The task of motion planning is to generate a feasible trajectory
between an initial configuration qinit ∈ Cfree and a goal configuration
qgoal ∈ Cfree. Motion planning for modular robots with many
degrees of freedom and many kinematic constraints can be solved
using sampling-based methods. These methods solve the planning
problem by creating a roadmap of free configurations in the
configuration space C. Due to the high dimension of the configuration
space, which is equal to the DOFs of the robot, the space
cannot be represented as a grid and standard state-search techniques
cannot be applied. Instead, a roadmap is built by random
sampling of the configuration space. The sampled configurations
are classified as free (i.e., q ∈ Cfree) or non-free using collision
detection between the modules and the obstacles. The free samples
are stored in the roadmap, and close configurations are connected
by oriented edges using a local planner. The roadmap is
represented as a graph, in which a path between two nodes describes
a motion in the workspace. Sampling-based methods can find the motion of robots with many DOFs and arbitrary shape.
Moreover, the kinematic and dynamic constraints can be taken into
account by the methods [49].