Fig 1.
The three DoF planar arm reaching task.
A: Both humans and simulated agents learned to move a three DoF planar arm with joints q1, q2 and q3 (three-dimensional motor space) to reach to targets in an x and y plane (two-dimensional goal space). B: Top: The home postures H1 and H2 are different but reach to the same point in goal space. Note that in home posture H1, the q2 joint is folded backwards (q2 = π) so the reach-endpoint is located on top of the q2 joint. Bottom: The colour map depicts the redundancy, that is the relative number of joint configurations (q1, q2, q3) that reach to a given point in the goal space (lighter colours imply more joint configurations to reach this point). The task is redundant, especially for targets close to the origin of the goal space. Participants were trained and tested on targets in the top quadrant of the goal space (green disks).
Fig 2.
Average performance across blocks.
Mean and standard error of the mean in Condition H2 (red) and in Condition H1 (blue). The black line indicates baseline performance if the hand is not moved at all (slightly lower during training as targets are spaced differently). A: Artificial Agents, test B: Human participants, test. C: Human participants, training.
Fig 3.
Synergy formation during motor skill acquisition.
The percentage of total variance explained by each PC in artificial agents (A) and in human participants during the test blocks (B) and the training blocks (C). Both agents and human participants need two PCs to explain >90% of the total variance in reach postures (q1, q2, q3) at the end of training. In human participants, this involves a dimensionality reduction, i.e., the amount of variance explained by PC1 goes up with training (sign-test difference beginning vs. end: p = 0.041 in test; training p = 0.263), whereas the amount of variance explained by PC3 goes down (sign test difference beginning vs. end: p<0.001 in test, p = 0.041 in training). The lines in panels A, B and C depict the across-participant median, the error bars the interquartile range.
Fig 4.
Examples of synergies learned.
Two example solutions from different participants in the test phase for Condition H1 (A+B) and Condition H2 (C+D) respectively (first two synergies PC1 and PC2). Panels A and C depict the PC1/PC2 solution plane in the three-dimensional motor space. The plane extends 2σ (standard deviations) away from the central posture in the directions of PC1 and PC2 respectively. The pale ‘shadows’ are projections of the results onto the planes defined by the coordinate axes for a better impression of 3D shape. The empty disks depict the two home postures H1 and H2. Panels B and D depict the same result in the goal space (colour code is identical to A and C). The thick lines depict the arm configurations that correspond to the points of the same colour in motor space. The thin lines depict the reach-endpoints along the grid that connects the dots. The inlays depict the respective home postures H1 and H2.
Fig 5.
Location of learned solutions in motor and goal space at the end of training.
A-C: Artificial Agents. D-G: Human Participants. Panels A and D depict the central postures (mid-point of learned solutions) in motor space for all 100 agents and 20 participants (Cond H1: blue, Cond H2: red). Panels B and E depict the corresponding arm configurations in goal space, which shows that the reach-endpoints of the central postures cluster around the mid-point of the array of test targets. Panels C, F and G depict the average location of solutions relative to H1 and H2 across time (population mean and standard error of the projection on the line connecting H1 and H2). Both agents (C) and humans (test F, training G) are biased towards the starting home posture, but this bias is weaker in humans.
Fig 6.
The relative use of DoFs in learned synergies.
A+C: Population median of the absolute values of q1, q2 and q3 in PC1, PC2 and PC3 (unit length vectors) in artificial agents (A) and human participants during training (C). Brighter colours indicate a higher absolute value of the respective DoF. B: Illustration of the home postures H1 (blue) and H2 (red) in goal space. Note that the q3 joint is contracted in H1 and extended in H2. D: Median and interquartile range of absolute q2 values in PC1 across agents (top) and participants during training (bottom).
Fig 7.
Absolute variability and influence of finger mapping on motor organization.
The summed variance of all three synergies for artificial agents (left) and human participants (right) across time (median and interquartile range).
Fig 8.
Percentage of variance in the across-participant reach-endpoint space that is explained by the first, second and third PC across time.
More variance explained by the first synergies indicates more organization of motor control. Left: PCA on human morphology (left index, right index, right middle fingers). Right: PCA on the task motor space (q1, q2, q3). Top: test blocks, bottom: training blocks.
Fig 9.
Setup and Procedure for the Experiment with Human Participants.
A: Participants experience the task as deforming a black ellipse to track the shape of a white ellipse by moving their left index (LI), right index (RI) and right middle (RM) fingers up and down (left). Internally, finger positions are mapped to the joint angles q1, q2 and q3 of the 3 DoF planar arm (bottom right, Method Sect Task). The size and elongation of the ellipses represents the position of target and reach-endpoint in goal space (top right). B: When a participant keeps the three fingers LI, RI and MI level (bottom left), this corresponds to taking the Baseline Posture q* (top left), which is in the middle of the two home postures (top middle and top right) in motor space. To take one of the home postures, the fingers have to be moved away from the midline in a manner that depends on the random mapping between fingers and joints (example mapping: (-2, 3, -1)). C: Each session consisted of 24 training and test blocks (right). A training block (top left) was started by taking the home posture. The deforming white target ellipse had to be tracked with the black ellipse (reach-endpoint) continuously for the next 80 s. In test blocks, only the white target ellipse was displayed and participants moved their finger till they reached a configuration they thought corresponds to the target and then submitted their response by pressing a foot pedal.