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In this paper, we discuss the issue of the optimal trajectory design for the purpose of identification of the inertial and load parameters of a robot. Two dynamical models have been introduced: differential and integral; both of them can be used to estimate the robot dynamic parameters in which they appear to be linear. ; Functions associated with the parameters are highly non-linear which in general involve joint positions, velocities and accelerations. A standard sequential least-squares technique can be used to estimate the unknown parameters. This method requires an information matrix which has to be inverted. ; For particular joint signals this matrix is singular. In this paper, we propose to optimize the condition number of this matrix in both formulations: differential and integral. This work illustrates the difficulty of maintaining persistent excitation during the experimental identification of robot and load dynamic parameters.