How can I compute expression with an integral?

Hi,

I am trying to estimate the contact force at the end-effector of a robotic manipulator which I'm trying to do with the so called residual method. I'm struggling however to compute the residual which is defined in an analytic expression as:

With 'r(t)' the residual, 'K_i' a constant diagonal gain matrix, M(q) the mass matrix, \tau the control inputs, C^T(q,\dot{q}) the Coriolis matrix, g(q) the gravity vector and q and \dot{q} the joint position and velocities respectively.

See also: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6942848&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6942848

The problem is the 'r(t)' within the integral. Is there any way to compute this?

Thanks in advance!

Fransis

Answer 1

[Roger Stafford]

If the derivative with respect to t is taken of your equation, the result is a differential equation in the dependent variable r and independent variable t. You can solve it using 'ode45' or some other ode function. Solving the differential equation takes the place of performing the integration. Just make sure your initial value of r is correct.