It is often overlooked by roboticists when designing locomotion controllers for their legged machines, that energy consumption plays an important role in selecting the best gaits for locomotion at high speeds or over long distances. The purpose of this study is to examine four similar asymmetrical quadrupedal gaits that are frequently observed in legged animals in nature. To understand how a specific footfall pattern will change the energetics of a legged system, we first developed a full body model of a quadrupedal robot called A1. And for each gait we created a hybrid system with desired footfall sequence and rigid impacts. In order to find the most energy efficient gait, we used optimal control methods to formulate the problem as a trajectory optimization problem with proper constraints and objective function. This problem was implemented and solved in a nonlinear programming framework called FROST. Based on the optimized trajectories for each gait, we investigated the values of cost of transport and the work done by all joints. Moreover, we analyzed the exchange of angular momentum in different components of the system during the whole stride cycle. According to the simulation results, bounding with two flight phases is likely to be the most energy efficient gait for A1 across a wide range of speed.

翻译：在为其足式机器设计运动控制器时，机器人学家常忽略一个关键因素：能量消耗对选择高速或长距离运动最佳步态的重要影响。本研究旨在分析自然界四足动物中常见的四种相似非对称步态。为理解特定足底接触模式如何改变足式系统的能量特性，我们首先构建了名为A1的四足机器人全身模型。针对每种步态，我们建立了具有预期足底触地序列和刚性碰撞的混合系统。为寻找最优能效步态，我们采用最优控制方法，将问题转化为带适当约束与目标函数的轨迹优化问题，并在名为FROST的非线性规划框架中实现求解。基于各步态的优化轨迹，我们分析了运输成本值与所有关节做功量，并进一步研究了整个步态周期内系统不同组件的角动量交换。仿真结果表明，双腾空相跳跃步态很可能是A1在宽速度范围内的最优能效步态。