Inverse kinematics along a geometric spline for a holonomic mobile manipulator

Kinematically, a mobile manipulator i.e. a robot arm mounted on the top of a mobile platform, is a concatenation of rigid body motions in SE(3), the Special Euclidean group and its subgroups. The formalism of matrix Lie groups is used to generate a smooth curve for the end-effector of the robot. In particular, different closed-form C² curves in SE(3) can be obtained from boundary data with the De Casteljau algorithm. Pseudoinversion techniques applied to the Jacobian of the kinematic chain allow then to transform the path of the end-effector into smooth joint space trajectories via the product of exponentials formula.