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.

翻译：基于学习的控制技术利用历史轨迹数据对具有不确定动态的系统进行控制。然而，此类控制器通常计算效率低下，限制了其实用性。为解决这一局限，我们提出一种利用微分平坦性（许多机器人系统普遍具有的特性）的基于学习的控制器。现有关于利用平坦性实现学习控制的研究存在局限性：要么（i）忽略输入约束，（ii）仅适用于单输入系统，或（iii）针对特定平台定制。相比之下，我们的方法采用系统扩展与块对角代价函数形式，可控制通用多输入非线性仿射系统。此外，该方法满足输入与半空间平坦状态约束，且仅通过两次序列凸优化即可保证概率李雅普诺夫递减。仿真实验表明，我们的方法性能与高斯过程模型预测控制器相当，但计算效率提升数倍；实际硬件实验也验证了其竞争性跟踪能力。