Many animals generate propulsive forces by coordinating legs, which contact and push against the surroundings, with bending of the body, which can only indirectly influence these forces. Such body–leg coordination is not commonly employed in quadrupedal robotic systems. To elucidate the role of back bending during quadrupedal locomotion, we study a model system: the salamander, a sprawled-posture quadruped that uses lateral bending of the elongate back in conjunction with stepping of the limbs during locomotion. We develop a geometric approach that yields a low-dimensional representation of the body and limb contributions to the locomotor performance quantified by stride displacement. For systems where the damping forces dominate inertial forces, our approach offers insight into appropriate coordination patterns, and improves the computational efficiency of optimization techniques. In particular, we demonstrate effect of the lateral undulation coordinated with leg movement in the forward, rotational, and lateral directions of the robot motion. We validate the theoretical results using numerical simulations, and then successfully test these approaches using robophysical experiments on granular media, a model deformable, frictional substrate. Although our focus lies primarily on robotics, we also demonstrate that our tools can accurately predict optimal body bending of a living salamander Salamandra salamandra.

许多动物通过协调腿部产生推力，这些腿随着身体的弯曲接触并推向周围，这只能间接地影响这些力。这种四肢协调在四足机器人系统中并不常用。为了阐明四足运动中背部弯曲的作用，我们研究了一个模型系统：sal，一种四肢姿势的四足动物，在运动过程中结合了四肢的踩踏使用了细长的背部的侧向弯曲。我们开发了一种几何方法，可以通过步幅位移量化身体和四肢对运动表现的低维度表示。对于以阻尼力为主的惯性力的系统，我们的方法可以洞悉适当的协调模式，并提高了优化技术的计算效率。特别是，我们演示了在机器人运动的向前，旋转和横向方向上，横向起伏与腿部运动相协调的效果。我们使用数值模拟验证了理论结果，然后使用机器人物理实验在颗粒介质（可变形的摩擦基底）上成功地测试了这些方法。尽管我们的重点主要放在机器人上，但我们也证明了我们的工具可以准确地预测活sal的最佳身体弯曲 然后使用机器人物理实验在颗粒介质（可变形的摩擦基底）上成功地测试了这些方法。尽管我们的重点主要放在机器人上，但我们也证明了我们的工具可以准确地预测活sal的最佳身体弯曲 然后使用机器人物理实验在颗粒介质（可变形的摩擦基底）上成功地测试了这些方法。尽管我们的重点主要放在机器人上，但我们也证明了我们的工具可以准确地预测活sal的最佳身体弯曲Salamandra salamandra。