Thanks to recent advancements in accelerating non-linear model predictive control (NMPC), it is now feasible to deploy whole-body NMPC at real-time rates for humanoid robots. However, enforcing inequality constraints in real time for such high-dimensional systems remains challenging due to the need for additional iterations. This paper presents an implementation of whole-body NMPC for legged robots that provides low-accuracy solutions to NMPC with general equality and inequality constraints. Instead of aiming for highly accurate optimal solutions, we leverage the alternating direction method of multipliers to rapidly provide low-accuracy solutions to quadratic programming subproblems. Our extensive simulation results indicate that real robots often cannot benefit from highly accurate solutions due to dynamics discretization errors, inertial modeling errors and delays. We incorporate control barrier functions (CBFs) at the initial timestep of the NMPC for the self-collision constraints, resulting in up to a 26-fold reduction in the number of self-collisions without adding computational burden. The controller is reliably deployed on hardware at 90 Hz for a problem involving 32 timesteps, 2004 variables, and 3768 constraints. The NMPC delivers sufficiently accurate solutions, enabling the MIT Humanoid to plan complex crossed-leg and arm motions that enhance stability when walking and recovering from significant disturbances.

翻译：得益于非线性模型预测控制加速技术的最新进展，如今已能够以实时速率为人形机器人部署全身NMPC。然而，由于需要额外迭代，为此类高维系统实时实施不等式约束仍然具有挑战性。本文提出了一种面向足式机器人的全身NMPC实现方案，该方案为具有通用等式与不等式约束的NMPC提供低精度解。我们不再追求高精度最优解，而是利用交替方向乘子法为二次规划子问题快速提供低精度解。大量仿真结果表明，由于动力学离散化误差、惯性建模误差及延迟等因素，实际机器人往往无法从高精度解中获益。我们在NMPC的初始时间步引入控制屏障函数来处理自碰撞约束，在不增加计算负担的情况下将自碰撞次数降低达26倍。该控制器以90Hz频率在硬件上稳定运行，可处理包含32个时间步、2004个变量和3768个约束的问题。该NMPC能提供足够精确的解，使MIT人形机器人能够规划复杂的交叉腿部和手臂运动，从而在行走及从显著扰动中恢复时增强稳定性。