Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific, interpretable low-dimensional dynamics directly from data. We propose a methodology that combines a linear autoencoder with symbolic regression to derive such models. The linear autoencoder provides a consistent latent embedding for configurations, velocities, accelerations, and inputs, enabling the sparse identification of nonlinear dynamics (SINDy) to operate in a compact, physics-aligned space. A multi-phase, hybrid-aware training scheme ensures coherent latent coordinates across contact transitions. We focus our validation on quadruped jumping-a representative, challenging, yet contained scenario in which a principled template model is especially valuable. The resulting symbolic dynamics outperform the state-of-the-art handcrafted actuated spring-loaded inverted pendulum (aSLIP) baseline in simulation and hardware across multiple robots and jumping modalities.

翻译：降阶模型是四足机器人运动规划与控制的核心，然而现有模板通常针对特定运动模态手工设计。这促使需要能够直接从数据中提取任务特定、可解释的低维动力学的自动化方法。我们提出一种结合线性自编码器与符号回归来推导此类模型的方法论。线性自编码器为构型、速度、加速度及输入提供一致的潜在嵌入，使非线性动力学稀疏辨识（SINDy）能够在紧凑、物理对齐的空间中运行。一种多阶段、混合感知的训练方案确保了接触转换间潜在坐标的连贯性。我们将验证重点放在四足跳跃——这一具有代表性、挑战性且边界清晰的场景上，其中基于原理的模板模型尤其有价值。所得符号动力学在仿真与硬件实验中，针对多种机器人与跳跃模态，均优于当前最优的手工设计驱动弹簧负载倒立摆（aSLIP）基线模型。