  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.
