346 A New Computational Structure For Real - Time Dynamics

We present an efficient structure for the computation of robot dynamics in real time. 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. The background tasks compute the inertial and gravitational coefficients as well as the forces due to the velocities of the joints. In each control sample period, the high-priority synchronous task computes the product of the inertial coefficients by the accelerations of the joints and performs the summation of the torques due to the velocities and gravitational forces. Kircanski et al. (1986) have shown that the bandwidth of the variation of joint angles and of their velocities is an order of magnitude less than the variation of the joint accelerations. This result agrees with the experiments that we have carried out using a PUMA 260 robot. Two main strategies contribute to reduce the computational burden associated with the evaluation of the dynamic equations. The first involves the use of efficient algorithms for the evaluation of the equations. The second is aimed at reducing the number of dynamic parameters by identifying beforehand the linear dependencies among these parameters, as well as carrying out a significance analysis of the parameters’ contribution to the final joint torques. We selected an iterative procedure for the computation of the inertial and gravitational coefficients (Featherstone 1984; Renaud 1985; Izaguirre and Paul 1986), and a recursive iteration for the computation of the velocity torques (Khalil et al. 1986). In our experiments with a PUMA 260, we obtained a set of 52 linearly independent parameters from an initial set of 78 parameters. Identification of the parameters revealed only 23 parameters to be significant. These reductions permit the calculation of the inertias and gravitational coefficients, for the PUMA 260 without load, with 98 multiplications and 70 additions and calculation of the velacity torques with 140 multiplications and 110 additions. In the case of an arbitrary load at the end effector, calculation of the inertias and gravitational coefficients requires 190 multiplications and 150 additions and that of the velocity torques, 200 multiplications and 170 additions. Velocity torques, inertial coefficients, and gravitational coefficients can be computed in the background in 20 ms using an Intel 8087 microprocessor. The synchronous task requires only six multiplications and six additions per joint. The actual code used to evaluate this dynamic model is entirely computer generated from experimental data, requiring no other manual intervention than performing a campaign of