利用微分平坦性提升多输入系统的学习型控制效率
Exploiting Differential Flatness for Efficient Learning-based Model Predictive Control of Constrained Multi-Input Control Affine Systems
- 通过系统扩展与块对角代价设计，适配多输入非线性系统
- 仅需两次凸优化即满足约束并保证概率李雅普诺夫递减
- 仿真效率为高斯过程MPC的数倍，真实硬件表现优异
基于学习的控制技术利用历史轨迹数据来应对动态不确定性，但通常计算效率低，限制了实际应用。针对这一问题，本文提出一种利用微分平坦性的学习型控制器，该性质存在于许多机器人系统中。现有基于平坦性的研究要么忽略输入约束，要么仅适用于单输入系统，或针对特定平台定制。相比之下，本方法通过系统扩展和块对角代价结构，可控制通用的多输入、非线性仿射系统，并同时满足输入约束与半空间平坦状态约束。该方法仅需两次顺序凸优化即可保证概率李雅普诺夫递减。仿真结果表明，本方法性能与高斯过程模型预测控制相当，但效率高出数倍；在真实硬件实验中也实现了具有竞争力的跟踪性能。
原文摘要 · Abstract (English)
Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.
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