ANALYSIS OF KINEMATIC INVARIANCES OF MULTIJOINT REACHING MOVEMENT

There is a no unique relationship between the trajectory of the hand, represented in cartesian or extrinsic space, and its trajectory in joi nt angle or intrinsic space in the general condition of joint redundan cy. The goal of this work is to analyze the relation between planning the trajectory of a multijoint movement in these two coordinate system s. We show that the cartesian trajectory can be planned based on the t ask parameters (target coordinates, etc.) prior to and independently o f angular trajectories. Angular time profiles are calculated from the cartesian trajectory to serve as a basis for muscle control commands. A unified differential equation that allows planning trajectories in c artesian and angular spaces simultaneously is proposed. Due to joint r edundancy, each cartesian trajectory corresponds to a family of angula r trajectories which can account for the substantial variability of th e latter. A set of strategies for multijoint motor control following f rom this model is considered; one of them coincides with the frog wipi ng reflex model and resolves the kinematic inverse problem without inv ersion. The model trajectories exhibit certain properties observed in human multijoint reaching movements such as movement equifinality, str aight end-point paths, bell-shaped tangential velocity profiles, speed -sensitive and speed-insensitive movement strategies, peculiarities of the response to double-step targets, and variations of angular trajec tory without variations of the limb end-point trajectory in cartesian space. In humans, those properties are almost independent of limb conf iguration, target location, movement duration, and load. In the model, these properties are invariant to an affine transform of cartesian sp ace. This implies that these properties are not a special goal of the motor control system but emerge from movement kinematics that reflect limb geometry, dynamics, and elementary principles of motor control us ed in planning. All the results are given analytically and, in order t o compare the model with experimental results, by computer simulations .