Stability of inverted pendulum reveals transition between predictive control and impedance control in grip force modulation.

During object manipulation, our sensorimotor sys-tem needs to represent the objects dynamics in order to better control it. This is especially important in the case of grip force control where small forces can cause the object to slip from our fingers, and excessive forces can cause fatigue or even damage the object. While the tradeoff between these two constraints is clear for stable objects, such as lifting a soda can, it is less clear how the sensorimotor system adjusts the grip force for unstable objects. For this purpose, we measured the change in the grip force of individual human participants while they stabilize five different lengths of an inverted pendulum. These lengths set different dynamics of the pendulum, ranging in their degree of controllability. We observed two main states during such manipulation, a marginally stable state of the pendulum and a stabilization state in which participants acted to stabilize the system. While during the stabilization state participants increased their applied grip force, for the stable state we observed a mixed behaviour. For small and less controllable pendulums, grip force increased while for larger pendulums, participants could modulate the the grip force according to the anticipated load forces. Based on these results, we suggest that the pendulum dynamics change the control strategy between predictive control and impedance control.

Contextual cues are not unique for motor learning: Task-dependant switching of feedback controllers.

The separation of distinct motor memories by contextual cues is a well known and well studied phenomenon of feedforward human motor control. However, there is no clear evidence of such context-induced separation in feedback control. Here we test both experimentally and computationally if context-dependent switching of feedback controllers is possible in the human motor system. Specifically, we probe visuomotor feedback responses of our human participants in two different tasks-stop and hit-and under two different schedules. The first, blocked schedule, is used to measure the behaviour of stop and hit controllers in isolation, showing that it can only be described by two independent controllers with two different sets of control gains. The second, mixed schedule, is then used to compare how such behaviour evolves when participants regularly switch from one task to the other. Our results support our hypothesis that there is contextual switching of feedback controllers, further extending the accumulating evidence of shared features between feedforward and feedback control.

Time-to-Target Simplifies Optimal Control of Visuomotor Feedback Responses.

Visuomotor feedback responses vary in intensity throughout a reach, commonly explained by optimal control. Here, we show that the optimal control for a range of movements with the same goal can be simplified to a time-to-target dependent control scheme. We measure our human participants' visuomotor responses in five reaching conditions, each with different hand or cursor kinematics. Participants only produced different feedback responses when these kinematic changes resulted in different times-to-target. We complement our experimental data with a range of finite and non-finite horizon optimal feedback control (OFC) models, finding that the model with time-to-target as one of the input parameters best replicates the experimental data. Overall, this suggests that time-to-target is a critical control parameter in online feedback control. Moreover, we propose that for a specific task and known dynamics, humans can instantly produce a control signal without any additional online computation allowing rapid response onset and close to optimal control.

A Technique for Measuring Visuomotor Feedback Contributions to the Control of an Inverted Pendulum.

We developed a new technique to measure the contributions of rapid visuomotor feedback responses to the stabilization of a simulated inverted pendulum. Human participants balanced an inverted pendulum simulated on a robotic manipulandum. At a random time during the balancing task, the visual representation of the tip of the pendulum was shifted by a small displacement to the left or right while the motor response was measured. This response was either the exerted force against a fixation position, or the motion to re-stabilize the pendulum in the free condition. Our results demonstrate that rapid involuntary visuomotor feedback responses contribute to the stabilization of the pendulum.

Feedback Delay Changes the Control of an Inverted Pendulum.

We recently developed a simulated inverted pendulum in order to examine human sensorimotor control strategies for stabilization. This simulated system allows us to manipulate the visual and haptic feedback independently from the physical dynamics of the task. Here we examine the effect of sensory delay in a balancing task. Human participants attempted to balance an inverted pendulum (simulated on a robotic manipulandum) with three different added delays (25, 50, and 75 ms), where the same delay was added to both the visual and haptic feedback. Increasing sensory delays decreased the ability of the participants to stabilize the pendulum. Investigation into the online control of the pendulum showed that with longer delays participants reduced their movement frequency but increased the amplitudes of their corrections.

LQG framework explains performance of balancing inverted pendulum with incongruent visual feedback.

Successful manipulation of objects requires forming internal representations of the object dynamics. To do so, the sensorimotor system uses visual feedback of the object movement allowing us to estimate the object state and build the representation. One way to investigate this mechanism is by introducing a discrepancy between the visual feedback about the object's movement and the actual movement. This causes a decline in the ability to accurately control the object, shedding light about possible factors influencing the performance. In this study, we show that an optimal feedback control framework can account for the performance and kinematic characteristics of balancing an inverted pendulum when visual feedback of pendulum tip did not represent the actual pendulum tip. Our model suggests a possible mechanism for the role of visual feedback on forming internal representation of objects' dynamics.

Controller Gains of an Inverted Pendulum are Influenced by the Visual Feedback Position.

In this study we experimentally test and model the control behavior of human participants when controlling inverted pendulums of different dynamic lengths, and with visual feedback of varying congruence to these dynamic lengths. Participants were asked to stabilize the inverted pendulum of L = 1 m and L = 4 m, with visual feedback shown at various distances along the pendulum. We fit a family of linear models to the control input (cart velocity) applied by participants. We further tested the models by predicting this control input for a pendulum with dynamic length L = 2 m and comparing the prediction to the experimental data. We show that the sum of proportional error correction and a term inversely proportional to visual feedback gain can well describe the control in human participants.

A Simulated Inverted Pendulum to Investigate Human Sensorimotor Control.

Sensorimotor control regulates balance and stability as well as adaptation to the external environment. We introduce the use of a simulated inverted pendulum to study human sensorimotor control, demonstrating that this system introduces similar control challenges to human subjects as a physical inverted pendulum. Participants exhibited longer stabilization of the system as the pendulum length between the hand and the center of mass increased while the required control input varied in a non-monotonic, yet predictable manner. Finally, we show that the experimental results can be modelled as a PD controller with a time delay of $\tau = 140$ ms, matching the human visuomotor delay. Our results provide evidence of the importance of vision in a control of unstable systems and serve as a proof of concept of a simulated inverted pendulum.

Influence of Visual Feedback on the Sensorimotor Control of an Inverted Pendulum.

We examine the visual influence of stabilization in human sensorimotor control using a simulated inverted pendulum. As the inverted pendulum is fully simulated, we are able to manipulate the visual feedback independently from the dynamics during the motor control task. Human subjects performed a balancing task of an upright pendulum on a robotic manipulandum in two different visual feedback conditions. First we examined how subjects perform a task where the visual feedback is congruent with the pendulum dynamics. Second we tested how subjects performed when the physical dynamics were fixed but the visual feedback of the pendulum length was modulated. Subjects exhibited deficits in the control of the pendulum when haptic and visual feedback did not match, even when the visual feedback provided more sensitive information about the state of the pendulum. Overall we demonstrate the importance of accurate feedback regarding task dynamics for stabilization.