In the final chapter we focus on motion planning and control of wheeled mobile robots that move without skidding on hard flat surfaces, such as this differential drive robot, which moves by independently controlling the rotation of two conventional wheels, and this omnidirectional mobile robot, which moves by independently controlling the rotation of mecanum wheels, which allow sideways slipping.

In all cases, we assume that we control wheel velocities, not torques, so we have a kinematic model mapping wheel speeds to the chassis velocity. The planar configuration of the robot chassis is written T_sb, an element of SE(2), or simply as the vector q equal to (phi, x, y), where phi is the heading angle of the chassis and (x,y) is the position of a reference point on the chassis. The velocity of the chassis is written either as the planar twist V_b, expressed in the body frame {b}, or as the time derivative q-dot. For a nonholonomic mobile robot, like the differential drive, the space of feasible chassis velocities is only 2-dimensional, because the robot cannot slide sideways. For an omnidirectional robot, the chassis can move in any direction in its 3-dimensional velocity space.

This chapter addresses the following issues for omnidirectional and nonholonomic wheeled robots:

Kinematic modeling for several different types of wheeled mobile robot. Motion planning for wheeled mobile robots. Feedback control to stabilize motion plans. Odometry, to estimate the configuration of the chassis based on data from the wheel encoders. And mobile manipulation, where the wheeled mobile base is equipped with a manipulator. In particular, we derive the Jacobian mapping wheel and joint velocities to the end-effector twist, and we use this to develop a coordinated controller for the mobile base and robot arm.

In the next video we begin our study with omnidirectional wheeled mobile robots.