This paper describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2D and 3D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g.,closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly-defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped's hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as "templates" from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2D and 3D biped walkers.

翻译：本文描述了一种从地形学角度出发,为发育不良的 2D 和 3D 双胞胎行走的行走步步步步器组建家庭,这些行走者受到结构不平等的限制、身体肉质学的限制(如闭路连接)和虚拟肉质限制(通过反馈控制实施的用户定义的限制)以及虚拟肉质限制(通过反馈控制实施的用户定义的限制)的制约。我们的方法在州-时间控制空间内构建了隐性定义的可行的定期行走步数,对双胞胎的混合轨迹进行了参数化参数。由于双胞胎的平衡配置往往属于这些马体,我们用平衡作为“板”来培养双胞胎家庭。“平衡”是建立幼崽家庭的可靠种子,在最优化框架内的可行轨迹上消除随机、不合适或生物激发的初步猜想。我们演示了数个2D 和 3D 双胞步行走者的方法。