Tag Archives: Kinematics

A new mathematical formulation of manipulator motion that simplifies dynamics and kinematics

Labbé, M. & Michaud, F., Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework, The International Journal of Robotics Research First Published May 20, 2018 DOI: 10.1177/0278364918772893.

This paper presents a novel unified theoretical framework for differential kinematics and dynamics for the optimization of complex robot motion. By introducing an 18×18 comprehensive motion transformation matrix, the forward differential kinematics and dynamics, including velocity and acceleration, can be written in a simple chain product similar to an ordinary rotational matrix. This formulation enables the analytical computation of derivatives of various physical quantities (e.g. link velocities, link accelerations, or joint torques) with respect to joint coordinates, velocities and accelerations for a robot trajectory in an efficient manner (O(NJ), where NJ is the number of the robot’s degree of freedom), which is useful for motion optimization. Practical implementation of gradient computation is demonstrated together with simulation results of robot motion optimization to validate the effectiveness of the proposed framework.

A nice review of the problem of kinematic modeling of wheeled mobile robots and a new approach that delays the use of coordinate frames

Alonzo Kelly and Neal Seegmiller, 2015, Recursive kinematic propagation for wheeled mobile robots, The International Journal of Robotics Research, 34: 288-313, DOI: 10.1177/0278364914551773.

The problem of wheeled mobile robot kinematics is formulated using the transport theorem of vector algebra. Doing so postpones the introduction of coordinates until after the expressions for the relevant Jacobians have been derived. This approach simplifies the derivation while also providing the solution to the general case in 3D, including motion over rolling terrain. Angular velocity remains explicit rather than encoded as the time derivative of a rotation matrix. The equations are derived and can be implemented recursively using a single equation that applies to all cases. Acceleration kinematics are uniquely derivable in reasonable effort. The recursive formulation also leads to efficient computer implementations that reflect the modularity of real mechanisms.