Dynamics is the study of the torques required at each joint to cause the manipulator to move in a certain manner. It is also concerned with the way in which a manipulator moves when certain torques are applied to its joints. The serial chain nature of manipulators makes it easy to use simple methods in dynamic analysis.
There are two problems related to the dynamics of a manipulator: controlling the manipulator, and simulating the motion of the manipulator. In the first problem, we have a set of required positions for each link, and we want to calculate the required torques to be applied at each joint. This is called inverse dynamics. In the second problem, we are given a set of torques applied to each link, and we wish to calculate the new position and the velocities during the motion of each link. The latter is used to simulate a mathematical manipulator model before building the physical model, which makes it possible to update and modify the design without the cost of changing or replacing any physical parts.
The dynamics equations for any manipulator depend on the following parameters:
The dynamics model we are using to control the manipulator is in the form:
To simulate the motion of a manipulator we must use the same model we have used in controlling that manipulator. The model for simulation will be in the form:
The dynamics module is the most time consuming part among the manipulator's modules. That is because of the tremendous amount of calculation involved in the dynamics equations. This fact makes the dynamics module a good candidate for hardware implementation, to enhance the performance of the control and/or the simulation system.
There are some parallel algorithms to calculate the dynamics of a manipulator. One approach described in [37], is to use multiple microprocessor systems, where each one is assigned to a manipulator link. Using a method called branch-and-bound, a schedule of the subtasks of calculating the input torque for each link is obtained. The problem with this method is that the scheduling algorithm itself was the bottleneck, thus limiting the total performance. Several other approaches have been suggested [29, 30, 43] based on a multiprocessor controller, and pipelined architectures to speed the calculations. Hashimoto and Kimura [17] proposed a new algorithm called the resolved Newton-Euler algorithm based on a new description of the Newton-Euler formulation for manipulator dynamics. Another approach was proposed by Li, Hemami, and Sankar [34] to drive linearized dynamic models about a nominal trajectory for the manipulator using a straightforward Lagrangian formulation. An efficient structure for real-time computation of the manipulators dynamics was proposed by Izaguirre, Hashimoto, Paul and Hayward [20]. The fundamental characteristic of this structure is the division of the computation into a high-priority synchronous task and low-priority background tasks, possibly sharing the resources of a conventional computing unit based on commercial microprocessors.