Almost all actions in daily life can be achieved in multiple ways that all can lead to the desired task goal. As an example, consider a driver steering a car on a curvy road to reach a target destination. She may choose different paths depending on whether she wants to maintain a consistent distance from the median strip or whether she aims to minimize changes in velocity. Both strategies can achieve her goal, i.e., arrive at her destination, maybe even arriving at the same time, although the precise path taken by the car in both situations will differ. How could one identify the underlying control objective from differences in observed behavior? In more technical terms, what is the objective/cost function that an individual aims to achieve/minimize to accomplish a task? A considerable number of studies in human movement neuroscience have aimed to identify the control objectives in a given task based on their kinematic manifestations (Braun et al., 2009; Izawa et al., 2008; Nagengast et al., 2009; Razavian et al., 2023; Uno et al., 1989; Wong et al., 2021). However, experimental tasks are often chosen to elicit consistent behavioral features across repetitions and individuals, not only to facilitate analysis, but also to constrain control to a single objective. Behavior in natural settings, however, tends to be more complex and highly variable across repetitions, because there is redundancy, meaning that a variety of ways exist to achieve the goal. Hence, individuals can employ a multitude of strategies to accomplish a task. To date, the understanding of such variable behaviors with underlying redundancy - let alone its neural bases - has posed formidable challenges (Croxson et al., 2009; Diedrichsen et al., 2010; Kawato, 1999; Scott, 2004).

Attempts to understand the neural underpinnings of control objectives have been pursued in research on both humans and non-human primates (Benyamini and Zacksenhouse, 2015; Cross et al., 2023; Croxson et al., 2009; Desrochers et al., 2015; Kao et al., 2021; Miall et al., 2007; Nashed et al., 2014; Omrani et al., 2016). Yet, with notable exceptions (e.g. Pruszynski et al., 2011), these two lines of inquiry have remained largely parallel with few direct bridges: human behavioral and computational research has mainly focused on the analysis of behavior, while animal research has used invasive methods such as intracortical recordings to understand the neural mechanisms of movement control. Experiments with humans tend to use detailed experimental manipulations to elicit features of motor behavior that afford insights into its governing principles. Using a wide range of tasks, from simple reaching to interacting with complex objects, mathematical models with specific control algorithms have been used to reproduce the salient features of behavior (Crevecoeur et al., 2019; Diedrichsen, 2007; Nagengast et al., 2009; Nayeem et al., 2021; Razavian et al., 2023; Yeo et al., 2016). However, understanding the neural underpinnings of movement control at the intracortical level in healthy humans has remained a challenge. On the other hand, animal research, in particular with non-human primates, allows sophisticated methods to directly record neural activity to afford insights into neural correlates of motor behavior. Ultimately, this knowledge should transfer to how the human brain functions (Badre et al., 2015), but those links have only been made few and far between.

To achieve this goal, cooperative study designs between human and animal motor research are needed to understand the neural basis of human motor skill (Badre et al., 2015; Rajalingham et al., 2022). However, there are difficult challenges to overcome: First, cooperative design requires matching behavioral tasks that can be performed similarly and with the same conditions by both humans and animals. While research on eye movement control has achieved such matching between human and non-human primate paradigms (e.g. the anti-saccade task or the Rashbass step ramp; Lisberger et al., 1987; Munoz and Everling, 2004; Rashbass, 1961; Robinson, 2022), this proves more challenging in limb coordination, where explicit goals and instruction become more important. Second, the constraints of behavioral studies with monkeys and humans are somewhat different, which can preclude a direct comparison. Behavioral tasks used with monkeys are typically simpler than those used with humans, due to the animals’ more limited cognitive capacities. Also, studies with monkeys aim for highly repeatable behaviors to facilitate the aggregation of neural activity across trials or days. This means that tasks with redundancy that allow multiple solutions to achieve the same goal do not readily lend themselves to investigation. In contrast, studies of human behavior can push toward tasks that are more sophisticated and capture the complexity and redundancy that abound in natural activities. Our experiments examine a behavioral task with redundancy that allows more than one solution to accomplish the task. Despite these challenges, our study aims to bridge the gap between human and monkey behavioral studies to build toward an understanding of the neural principles of human motor control.

We used an experimental paradigm, the Critical Stability Task (CST), that can be performed by both humans and monkeys (Quick et al., 2018). The CST requires the subject to balance an unstable virtual system governed by a very simple dynamical equation (see Methods). Performing the task is akin to balancing a virtual pole. The CST has features that make it suitable for the study of more complex motor behaviors. First, while the goal remains the same, the difficulty of the task can be titrated. Second, it involves interactions with an object, albeit virtual in our case, so that continuous adjustments are required to succeed. Each trial evokes unique behavior that may reflect different control strategies to accomplish the task. In addition, even if the same control strategy is employed, each trial generates different behavior due to sensorimotor noise and the task’s instability. These features are ubiquitous in all everyday actions and our choice of CST was to explicitly address such behavior that is closer to naturalistic behaviors. As in the car driving analogy, the subjects might seek to optimize position, or they might seek to optimize velocity, while both strategies may lead to equal success.

Because of its complexity and redundancy, each trial of the CST is unique. The goal of the study is to infer the subject’s control objective (i.e. minimization of errors in position or velocity) from observations of their behavior. When the subjects are humans, it is possible to instruct them to employ a particular strategy or to ask them post-hoc what strategy they adopted to succeed at the task. This explicit route is definitely not available with monkeys. As we are still quite far from ‘reading out’ strategies from neural activity, we need to start with behavior to infer the control objectives. Hence, this study adopted a computational approach based on optimal control theory to simulate behavior during the CST in various conditions. This approach allowed us to make predictions about the behavioral signatures associated with different control policies, which we then used to analyze the experimental data from both humans and monkeys.

In overview, this study investigated, through behavioral data and model-based simulations, the sensorimotor origins of observed kinematic strategies in humans and non-human primates performing the CST. We developed the experimental paradigm such that humans and monkeys executed the task under matching conditions while recording movement kinematics in exactly the same way. An optimal control model was used to simulate two different control objectives, through which we identified these different objectives in the experimental data of humans and monkeys. We discuss how in the future these results could guide the analysis of neural data collected from monkeys to understand the neural underpinnings of different control policies in an interactive feedback-driven task with redundancy.

The CST involved balancing an unstable system using horizontal movements of the hand to keep a cursor from moving off the screen (Figure 1A and B). This study collected data from human subjects performing the CST and compared it to previously collected data from monkeys performing the same task. The hand’s displacements were recorded by 3D motion capture (Qualisys, Gothenburg), with a reflective marker attached to the hand. The cursor dynamics were generated by a linear first-order dynamical system, relating hand and cursor kinematics as described in Quick et al., 2018:

Figure 1

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where $x$ and $\dot{x}$ are the horizontal cursor position and cursor velocity on the screen, $p$ is the horizontal hand position, and $\lambda$ is a positive constant fixed at the beginning of each trial. The parameter $\lambda$ sets the gain of the system. When $\lambda$ is larger, the cursor would tend to move faster, making the task more difficult as faster and more precise hand movements were required to maintain balance. Correspondingly, success rates at the task decreased with increasing $\lambda$. To summarize the skill of human and monkey participants, we identified the value at which subjects succeeded at only 50% of the trials and defined that value as the ‘critical’ value, ${\displaystyle {\lambda }_c}$.

The task goal was to keep the cursor within a range of space shown on the screen for a duration of 6 s. The range of the workspace was defined as $-c\le x\left(t\right)\le c$, where $c$ was a positive constant (c=5 cm or 10 cm; see Methods). This created a redundancy in achieving the task goal as there were infinitely many ways in which one could balance the cursor inside the specified region. We examined movement kinematics to identify control strategies employed by different subjects, and across different trials.

In a previous study, two Rhesus monkeys were trained to perform the CST under increasing difficulty levels (Quick et al., 2018). Similarly, here 18 human subjects were recruited to perform the same task under comparable experimental conditions as the monkeys (see Methods). Figure 1 illustrates the experimental setup for both monkeys and humans (Figure 1A and B) and shows examples of their behavior (Figure 1C and D). Overall, there were similarities in performance between humans and monkeys. To further quantify and compare this performance across humans and monkeys, we defined a set of control metrics to assess different aspects of control as detailed in the following.

Experiment 1: CST performance without instructed strategy

In the first experiment, six human subjects performed the CST with the only instruction to ‘perform the task without failing to the best of your ability’. Failure occurred if the cursor escaped the boundaries of the screen (±10 cm from the center) within the trial duration of 6 s. Subjects received categorical feedback about the outcome at the end of each trial in a text appearing on the screen reading ‘Well done!’ for success, and ‘Failed!’ for failure. The degree of difficulty, set by $\lambda$, was increased stepwise across trials until the subject could no longer perform the task (see Methods for the specifics about the setting of $\lambda$ values).

We first sought to examine the main characteristics of behavior in CST performance and how it compared between humans and monkeys. To quantify the overall behavior, four main metrics were employed as described and motivated below. To begin, we considered the overall success rate in the task among different individuals, before focusing on the kinematics of task performance. Figure 2A illustrates the success rates and how they dropped as the task difficulty increased. Both humans and monkeys showed a similar pattern of decrease in success rate which was well-captured with a sigmoidal function. Expectedly, individuals varied in their ability to achieve high difficulty levels as a measure of skillful performance, indicated by their ‘critical $\lambda$ value’ ${\lambda }_c$, that is, the value of $\lambda$ when the success rate dropped below 50%.

Figure 2

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To investigate the performance in more detail, the kinematics of movement were examined, specifically the hand and cursor position during each trial. As indicated in Equation 1, the hand position $p$ was the control input to the system which aimed to control the cursor position $x$ as the variable of interest. Due to the unstable nature of the task, drifting of the cursor towards the edge of the screen demanded a response by the hand movement to avoid failure. As such, two simple metrics characterized control, one quantifying how the movement of hand and cursor correlated, and a second one to what degree the hand response lagged cursor displacements. Figure 2B shows the correlation between the cursor and hand movements as a function of task difficulty. The strength of the correlation increased as trials became more challenging in both monkeys and humans, asymptoting towards –1. According to Equation 1, this behavior was equivalent to reducing the sum $\left(p+x\right)$ to mitigate the effect of large $\lambda$ values on cursor velocity $\dot{x}$ , and, hence, reduce the chance of failure.

The response lag from the cursor movement (observed feedback) to the hand movement (control response) is an important characteristic of a control system. As shown in Figure 2C, by increasing the task difficulty $\lambda$, the lag decreased for all subjects. Coupled with the increase in the strength of the correlation with increasing $\lambda$, these findings indicate that subjects generated faster and more precise corrective responses to cursor displacements in more difficult trials.

As the fourth metric, we calculated the ratio of root mean squared (RMS) of hand position to the RMS of cursor position for each trial, as a measure of response strength. This measure determined to what extent the control signal (hand movement) compared in magnitude to the cursor movement. A large RMS ratio meant that on average across a trial, the hand exhibited larger movements than necessary to correct for cursor deviations. Figure 2D illustrates the calculated RMS ratio as a function of task difficulty for humans and monkeys. Except for Monkey J, the RMS ratio showed a gradual decrease as the task difficulty increased for most individuals. The seemingly divergent behavior of Monkey J was likely due to subject-to-subject variability, as also observed in human performers (Appendix 1—figure 1). Such decrease could be justifiable due to larger cursor movements at higher difficulty levels, and perhaps more efficient corrective hand responses to cursor displacements. It is worth noting that for high ${\displaystyle \lambda }$ values, small hand movements could cause large cursor displacements, which were detrimental to the task success. Therefore, pruning any task-irrelevant hand movements, consistent with promoting efficiency, seemed essential to succeed in more difficult trials.

Overall, the control metrics presented in Figure 2 give insight into how the CST was performed: as the task difficulty increased, subjects tended to respond to cursor displacements faster (that is, with lower lag), more precisely (seen in the stronger hand-cursor correlation), and more efficiently (with lower RMS ratio). Behavior was comparable between humans and monkeys, which suggests that there were similar control strategies used by both species. Next, we sought to detect those control strategies.

Redundancy of control strategies in CST performance

The CST, as described earlier, affords redundancy in the behavioral strategies that could result in task success. Although covert in aggregate level of performance (i.e. Figure 2), single trial observations of hand and cursor trajectories suggested that different underlying control objectives might be at play. Two types of behavioral patterns appeared recognizable in the data. In one case, the cursor seemed to be always balanced around the center of the screen, and any deviations from the center induced a response to bring the cursor back to the center. This was reflected in the oscillatory movements of the cursor around the center, shown in example trials in Figure 1C and D (first row). In other trials, the cursor either exhibited a slow drift from the center or remained relatively still anywhere within the boundaries of the screen, with only limited attempts to bring the cursor back to the center (for example, Figure 1C and D, second row). We hypothesized that these patterns of behavior arise from different control objectives, each focused on a different state variable in the state-space of the cursor movement. In the former case, the position of the cursor appeared to be the primary control variable. Under this strategy, subjects might pursue the objective of keeping the cursor near the center of the screen. We refer to this strategy as Position Control. In the latter case, the cursor velocity seemed to be of primary importance for control, with the objective to slow down cursor velocity regardless of its position in the workspace. We refer to this strategy as Velocity Control.

Can we distinguish between different control strategies by examining behavior? To test this idea, we took a computational approach by developing a generative model based on optimal feedback control (Todorov and Jordan, 2002) that could simulate the task under different conditions and with different objectives (Todorov and Jordan, 2002). The model involved a controller that generated optimal motor commands based on a given objective to perform the CST via a simple effector model. The model also contained a state estimation block that estimated the states of the system based on the given feedback (Todorov, 2005). In this case, cursor position and cursor velocity were used as feedback to the controller at each time step. Figure 3A illustrates a block diagram of this model.

Figure 3

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The control gains used in the controller to generate the motor commands were optimally found by minimizing the sum of two cost functions: the cost of effort to reduce energy, as well as the cost of accuracy that prevented the states of the system from making large deviations (2):

(2) ${\displaystyle J=\sum _{t=1}^n\left({\mathbf{x}}_t^{T}Q{\mathbf{x}}_t+u_t^{T}U{u}_t\right)}$

where $u$ and $x$ represented the motor command and the state vector of the system, respectively. In this model, the state vector consisted of six states: the position, velocity and acceleration of the hand, as well as the position, velocity and acceleration of the cursor (see Methods). Variables $t$ and $n$ represent the time, and the total number of time steps in a trial, respectively. The matrix $Q$ and the scalar $U$ determined the weight of accuracy and effort in the cost function, respectively. Importantly, the matrix $Q$ allowed for determining which states of the system were of primary importance in the control process. Therefore, the implementation of different control objectives in the controller was done through setting the $Q$ matrix appropriately. As such, a Position Control strategy was implemented by setting the weight of cursor position in the $Q$ matrix to a large value, emphasizing the primacy of cursor position as a control variable. Similarly, to implement the Velocity Control strategy, the weight of the cursor velocity in the $Q$ matrix was set to a large value (see Methods). By simulating the task for each control strategy, we could generate synthetic behavior similar to that of humans and monkeys. Figure 3B and C illustrate a few example simulations of the task under different difficulty levels for the Position Control and Velocity Control, respectively. As exemplified, the simulated trials for Position Control show oscillatory movements of the cursor around the center, whereas the trials generated based on Velocity Control, exhibited slow drift of the cursor from the center with minimal attempt to correct for such drift. These characteristics were similar to the observed patterns of behavior in human and monkey data (Figure 1C and D).

To further identify the behavioral signatures associated with each control objective, beyond the apparent differences between single trials, we conducted a series of simulations in which the model performance was examined for a range of task difficulties. Novel predictions of the model for each control objective were assessed. For each objective, the task was simulated for different difficulty levels, ranging from $\lambda =1.5$ to $\lambda =7$, with increments of $∆\lambda =0.2$. For each difficulty level, 500 trials were simulated (see Methods for details). In the first step, we performed the same set of analyses as reported in Figure 2 to evaluate how the model compared to human and monkey behavior at an aggregate level of CST performance. Figure 4A illustrates the overall performance of the model for both Position Control and Velocity Control. As shown, for each metric, the model exhibited comparable behavior to the experimental data with regard to the task difficulty: the success rate dropped in a sigmoidal fashion, the strength of the correlation between hand and cursor position increased, and the response lag between hand and cursor as well as the hand/cursor RMS ratio decreased. These results showed that, overall, both simulated control objectives produced similar behavioral characteristics as humans and monkeys. More interestingly, the model predicted that Position and Velocity Control performed comparably in success rate and hand-cursor correlation (Figure 4A, top two panels), but differed significantly in the response lag and the hand/cursor RMS ratio (Figure 4A, bottom two panels). Specifically, Position Control consistently showed larger values for lag and RMS ratio for most task difficulty levels.

Figure 4

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Behavioral traces of control objectives in an individual’s overall performance

To further investigate what control objective was preferred by an individual or in a given trial, we examined the predictions of the model about the cursor behavior in state space, and then tested these predictions using experimental data from Experiment 2. Two metrics were defined that captured the state-space behavior of the cursor in each trial. First, we examined the average cursor position and cursor velocity in each trial, represented in the state space of cursor movement. This provided a single data point for each trial in state space, indicating whether on average there was a drift in cursor position and its velocity away from zero ($x=\dot{x}=0$). It was expected that for Position Control, all trials scattered around the origin of the state space, whereas for Velocity Control, they could deviate from the origin. We also examined whether there was a correlation between the cursor mean position and its mean velocity. This, in essence, was equivalent to the autocorrelation of cursor position, i.e., correlation between mean position and final position. Figure 5A illustrates the state-space representation of cursor movement based on model simulations for both Position Control (top) and Velocity Control (bottom), where each data point represents one simulated trial. As shown, the distribution of trials in this space differed markedly between the two control objectives (also see Appendix 1—figures 2 and 3). Position Control resulted in a distribution with little correlation between cursor position and its velocity, and closely scattered around the center. In contrast, Velocity Control revealed an elongated distribution with a relatively strong correlation between the cursor position and its velocity.

Figure 5

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We further examined whether such distinction in behavior was solely due to a change in the control objective, or whether varying other parameters in the model simulations, such as motor noise, delay, or effort cost, could also generate similar distinctive patterns. These sensitivity analyses showed that different magnitudes of noise and delay only affected the success rates, but no other features, as to be expected. Effort cost also could not account for the observed differences in the above mentioned movement distributions (Appendix 1—figures 4–6). Therefore, this robustness to variations in the model parameters allowed us to probe performance based on the underlying control objective.

To validate the model predictions, the same analyses of cursor position and velocity were performed on the empirical data from Experiment 2. Figure 5B illustrates three example subjects from the Position Control and Velocity Control groups, and Figure 5C shows a summary of how the correlation values differed across control objectives for the model and the empirical data. As shown, overall, subjects in the Velocity Control group showed significantly larger correlations than individuals in the Position Control group (unpaired t-test on the Pearson correlation coefficient: t₁₀=4.06, p=0.002). Based on the within-group variability, this allowed us to determine how pronounced a subject executed their respective strategy compared to other subjects in the same group.

It should be noted that Figure 5B shows the data for an ensemble of trials ranging in difficulty levels from easy up to the critical ${\lambda }_c$ values, corresponding to success rates ranging from 100% to 50%. Additional analyses probed whether these behavioral features changed as a function of the difficulty levels. When grouping the trials into easy and moderate difficulty trials, the cursor position and velocity relations did not change and the correlations for the two control objectives continued to reveal the same relative difference between the control objectives (see Appendix 1—figures 7 and 8).

The effects of control objective at a single-trial level of behavior

Due to the task’s redundancy, the control objective may not be fixed for an individual throughout their performance and might vary from one trial to the next. It is therefore of great interest to determine, in a given trial, to what extent the behavior is the outcome of Position or Velocity Control. To this end, we examined the magnitude of cursor movement calculated as the root mean squared (RMS) of its position and velocity in each trial. This was directly related to the cost functions used in the model (Equation 2), which provided a more direct comparison regarding the primacy of Position versus Velocity Control of the cursor: Position Control aimed to minimize the RMS of cursor position, while Velocity Control aimed to minimize the RMS of cursor velocity. This distinction could be well represented in the state-space of the cursor movement.

Figure 6A illustrates the model prediction for the RMS of cursor position and cursor velocity plotted against each other for Position Control (top) and Velocity Control (bottom). For Position Control, the distribution of trials leans towards the vertical axis (restricting cursor position but allowing large cursor velocities), whereas for Velocity Control, it leans mainly towards the horizontal axis (a larger range of cursor positions but restricted velocities). This distinction could be quantified by the slope of a fitted regression line to the data, with relatively larger slopes indicating Position Control and smaller slopes signaling Velocity Control. Similar patterns of behavior could be observed in the human data from Experiment 2 as illustrated in Figure 6B and C, with the Position Control group showing significantly larger regression slope than the Velocity Control group (unpaired t-test, t₁₀=6.33, p<0.001). The regression slope could more clearly distinguish between individual trials than could the correlation coefficient metric shown in Figure 5, regarding their corresponding control objective: if a given trial in the RMS space of the cursor movement lay below/above a certain slope threshold, its performance could be considered the result of Velocity/Position Control. We could therefore use this behavioral feature to develop a classifier that inferred, with a certain level of confidence, the underlying control objective in the performance of an individual in any given trial.

Figure 6

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Inferring control objectives from behavior during CST performance

When monkeys performed the CST, we lacked explicit knowledge about which strategy they might have employed. This resembles Experiment 1 when humans performed the CST with no specific instructions and their control objective was not explicitly available. To achieve the goal of inferring an individual’s control objective based on their performance, we used the control characteristics that our computational approach introduced to distinguish between different control objectives. To this end, the simulation results based on the cursor movement in its RMS space (Figure 6A) were used to train a simple classifier, a support vector machine (see Methods). This classifier then determined, based on the learned regression slopes from the RMS distributions (Figure 7A), whether a given trial was likely performed as Position Control, or Velocity Control.

Figure 7

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We first evaluated the accuracy of the classifier based on simulated data, where the classifier was trained on synthetic data generated with Position and Velocity Control (2250 trials each), and then tested on a separate set of trials from either control objective (2500 trials). For any given trial, the classifier obtained a posterior probability indicating to what extent that trial was generated under Position Control. The probability of 95% and higher identified the given trial as Position Control, while the probability less than 5% labeled the trial as Velocity Control; anything in between was considered ‘Uncertain’ as to the underlying control objective. We also measured how often the classifier misclassified a Position Control trial as Velocity Control, and vice versa. The results showed that 6.2% of trials that were generated with Position Control were misclassified as Velocity Control, and 5.5% of trials that were generated with Velocity Control were misclassified as Position Control. This provided a reasonable accuracy for the classifier applied to the experimental data.

Next, we tested the performance of the classifier on the empirical data from Experiment 2, where the intended control objective used by each subject was known. We asked how well the classifier could recover the control objective used by each subject. Figure 7B shows the cursor RMS data from three example subjects in each instructed group (similar to Figure 6). For each trial (data point) the probability of Position Control was estimated by the classifier, and the trial was identified as Position or Velocity Control based on the estimated probability (>95% for Position, and <5% for Velocity Control). As shown in Figure 7B, for the Position Control group, most of the trials were rightfully classified as Position Control, and similarly for the Velocity Control group, the majority of trials were classified as Velocity Control. The average probability across all trials for each individual was also obtained as an overall measure of the control objective for that subject. This average measure is shown in Figure 7B for the example subjects and summarized in Figure 7C for all subjects in each group. This showed that the classifier correctly determined the control strategy of each individual without being trained on any experimental data.

The ultimate test of our approach would be to infer the control strategy used by individuals whose control objective was unknown, that is the monkeys and the humans who received no instructions about the control strategy in Experiment 1. After representing the performance of each subject in the RMS space, the classifier was used to determine what control objective was used in each trial. Figure 8 illustrates the classification results for human subjects of Experiment 1 as well as two monkeys (Monkey I and J from Quick et al., 2018). The model simulations are also provided as reference in Figure 8A. Figure 8B and C show the data from three example human subjects, as well as two monkeys, in which each trial is either labeled as Position Control (brown), Velocity Control (cyan), or Uncertain (grey). Two example trials, one from each inferred control strategy are also singled out from each subject’s performance in Figure 8B and C (bottom row) to show how the hand and cursor movement behaved under each control objective. Calculating the average probability of control objective for each individual, similar to Figure 7, we could infer which control objective was of primary importance for each subject (Figure 8D). For example, human subject NI-S2 more likely adopted Velocity Control, while human subject NI-S4 mainly performed the task with Position Control (Figure 8B). Similarly, Monkey I seemed to prefer Velocity Control, while Monkey J most likely adopted Position Control (Figure 8C).

Figure 8

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Ultimately, our procedure enabled us to not only infer the underlying control objective at a single trial level, but also identify which objective was overall preferred by humans and monkeys when no explicit knowledge about their strategy was available. These results are encouraging as they constitute an important step towards bridging our findings between human and monkey research, and ultimately guide neurophysiological analyses to identify the neural underpinnings of control objectives in the primates’ brain.

As we seek to understand the neural basis of human motor control, it is important to build links between studies in humans, where behavior can be complex and naturalistic, and monkeys, where direct neural recordings are possible (Badre et al., 2015). Doing so requires close coordination between researchers who work with humans and animals, because this work is typically done in separate labs with a few notable exceptions (Kurtzer et al., 2008; Pruszynski et al., 2011). With the goal to advance insights into movement control, the current work explicitly paralleled human-monkey behavior in a novel paradigm for monkey research. In a matching task design, humans and monkeys performed a virtual balancing task, where they controlled an unstable system using lateral movements of their right hand to keep a cursor on the screen. The task was challenging and, importantly, exhibited different ways to achieve task success. The task required skill that was nevertheless simple enough for monkeys to learn and ultimately achieve the same level of proficiency as humans.

The results showed that both humans and monkeys exhibited the same behavioral characteristics as the task was made progressively more difficult: success rates dropped in a sigmoidal fashion, the correlation magnitude between hand and cursor position increased, and the response lag from cursor movement to hand response decreased. Further observations based on single trials showed that the task was possibly achieved with different control objectives, both across subjects and across trials. Our goal was to identify the underlying control objectives that led to different behavior; a model based on optimal feedback control was developed that identified two different control objectives that successfully captured the average performance features of humans and monkeys: Position Control and Velocity Control. Both strategies produced behavior that was consistent with observations even at the single trial level. Additional experiments revealed that humans who followed specific instructions as to performing the task with Position Control (‘keep the cursor at the center’) or Velocity Control (‘keep the cursor still’) matched the behavior predicted by the two simulated control objectives. Model simulations exhibited features that served to identify these two control objectives in humans and monkeys who received no specific instructions at a single trial level.

Studies in motor neurophysiology have largely relied on simple paradigms such as center-out movements (Batista et al., 1999; Cisek et al., 2003; Georgopoulos et al., 1986; Pruszynski et al., 2011; Scott and Kalaska, 1997), which were brief in duration, highly stereotypical across repetitions, and could be performed to a reasonable degree of success with limited sensory feedback. Such characteristics were needed to make sense of noisy neural data through averaging trials over many repeats of highly similar behaviors. However, such constrained behaviors are not common in natural settings, where we continually utilize sensory feedback to respond to our environment, interact with objects around us, and never do the same action the exact same way. Indeed, such fluid, prolonged and feedback-driven interactions are what we seek to understand both at the behavioral and neural levels. To this end, we need to investigate more complex tasks that involve sensory-driven control and allow for different control strategies while still within a sufficiently controlled scope. The task employed here, the CST, continuously engages feedback-driven control mechanisms for a prolonged period of time and is rich in its trial-to-trial and subject-to-subject variability. As we can titrate the difficulty of the task, both monkeys and humans can learn it and we can study and model their behavior. This opens the gate towards understanding the neural principles of skill learning beyond simple reaching tasks. This study showed that CST afforded the examination of control strategies through a computational approach that modeled monkey and human behavior in comparable fashion.

Looking across monkey and human behavior is not new per se. In the eye movement literature, comparisons between features in monkeys and humans have been more common (e.g. Dorris et al., 2000; Groh and Sparks, 1996). In fact, experimental findings in primates have been instrumental to understanding impairments in eye movement control in humans. And yet, due to practical considerations, experiments in non-human primates take considerably longer than human behavioral studies; due to the logistic problems of having research facilities for both monkeys and humans, combined studies in a single lab have largely remained elusive. Direct comparative studies conducted in different laboratories with exact matches between experimental conditions are harder to achieve.

Another possible avenue for bridging insights between human and monkey behavior is through a computational approach applied to both human and monkey performance (Badre et al., 2015; Rajalingham et al., 2022). In an earlier attempt of modeling CST, a simple PD controller with delay in sensory feedback was proposed to explain the recorded behavior (Quick et al., 2018). However, the model was limited in its ability to capture most features observed in the data, such as success rate or correlation between hand and cursor position. In the past years, optimal feedback control (OFC) has been introduced as an effective approach to understanding the control mechanisms of reaching movements at the level of behavior (Diedrichsen et al., 2010; McNamee and Wolpert, 2019; Pruszynski and Scott, 2012; Scott, 2004; Todorov, 2004), separately in human research (Liu and Todorov, 2007; Nagengast et al., 2010; Nashed et al., 2014; Razavian et al., 2023; Ronsse et al., 2010; Todorov, 2005; Todorov and Jordan, 2002; Yeo et al., 2016) and monkey research (Benyamini and Zacksenhouse, 2015; Cross et al., 2023; Kalidindi et al., 2021; Kao et al., 2021; Takei et al., 2021). Here, the OFC framework was used to account for and make novel predictions about behavioral features in CST.

Note that there are fundamental differences between reaching and CST movements, which needed to be accounted for in the modeling process. Unlike center-out reaching, the CST did not have a stationary target toward which the hand needed to move; rather, it required the hand/cursor to remain anywhere within a predefined area for a prolonged period of time. Also, the behavior was not tracking a point on the screen, but rather moving in opposite direction of the cursor, a behavior that probably requires more cognitive resources. Despite these advanced task features, OFC as a feedback control framework proved an appropriate approach to examine this demanding interactive and sensory-driven task.

A few aspects in our computational approach are worth discussing. First, we examined control objectives that only involved two main kinematic quantities of movement: cursor position and cursor velocity. One might argue that other kinematic features could be explored, such as acceleration or other higher derivatives of the cursor and/or the hand. However, it is important to note that, given the task of keeping the cursor within a specified area for a period of time, cursor position and velocity are the most directly related quantities to the goal of the task. These quantities were also less demanding to predict from sensory feedback, compared to, for example, acceleration (Hwang et al., 2006; Sing et al., 2009). Also note that the kinematics of the hand were not the variables of interest in the task, as the goal was to control the cursor, and not the hand.

Second, there may indeed exist simpler control models that can exhibit similar distinctions in behaviors simply by finding the right control gains for each behavioral pattern. In essence, our modeling approach also generates such patterns using control gains at the extremes of the spectrum of Position and Velocity Control. However, in contrast to models with a simple gain modulation, our model provides a normative account of what control gains are needed to account for the observed data, and what objectives underlie the choice of such gains (see Appendix 1—figure 9, for the optimal gain modulation across control objectives and difficulty levels). In this case, the two control objectives not only demonstrated the ability to generate the distinct behavioral traces of our data, but also accounted for the main performance features such as success rate, lag, RMS ratio, and correlations across a wide range of difficulty levels. And yet, we do not claim that our approach provides a ‘ground truth’. Rather, it presents a reasonable account of behavior with an intuitive explanation about human and monkey performance in our virtual balancing task.

Third, we mainly explored Position and Velocity Control separately to identify distinctive behavioral features associated with each one. Experimental data, however, shows that a large number of trials fall somewhere between the Position and Velocity Control boundaries (Figures 7 and 8). This could be due to a mixed control strategy, where both Position and Velocity Control contribute simultaneously to achieving the task goal, or where subjects switch strategies of their own accord. Here, we aimed to determine the behavioral signatures of the extreme cases, either predominantly based on position, or velocity of the cursor movement. This may increase the chance to detect differences more clearly in neural activity associated with each control objective in further analysis of monkeys’ neurophysiological data.

Even though in this experiment only a subset of trials was amenable to a clear identification as one control strategy, it is possible with monkeys to collect tens of thousands of trials over many days accumulating enough trials for analysis. Furthermore, employing more sophisticated experimental manipulations in future studies, such as introducing perturbations during task performance, could potentially enhance the distinction between control objectives and elucidate their underlying neural mechanisms. This was briefly tested in a series of additional simulations in our study, whereby introducing a simple random offset in the initial cursor position more clearly distinguished between different control objectives (Appendix 1—figure 10). Experimental evaluation of these model predictions is left for future studies.

Having identified control objectives in behavior, the next intriguing question is what neural activity could underlie these different behavioral signatures. As our task is quite novel to the field, it is difficult to formulate exact predictions. However, one first step amenable to analysis is how neural activity differs when preparing for the trial. Previous work has shown that the motor cortex is highly active prior to an action and neural dynamics become specific to the task as monkeys prepare for a cued movement (Ames et al., 2014; Cisek and Kalaska, 2005; Dekleva et al., 2018; Elsayed et al., 2016; Kaufman et al., 2014; Lara et al., 2018; Perich et al., 2018; Vyas et al., 2018; Zimnik and Churchland, 2021). It seems possible that the control objectives we observed elicit different preparatory activity in the motor cortex.

To conclude, despite potential limitations, our approach was successful in two main ways. First, it provided a normative explanation for the macro-level characteristics of behavior observed in human and monkey data. Second, due to its generative nature, model simulations also provide for not yet seen conditions and can make predictions about the behavior under new control objectives. Hence, our behavioral analysis holds promise to generate crucial insights into neural principles of skillful manipulation, not only in monkeys but also, by induction, in humans.

All data and scripts have been deposited in Dryad: https://doi.org/10.5061/dryad.p2ngf1vzt.

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Author details

1. Mohsen Sadeghi

   Department of Biology, Northeastern University, Boston, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Visualization, Writing – original draft, Writing – review and editing

   Contributed equally with

   Reza Sharif Razavian

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2573-146X

2. Reza Sharif Razavian

   1. Department of Biology, Northeastern University, Boston, United States
   2. Department of Electrical and Computer Engineering, Northeastern University, Boston, United States
   3. Department of Mechanical Engineering, Northern Arizona University, Flagstaff, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Writing – original draft, Writing – review and editing

   Contributed equally with

   Mohsen Sadeghi

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-1190-0816

3. Salah Bazzi

   1. Department of Biology, Northeastern University, Boston, United States
   2. Department of Electrical and Computer Engineering, Northeastern University, Boston, United States
   3. Institute for Experiential Robotics, Northeastern University, Boston, United States

   Contribution

   Conceptualization, Formal analysis, Writing – review and editing

   For correspondence

   s.bazzi@northeastern.edu

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-8631-0426

4. Raeed H Chowdhury

   Department of Bioengineering, and Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, United States

   Contribution

   Conceptualization, Data curation, Writing – review and editing

   Competing interests

   No competing interests declared

5. Aaron P Batista

   Department of Bioengineering, and Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-1719-0061

6. Patrick J Loughlin

   Department of Bioengineering, and Center for the Neural Basis of Cognition, University of Pittsburgh, Pittsburgh, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Visualization, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

7. Dagmar Sternad

   1. Department of Biology, Northeastern University, Boston, United States
   2. Department of Electrical and Computer Engineering, Northeastern University, Boston, United States
   3. Institute for Experiential Robotics, Northeastern University, Boston, United States
   4. Department of Physics, Northeastern University, Boston, United States

   Contribution

   Conceptualization, Supervision, Funding acquisition, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0001-9318-2920

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