Locomotion gaits are fundamental for control of soft terrestrial robots. However, synthesis of these gaits is challenging due to modeling of robot-environment interaction and lack of a mathematical framework. This work presents an environment-centric, data-driven and fault-tolerant probabilistic Model-Free Control (pMFC) framework that allows for soft multi-limb robots to learn from their environment and synthesize diverse sets of locomotion gaits for realizing open-loop control. Here, discretization of factors dominating robot-environment interactions enables an environment-specific graphical representation where the edges encode experimental locomotion data corresponding to the robot motion primitives. In this graph, locomotion gaits are defined as simple cycles that are transformation invariant, i.e., the locomotion is independent of the starting vertex of these periodic cycles. Gait synthesis, the problem of finding optimal locomotion gaits for a given substrate, is formulated as Binary Integer Linear Programming (BILP) problems with a linearized cost function, linear constraints, and iterative simple cycle detection. Experimentally, gaits are synthesized for varying robot-environment interactions. Variables include robot morphology - three-limb and four-limb robots, TerreSoRo-III and TerreSoRo-IV; substrate - rubber mat, whiteboard and carpet; and actuator functionality - simulated loss of robot limb actuation. On an average, gait synthesis improves the translation and rotation speeds by 82% and 97% respectively. The results highlight that data-driven methods are vital to soft robot locomotion control due to the significant influence of unexpected asymmetries in the system and the dependence of optimal gait sequences on the experimental robot-environment interaction.

翻译：运动步态对于地面软体机器人的控制至关重要。然而，由于机器人-环境相互作用的建模困难以及缺乏数学框架，这些步态的合成极具挑战性。本研究提出了一种以环境为中心、数据驱动且具有容错性的概率无模型控制（pMFC）框架，使多肢体软体机器人能够从环境中学习，并为实现开环控制合成多样化的运动步态。在该框架中，主导机器人-环境相互作用的因素的离散化，使得能够构建一种环境特定的图形表示，其中边的权重编码了与机器人运动基元相对应的实验运动数据。在此图中，运动步态被定义为变换不变的简单循环，即运动与该循环的起始顶点无关。步态合成，即针对给定基底寻找最优运动步态的问题，被形式化为具有线性化成本函数、线性约束和迭代简单循环检测的二进制整数线性规划（BILP）问题。实验针对不同的机器人-环境相互作用合成了步态。变量包括：机器人形态（三肢机器人TerreSoRo-III和四肢机器人TerreSoRo-IV）、基底（橡胶垫、白板、地毯）以及执行器功能（模拟机器人肢体驱动功能丧失）。平均而言，步态合成使平移速度和旋转速度分别提高了82%和97%。结果表明，由于系统中意外不对称性的显著影响以及最优步态序列对实验性机器人-环境相互作用的依赖性，数据驱动方法对于软体机器人运动控制至关重要。