## 1 Introduction  
Investigations on human motor tasks is a wide and interdisciplinary field of research with application in human factors, human-computer-interface, robotics, and biomechanics for rehabilitation, to mention a few. The accuracy of individuals in following the nominal trajectory aiming at reducing the distance between the actual position with the planned nominal one is of great interest in many fields. In a work environment, precision of a worker in reaching a target area for grasping or releasing an object, for manual assembly activities or in maintenance tasks, need to be assessed for optimizing manual task allocation. Measuring the accuracy in following a trajectory is crucial also in biomechanical applications to assess, for example, the effectiveness of the rehabilitation programs. Modeling human motor tasks generally refers to classical studies most of them considering the well-known Fitts' law [1]. Some authors improved the findings of the Fitts' experience by investigating its applicability in control theory [2; 3; 4] or in estimating psychomotor movement delays [5; 6] by computer modeling of the physical environment [7] as well as by virtual reality devices [8]. In the [PERSON] experience, the motor task of human subjects consisted of a reaching task of a target of width \(W\) from an initial starting point to a final one following a trajectory of length \(A\): a short trajectory with a wide target width was significant of an easy reaching task; on the contrary, meeting low target width following a long trajectory was representative of a difficult task. The basic idea of the [PERSON] law consists of expressing the movement time by the index of performance (IP), representing the amount of information processed in a unit time (bits/s), and the information content of the task (ID), characterizing the difficulty in the task execution (bit). Consistently, for modeling the movement time (MT) of a subject in a reaching motor task, the [PERSON] law was formulated as:  
\[\text{MT}\ =\ \frac{\text{ID}}{\text{IP}} \tag{1}\]  
Many formulations of ID have been tested [1; 9; 10]. [PERSON] suggested and proved by experiments that the ID in a reaching task of length A with target width W can be expressed by: \(\text{ID}\ =\ \log_{2}\frac{2*\text{A}}{\text{W}}\). Other studies suggested adjustments to the [PERSON] ID formulation by proposing \(\text{ID}\ =\ \log_{2}\left(\frac{\text{A}}{\text{W}}+\text{c}\right)\) with c = 0.5;1 according to the experiments carried out. In [10], a literature review of the best fitting of different ID formulations with experimental results is provided. The [PERSON] law was derived by analogy with the Shannon theorem n\({}^{\circ}\) 17 [11], theorized within the information-communication theory. The theorem expresses the effective information capacity C (bits/s) of a communication channel of bandwidth B (1/s) as:  
\[\text{C}\ =\ \text{B}*\log_{2}\left(\frac{\text{S}+\text{N}}{\text{N}}\right) \tag{2}\]  
where S is the signal power transmitted by the channel and perturbed by a white noise of power N; N represents the uncertainty induced in the transmission of the signal that limits the information capacity of the channel. In the analogy proposed by [PERSON], the channel capacity C is associated with the movement time in a reaching motor task while the bandwidth B corresponds to the information processing rate and the power of the signal S represents the length of the trajectory followed. Finally, the noise N corresponds to the tolerance in getting the target in the motor task, i.e., the target's amplitude. In a perfect analogy, the motor task ID of the [PERSON] experience would be expressed as: \(\log_{2}\frac{\text{A}+\text{W}}{\text{W}}\). In [12], it is stated that this perfect analogy in the ID calculation leads to a model that better fits empirical data.