Optimal control (OC) using inverse dynamics provides numerical benefits such as coarse optimization, cheaper computation of derivatives, and a high convergence rate. However, to take advantage of these benefits in model predictive control (MPC) for legged robots, it is crucial to handle efficiently its large number of equality constraints. To accomplish this, we first (i) propose a novel approach to handle equality constraints based on nullspace parametrization. Our approach balances optimality, and both dynamics and equality-constraint feasibility appropriately, which increases the basin of attraction to high-quality local minima. To do so, we (ii) modify our feasibility-driven search by incorporating a merit function. Furthermore, we introduce (iii) a condensed formulation of inverse dynamics that considers arbitrary actuator models. We also propose (iv) a novel MPC based on inverse dynamics within a perceptive locomotion framework. Finally, we present (v) a theoretical comparison of optimal control with forward and inverse dynamics and evaluate both numerically. Our approach enables the first application of inverse-dynamics MPC on hardware, resulting in state-of-the-art dynamic climbing on the ANYmal robot. We benchmark it over a wide range of robotics problems and generate agile and complex maneuvers. We show the computational reduction of our nullspace resolution and condensed formulation (up to 47.3%). We provide evidence of the benefits of our approach by solving coarse optimization problems with a high convergence rate (up to 10 Hz of discretization). Our algorithm is publicly available inside CROCODDYL.

翻译：利用逆动力学进行最优控制具有粗粒度优化、导数计算成本低及收敛速度快等数值优势。然而，为在腿式机器人的模型预测控制（MPC）中充分发挥这些优势，必须高效处理其大量等式约束。为此，我们首先（i）提出了一种基于零空间参数化的等式约束新处理方法。该方法通过引入价值函数（ii）改进可行性驱动搜索，在最优性、动力学可行性和等式约束可行性之间实现合理平衡，从而扩大高质量局部最优解的吸引域。同时，（iii）提出考虑任意执行器模型的逆动力学紧凑表达式。此外，（iv）在感知运动框架内设计了基于逆动力学的新型MPC算法。最后，（v）从理论上对比了基于前向动力学与逆动力学的最优控制方法，并进行了数值评估。本研究首次实现了逆动力学MPC的硬件部署，在ANYmal机器人上实现了当前最先进的动态攀爬性能。通过涵盖广泛机器人学问题的基准测试，生成了敏捷复杂的机动动作。实验表明，所提出的零空间分解与紧凑表达式可降低计算量（最高达47.3%），并支持高收敛速度（离散化频率达10 Hz）的粗粒度优化求解。相关算法已开源至CROCODDYL工具包。