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Hand synergies are goal-directed, combining muscle and kinematic activation, leading to a reduction of the dimensionality of the motor and sensory space [18]. In robotics, hand synergies have represented a highly effective solution for the fast and simplified design and control of artificial systems [19,20]. Under a kinematic point of view, hand synergies can be defined in terms of inter-joint covariation patterns, which were observed both in free hand motion [4] and object manipulation [21]. In [12], following the approach introduced in [4], we embedded synergy information in an a priori grasp set that we obtained using the PhaseSpace motion capture system (PhaseSpace Inc., San Leandro, CA, USA). [http://www.selleckchem.com/products/gsk1120212-jtp-74057.html Trametinib nmr] In particular, we asked experiment participants to grasp a set of imagined objects and collected [http://en.wikipedia.org/wiki/FKBPL FKBPL] a large number N of postures, into a matrix X��Rn��N. This information can be summarized in a covariance matrix Po��Rn��n, which is a symmetric matrix computed as Po=(X-x?)(X-x?)TN-1, where x? is a matrix n��N whose columns contain the mean values for each joint angle arranged in vector ��o��Rn. According to [16], the hand pose reconstruction can be obtained through the minimum variance estimation (MVE) technique as: x^=(Po-1+HTR-1H)-1(HTR-1y+Po-1��o) (2) where matrix Pp=(Po-1+HTR-1H)-1 is the a posteriori covariance matrix. Equation (2) can be rewritten as: x^=��o-PoHT(HPoHT+R)-1(H��o-y) (3) and the a posteriori covariance matrix becomes Pp=Po-PoHT(HPoHT+R)-1HPo. 2.1.2. Synergy-Based Optimal HPR System Design The a posteriori covariance matrix depends on the measurement matrix H and can be used as a measure of how much information an observable variable carries about unknown parameters. In [13,17], we explored the role of the measurement matrix H on the estimation procedure and obtained as a result the optimal placement of sensors for a sensing device in order to obtain the maximum amount of the information on the complete hand posture. In the ideal case of measures with no noise (R=0), the covariance matrix Pp becomes a zero matrix when H is full rank, which means that the measures contain complete information on the hand posture. However, in the case of noisy measures and/or when the number of measurements m is less than the hand [http://www.selleckchem.com/products/AZD2281(Olaparib).html Olaparib cell line] model DOFs n, the covariance matrix is not null. In these cases, we can consider the problem of finding the optimal matrix H* such that the hand posture information contained in it is maximized. Without loss of generality, we assume H to be full row rank and consider the problem of finding H��Rm��n, with m