基于能量最小化的控制问题解流形学习
Learning Solution Manifolds for Control Problems via Energy Minimization
摘要：
各种控制任务，如逆运动学（IK），轨迹优化（TO），和模型预测控制（MPC）通常被制定为能量最小化问题。这类问题的数值解是公认的。然而，这些通常太慢而不能直接用于实时应用。另一种方法是在离线阶段学习控制问题的解流形。虽然这个蒸馏过程可以被平凡地制定为一个行为克隆（BC）的问题，在模仿学习设置，我们的实验突出了一些显着的缺点，由于不兼容的局部极小值，插值文物，和状态空间的覆盖不足。在本文中，我们提出了一种替代BC，是有效的和数值鲁棒性。我们制定的解决方案流形的学习作为一个最小化的控制目标集成在感兴趣的问题的空间的能量项。我们尽量减少这种能量积分与一种新的方法，结合蒙特卡洛启发的自适应采样策略的衍生物用于解决个别情况下的控制任务。我们评估了一系列复杂性不断增加的机器人控制问题的性能，并通过与传统方法（如行为克隆和数据集聚合（匕首））的比较，突出了其优点。
英文摘要：
A variety of control tasks such as inverse kinematics (IK), trajectory optimization (TO), and model predictive control (MPC) are commonly formulated as energy minimization problems. Numerical solutions to such problems are well-established. However, these are often too slow to be used directly in real-time applications. The alternative is to learn solution manifolds for control problems in an offline stage. Although this distillation process can be trivially formulated as a behavioral cloning (BC) problem in an imitation learning setting, our experiments highlight a number of significant shortcomings arising due to incompatible local minima, interpolation artifacts, and insufficient coverage of the state space. In this paper, we propose an alternative to BC that is efficient and numerically robust. We formulate the learning of solution manifolds as a minimization of the energy terms of a control objective integrated over the space of problems of interest. We minimize this energy integral with a novel method that combines Monte Carlo-inspired adaptive sampling strategies with the derivatives used to solve individual instances of the control task. We evaluate the performance of our formulation on a series of robotic control problems of increasing complexity, and we highlight its benefits through comparisons against traditional methods such as behavioral cloning and Dataset aggregation (Dagger).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
