To begin each experiment, participants were asked to perform reach and precision grasp movements to a triangular prism presented at randomised target orientations. As expected, subjects transitioned from using Grasp 1 to Grasp 2 as the object sampled more clockwise angles (e.g. Fig. 1c). Across all participants’ calibration sessions, the switch-point ranged between − 58.1° and 32.8°, relative to the vertical axis, with varying degrees of sharpness (Halfwidth = 17.09 ± 2.15°); the calculation of halfwidth is provided in Online Resource 1 and exemplified in Fig. 1c.

To confirm previous findings that prior information can bias grasp behaviour, the static experiment task added an additional component before grasping of the target angle: an initial angle which subjects would not reach for but only observe. Here, subjects were presented with this initial angle for a brief moment before LCD goggles occluded their view of the task, at which point the object rotated either CW or CCW to the target angle. Post-rotation, the LCD goggles then became transparent, triggering subjects to grasp the object at the target angle.

A visualisation of the generalised linear mixed effect model (GLME) fitted to the data for the static experiment is shown in Fig. 2a–c. As expected from the design of the experiment, target angle was found to be a significant factor on grasp choice (Table 1; p < 0.001). Furthermore, there was a significant effect of shift direction on grasp choice (p < 0.001), suggesting that the orientation of initial angle influenced the planning of the grasp for the target angle, i.e., the presentation of the object at an initial position that would likely require Grasp 1 increased the likelihood of subjects then later adopting Grasp 1 for the ambiguous target angle. The sizes of both these significant effects are above the minimally detectable effect with a power of 0.8. To gain an intuitive understanding of how grasp choice is different between CW and CCW object rotation directions, we calculated from the model prediction the difference in probability of Grasp 2 at the switch point angle (indicated by black lines on Fig. 2a–c). For shift magnitudes of 5.4°, it was 0.08, whereas for larger shift magnitudes of 14.4° and 28.8°, the difference was larger at 0.11 and 0.15. However, neither shift magnitude nor any interactions were found to be significant (see Table 1).

GLME visualisation from all subjects of the Static Experiment (a–c), Dynamic Exp.1 (d–f), Dynamic Exp. 2 (g–i) and Dynamic Exp. 3(j–l). Choice is predicted separately by the corresponding GLME for each rotation direction (red and blue lines) and shift magnitude [5.4° shown in (a, d, g, j), 14.4° shown in (b, e, h, k), 28.8° shown in (c, f, i, l)] for target angles 50° either side of the centre of ambiguity. a–c GLME model for the static experiment: C ~ TA + Di + SM + TA:Di + TA:SM + Di:SM + (1|S). d–l GLME model for combined dynamic experiments 1–3: C ~ TA + Di + SM + DE + TA:Di + TA:SM + TA:DE + Di:SM + Di:DE + SM:DE + (1|S). The SEM across all subjects is illustrated by line thickness. The difference in probability at 0° for each rotation direction is illustrated with vertical black lines at 0° target angle. C, choice; TA, target angle; Di, direction; SM, shift magnitude; DE, delay duration; S, subject; CW, clockwise; CCW, counter-clockwise

To summarise, the influence of prior object position on grasp choice at an ambiguous target is in agreement with the priming effects previously reported in the literature (Gallivan et al. 2015, 2016). Furthermore, there is weak evidence to suggest that the higher the likelihood of the initial position requiring Grasp 1, the stronger the effect of subjects then later adopting Grasp 1 for the ambiguous target angle, however this was not statistically significant.

To investigate any possible influences that prior dynamic visual information could have on grasping in ambiguous settings, the following experiment kept the same conditions as the static experiment, but without the LCD goggles, allowing subjects to watch the object rotate from the initial angle to the target angle.

As expected, the target angle was found to be a significant factor (Table 2; p < 0.001). The direction of object rotation was also found to be a significant factor (p < 0.001), yet the effect was opposite to that observed in the Static Experiment, i.e., the presentation of the object at an initial position that would likely require Grasp 1 increased the likelihood of subjects then later adopting Grasp 2 for the ambiguous target angle, referred to hereon as the ‘inverse bias effect’. The sizes of both these significant effects are above the minimally detectable effect with a power of 0.8. To again gain an intuitive understanding of how grasp choice is different between CW and CCW object rotation directions, we calculated from the model prediction the difference in probability of Grasp 2 at the switch point angle (indicated by black lines on Fig. 2d–f). For shift magnitudes of 5.4°, it was − 0.14, whereas for larger shift magnitudes of 14.4° and 28.8°, the absolute difference was even greater at − 0.17, and − 0.23, respectively. However, neither shift magnitude nor any interactions were found to be significant (see Table 2).

To summarise these findings, a clockwise rotation to an ambiguous target angle increased the probability of Grasp 2 (a grasp non-congruent with the initial position) at the switch-point in comparison to Grasp 1 (a grasp congruent with the initial rotation), while a counter-clockwise motion increased the likelihood of Grasp 1. Although the difference between grasp choices appears larger for larger shift magnitudes (Fig. 2d–f), both effect sizes for rotation magnitude and its interaction with direction were smaller than the estimated minimal effect size at the power of 0.8, given the sample size. This is a potential reason for both factors being non-significant.

To investigate whether the timing of the go-cue relative to object rotation can influence the strength of the inverse bias effect, this delay was varied from − 50 ms in Dynamic Exp. 1, to 150 and 500 ms in Exp. 2 and 3 respectively (see Fig. 1b). We predicted that the longer subjects have to observe the target angle before receiving the go cue, the inverse bias effect would become weaker, owing to the prior information becoming more historical and therefore less influential. Thus, data from Exp. 1, Exp. 2 and Exp. 3 were combined into one model with delay was added as a factor into the GLME.

The visualisation of the results of the model fitted to the data when the go cue was delayed until 150 ms and 500 ms post-rotation are shown in Fig. 2g–i and j–l respectively, with the results for a delay of − 50 ms shown in Fig. 2d–f. Target angle again remained significant (Table 3; p < 0.001), as expected. The direction factor also remained significant (p < 0.001). There was no significant effect of go cue delay on choice (p = 0.128), nor a significant direction-delay interaction (p = 0.144). Though this latter observation is suggestive of a constant inverse bias effect for all planning times, we cannot rule out the possibility of a small effect that was not significant due to smaller sample size. Indeed visually, the difference in grasp choice probability at the switch point between CW and CCW directions narrows, decreasing from 0.13 to 0.07 for shift magnitudes of 5.4°, from 0.17 to 0.12 for 14.4° shifts, and 0.25 to 0.19 for 28.8° shifts (Fig. 2d–l). Importantly, there was a significant interaction between target angle and delay (p < 0.001), indicating a steeper transition between Grasp 1 and Grasp 2, suggestive of greater certainty in grasp choice with greater planning time. The sizes of all significant effects described here are above the minimally detectable effect with a power of 0.8. To quantify these effects, we estimated the change in Halfwidths from the individual subjects’ GLME predictions. Between delays of − 50 ms, 150 ms and 500 ms, the Halfwidth reduced from 20.8° to 15.8° to 10.2° for CW and from 21.6° to 16.3° to 10.3° for CCW. Shift magnitude did not have a significant effect on grasp choice (p = 0.092), however, a significant interaction between direction and shift magnitude was found (p = 0.003), indicative of a stronger bias effect with a larger rotation between the initial and target angles. None of the other interactions were significant (see Table 3).

To summarise, when the delay between target angle presentation and the go cue increased from − 50 to 500 ms, subjects showed less ambiguity in their grasp choice. Furthermore, the inverse bias effect persisted even with greater planning time allowance and was influenced by the magnitude of rotation.

When completing each trial, participants were instructed to act quickly but with priority to accuracy and comfort. As such, each experiment was not designed as a RT task. Yet, one might predict that the greater the uncertainty induced by the experimental conditions, the longer the RT (Wood and Goodale 2011). Indeed, significant differences in RTs were observed both within (ambiguous vs. determinate target angles) and across (go cue timing) experiments.

To quantify the relationship between each of our behavioural measures and delay timings, three separate GLME analyses were performed with delay as the sole (continuous) variable and estimated values of HW, mean reaction and movement times as each independent variable (Fig. 3a–c). Each analyses showed a significant effect of delay on halfwidth (DE CE = − 0.406 (95% CI [− 0.652, − 0.161]), t-stat = − 3.4, dF = 30, p = 0.002), reaction time (DE CE = − 0.476 (95% CI [− 0.727, − 0.225]), t-Stat = − 3.9, dF = 30, p < 0.001), and movement time (DE CE = − 0.248 (95% CI [− 0.438, − 0.059]), t-Stat = − 2.7, dF = 30, p = 0.012). The effect sizes described here are close but below the minimally detectable effect with a power of 0.8, yet are significant (p < 0.05). Given the sample size, this might be a false positive; however, it might also be a genuine effect present in our data.

Effect of delay from target angle onset to go cue on behavioural measures. a Halfwidth was estimated for each subject and delay, predicted from individual GLM analysis (GLM model: C ~ TA). GLME model: HW ~ 1 + delay + (1|S). b Mean movement times were calculated following outlier removal for each subject and delay. GLME model: MT ~ 1 + delay + (1|S). c Mean reaction times were calculated following outlier removal for each subject and delay. GLME model: RT ~ 1 + delay + (1|S). Shading illustrates prediction of each model with confidence intervals at 95%

To investigate the effect of target angle on RTs, a LME approach was used. In agreement with previous work, RTs for target orientations closer to the centre of ambiguity were greater than those more determinate (log transformed raw values are shown in blue in Online Resource 2).

To summarise these experiments, as the experimental delay increases, there is both greater uncertainty as shown by the halfwidth measure, as well as greater RTs within and across experiments.

Given the finding that the directionality of object rotation can influence grasp choice, we investigated whether this could be attributed to changes in how the target position is perceived after observing object rotation. In this secondary study, subjects were asked to observe object rotation from initial to target angles as for the Dynamic Experiments, except after target angle presentation, visual input was briefly blocked. Subjects were then re-shown the object at a test angle and asked to report whether it appeared further CW, CCW, or ‘unchanged’ from the target angle position (Fig. 4a). On non-catch trials, the test angle was identical to the target angle, and thus a ‘correct’ answer would therefore be ‘Unchanged’.

Experimental timeline and behavioural results from the Perception Experiment. a Timeline of a single trial during the perception experiment. Periods of object visibility and obscurity are illustrated by light and dark bars respectively. The time given to observe the target angle was 100 ms, whilst the duration of visual blocking before test angle presentation was 500 ms. b Following observation of object rotation (CW or CCW) from an initial angle to target angle, then subsequent presentation of the test angle, a decision of ‘CCW’ reflects that the subject perceived the test position to be further counter-clockwise than the target position, whilst ‘CW’ reflects that it appeared further clockwise. Here, averaged perceptual decisions are taken only from trials wherein the test position was unchanged from the target position. c Averaged perceptual decisions taken only from trials wherein the test position was different from the target position, following either CW or CCW rotation from the target angle to test angle. The error bars represent confidence intervals of 95%. NS: No significant difference. **p < 0.01

Average choices on non-catch trials (i.e. target angle = test angle) are shown in Fig. 4b. There was no significant difference between the error rate in reporting ‘CCW’ (p = 0.296) when the rotation direction from initial to target angle was CW versus CCW, nor in reporting ‘CCW’ (p = 0.253). Thus, there does not seem to be a bias in perceived object position at the target angle following object motion from the initial angle. Whist a misjudgement in object position cannot explain the inverse bias effect, potential contributions from other perceptual phenomena cannot be fully ruled out.

To confirm that participants were attending to and comparing test angle position relative to target angle, catch trials were separately analysed (Fig. 4c). Here, the object, rather than remaining at the target angle following the initial angle to target angle transition as for the above, rotated to the test angle. When this rotation was CW, subjects were on average significantly more likely to correctly report that the test angle appeared CW relative to the target position than CCW (CW 38.01% vs. CCW 6.36%, p = 0.0056), and significantly more likely to correctly report CCW than CW on a CCW rotation (CW 8.26% vs. CCW 45.45%, p = 0.0054). The error rate on catch trials was 53.72% for CW shifts and 48.18% for CCW, a reflection of a task difficulty that was necessary to induce in order to investigate participant accuracy in judging object position on non-catch trials. These findings confirmed that subjects were attending to the task, and that the lack of bias found on non-catch trials cannot be attributed to lack of engagement.