The Planning Horizon for Movement Sequences

Abstract

When performing a long chain of actions in rapid sequence, future movements need to be planned concurrently with ongoing action. However, how far ahead we plan, and whether this ability improves with practice, is currently unknown. Here, we designed an experiment in which healthy volunteers produced sequences of 14 finger presses quickly and accurately on a keyboard in response to numerical stimuli. On every trial, participants were only shown a fixed number of stimuli ahead of the current keypress. The size of this viewing window varied between 1 (next digit revealed with the pressing of the current key) and 14 (full view of the sequence). Participants practiced the task for 5 days, and their performance was continuously assessed on random sequences. Our results indicate that participants used the available visual information to plan multiple actions into the future, but that the planning horizon was limited: receiving information about more than three movements ahead did not result in faster sequence production. Over the course of practice, we found larger performance improvements for larger viewing windows and an expansion of the planning horizon. These findings suggest that the ability to plan future responses during ongoing movement constitutes an important aspect of skillful movement. Based on the results, we propose a framework to investigate the neuronal processes underlying simultaneous planning and execution.

Keywords: memory capacity; motor planning; practice effects; sequence production; skillful movement.

Figure 1.

Varying viewing window in a DSP task. A, Example trial in a DSP task with viewing two items ahead of the current keypress, while the remaining items are masked by asterisks. B, Viewing window size (w) manipulation, from w = 1 (equivalent to a simple reaction time (RT) task), to w = 14 (display of the entire sequence at once). The arrow indicates the from-left-to-right direction of response order. Participants could start each sequence whenever they felt ready and were rewarded on the basis of their movement time (MT) (the time from the first keypress to the release of the last key in the sequence).

Figure 2.

The benefit of planning ahead on sequential performance. A, Average MT as a function of viewing window, across the 5 d of practice. B, Method used to estimate the effective planning horizon. Example data from one participant (gray) is fit to an exponential model (magenta). The intersection between performance at 99% of asymptote and the Exponential fit was chosen as criterion to determine the effective planning horizon. Box plots show the median and whole range of individual data points (one per participant). Shaded areas reflect SEM.

Figure 3.

The effective planning horizon increases with practice. A, Average MT as a function of viewing window (w), separately for early (day 1, red) and late (day 5, blue) stages of sequence practice. B, Difference in performance (sequence MT) between early and late practice (data in A), normalized by average MT for each w, as a function of w. C, Mean effective planning horizon (estimated as shown in Fig. 2B) for each day of practice. D, Correlation between mean MT for w > 5 (which enabled planning ahead) and mean effective planning horizon, separately for different days (days 1–5 in gradient red to blue). For this analysis, planning horizon was estimated on odd blocks and MT on even blocks. Dots reflect individual data points (one per participant). Box plots show the median and quartiles of group data. Shaded areas reflect SEM; *p < 0.05, two-tailed paired-samples t tests.

Figure 4.

Longer RTs for larger viewing windows. A, Average RT as a function of viewing window. B, Subset of data in A, separating between early (day 1, red) and late (day 5, blue) stages of practice. Box plots show the median and whole range of individual data points (one per participant). Shaded areas reflect SEM.

Figure 5.

Predictions and analysis of IPIs. Average IPI as a function of transition number within each sequence, separately for viewing window size (w, different shades of gray). 4+ indicates w ≥ 4. A, Prediction 1 (null hypothesis): no effect of w, all IPIs roughly in the same range. B, Prediction 2: fast early IPIs reflect the benefit of preplanning, but for unplanned keypresses the benefit of viewing ahead is minimal. C, Prediction 3: even mid to late IPIs benefit from larger w, indicating that both preplanning and online planning are contributing to fast sequence production. D, Actual group data of mean IPIs for each keypress transition, separately for each viewing window.

Figure 6.

Improvements in preplanning and online planning with practice. A, Mean IPI as a function of transition number, separately for practice stage (day 1, red; day 5, blue) and viewing window size (w = 1, 2, 3, 4+ in separate plots). B, Average IPI difference between day 1 and day 5, normalized by average IPI for each day, separately for each w and planning process (S-R mapping, purple; preplanning, green; online planning, orange). Box plots show the median and whole range of individual data points (one per participant). Shaded areas reflect SEM; *p < 0.05, two-tailed paired-samples t tests; °p < 0.05, two-tailed one sample t test.

Figure 7.

Eye movement strategies do not change with practice. Mean eye position relative to current press at the time of press as a function of press number, for different days of practice (day 1, red; day 5, blue) and for different viewing windows (w, gray shaded areas). Viewing windows of size of 4 or larger were grouped together as 4+. Shaded areas reflect SEM. Dashed line indicates eye position that would be equivalent to looking directly at the digit corresponding to the current finger press. Positive numbers indicate that the eyes are further ahead than the current press, and negative numbers indicate that the eyes are lagging behind.

Figure 8.

Planning capacity and hypothetical neural implementation of sequential behavior. A, The “soft” horizon of sequence planning depends on the amount of resource available. In this illustrative example, most resources are invested in the planning of the immediately upcoming press (+1, 2, blue). The further in time a press is from the current press (0, 4, red), the smaller the corresponding planning investment. Once a press has been initiated, the resources are redistributed by shifting the planning curve one step ahead, thus allowing for continuous online planning of future presses (e.g., +2, 3, yellow). B, Hypothetical neuronal population activity in brain regions involved in planning and execution processes. Each plane refers to an independent subspace of the multidimensional population activity with possible neural trajectories for the current action (0), and future actions (+1, +2), color-coded as in A. Shaded areas reflect single trial variability. The current neural state is indicated by a black dot. Planning of the next (+1) and future actions (+2) may evolve in separate regions or in orthogonal subspaces within the same region.