Mobile robotic devices and systems

A system for controlling a mobile robot, comprising:

• at least one processing unit configured to control positioning and/or rotation of each a plurality of contact elements, the plurality of contact elements including a first contact element and a second contact element, the at least one processing unit configured to, collectively:
• encode hybrid dynamic modes of contact statuses for each of the plurality of contact elements;
• determine at least one specific time at which guard conditions are met, resulting in transitions between discrete mode encodings;
• construct dynamical models for hybrid dynamic modes of the system at runtime by procedurally integrating appropriate equations of motion and kinodynamic constraints into forward dynamics;
• simulate possible future robot hybrid trajectories;
• plan a trajectory based on the hybrid dynamical models;
• and
• control the robot to follow a planned trajectory by causing at least the first contact element to spatially move relative to the second contact element based on the trajectory.

A method for controlling a robot, including a hybrid dynamical simulation procedure, comprising:

• a. receiving inputs defining a robot hybrid state at time t, robot physical parameters, an aggregate effect of generalized forces and external physical forces acting on the robot at time t, a stepsize (dt), and a map of an environment surrounding the robot, the robot hybrid state at time t comprising a discrete mode at time t and a continuous state at time t, the map comprising geometric structures and mechanical properties of the environment;
• b. utilizing inputs to construct equations of motion at runtime for the robot hybrid dynamics;
• c. numerically integrating the equations of motion (“flow”) within the discrete robot mode at time t to obtain a continuous robot state at a subsequent timestep:
• t+dt;
• and
• d. determining if a discrete mode transition (“jump”) occurred between time t and t+dt by checking for guard conditions occurring between the continuous robot state at time t and the continuous robot state at time t+dt.