT and Openloong, in turn, demonstrates the effectiveness and robustness of our approach.
随着类人机器人双足运动技术的进步，一个关键挑战在于生成有界步态，以确保在复杂环境中稳定运行。基于线性倒立摆（LIP）或推车-桌子（C-T）方法的传统模型预测控制（MPC）方法简单且线性，但不适用于具有灵活关节和连杆的机器人。为克服这一局限性，我们提出了一种灵活MPC（FMPC）框架，该框架纳入了关节动力学建模，并强调有界步态控制，以使类人机器人能够在各种条件下实现稳定运动。FMPC基于增强的灵活C-T模型作为运动模型，其特点是有一个弹性层和一个辅助第二质心（CoM）来模拟关节系统。灵活C-T模型的逆推导使其能够有效地转化为FMPC的预测方程，从而丰富了其灵活动态行为表示。我们进一步将零力矩点（ZMP）速度用作控制变量，并整合多个约束，这些约束强调CoM约束、嵌入显式有界约束和整合ZMP约束，从而实现对模型灵活性的控制并增强稳定性。由于上述所有约束在控制变量中均显示为线性，因此建立了一个二次规划（QP）问题，以保证CoM轨迹是有界的。最后，仿真验证了所提方法的有效性，强调了其在各种条件下生成有界CoM/ZMP轨迹的能力，突出了其增强步态控制的潜力。此外，在机器人CASBOT和Openloong上对真实机器人运动的仿真验证，反过来证明了我们方法的有效性和鲁棒性。
