Planning multicontact motions in a receding horizon fashion requires a value function to guide the planning with respect to the future, e.g., building momentum to traverse large obstacles. Traditionally, the value function is approximated by computing trajectories in a prediction horizon (never executed) that foresees the future beyond the execution horizon. However, given the nonconvex dynamics of multicontact motions, this approach is computationally expensive. To enable online receding horizon planning (RHP) of multicontact motions, we find efficient approximations of the value function. Specifically, we propose a trajectory-based and a learning-based approach. In the former, namely RHP with multiple levels of model fidelity, we approximate the value function by computing the prediction horizon with a convex relaxed model. In the latter, namely locally guided RHP, we learn an oracle to predict local objectives for locomotion tasks, and we use these local objectives to construct local value functions for guiding a short-horizon RHP. We evaluate both approaches in simulation by planning centroidal trajectories of a humanoid robot walking on moderate slopes, and on large slopes where the robot cannot maintain static balance. Our results show that locally guided RHP achieves the best computation efficiency (95%–98.6% cycles converge online). This computation advantage enables us to demonstrate online RHP of our real-world humanoid robot Talos walking in dynamic environments that change on-the-fly.

中文翻译：

---

通过价值函数逼近的在线多接触后退地平线规划

以地平线后退的方式规划多接触运动需要一个价值函数来指导未来的规划，例如，建立穿过大型障碍物的动力。传统上，价值函数是通过计算预测范围（从未执行）中的轨迹来近似的，该预测范围预见了执行范围之外的未来。然而，考虑到多接触运动的非凸动力学，这种方法的计算成本很高。为了实现多接触运动的在线后退地平线规划（RHP），我们找到了价值函数的有效近似。具体来说，我们提出了一种基于轨迹和基于学习的方法。在前者，即具有多个模型保真度级别的 RHP 中，我们通过使用凸松弛模型计算预测范围来近似价值函数。在后者，即局部引导 RHP 中，我们学习预言机来预测运动任务的局部目标，并使用这些局部目标构建局部价值函数来指导短时程 RHP。我们通过规划人形机器人在中等坡度和机器人无法保持静态平衡的大坡度上行走的质心轨迹来评估模拟中的两种方法。我们的结果表明，本地引导的 RHP 实现了最佳计算效率（95%–98.6% 的循环在线收敛）。这种计算优势使我们能够演示现实世界中的人形机器人 Talos 在动态变化的动态环境中行走的在线 RHP。