Response to perturbation in constant tau-dot versus constant proportional rate models of visually guided braking

Stable visually guided reaching does not require an internal feedforward model to compensate for internal delay: Data and model

Visually guided reaches are performed in ≈1s. Given unstable feedback control with neural transmission delay, stable visually guided reaching is assumed to require internal feedforward models that generate simulated feedback without delay that combines with actual feedback for stability. We investigated whether stable visually guided reaching requires internal models to handle such delay. Participants performed rapid targeted reaches in a virtual environment with different mappings between speeds of the hand and hand avatar. First, participants reached with visual guidance and constant mapping. Second, feedforward reaches were performed with constant mapping and hand avatar only visible at reach start and end. Reaches were accurate. Third, participants performed reaches with visual guidance and different mappings every trial. We expected performance as in the first condition. Finally, feedforward reaches with variable mapping yielded large errors showing visual guidance in the previous condition was successful despite an ineffective internal model. We simulated reaches using a proportional rate model with disparity Tau controlling the virtual Equilibrium Point in an Equilibrium Point (EP) model. The time dimensioned information and dynamic remained stable with delayed feedback. Finally, we fit movement times using the proportional rate EP model with 0msec, 50msec, and 100msec delay. With the fitted model parameters, we compared the model reach trajectories with the behavioral trajectories. Stable visually guided reaching did not require an internal feedforward model.

Time for Space and the Stability of Prospective Control: Reaching-to-Grasp Gibson

Gibson formulated an approach to goal-directed behavior using prospective information in the context of visually guided locomotion and manual behavior. The former was Gibson's paradigm case, but it is the rapidity of targeted reaching that has provided the special challenge for stable control. Recent treatments of visually guided reaching assume that internal forward models are required to generate stable behavior given delays caused by neural transmission times. Internal models are representations of the sort eschewed by Gibson in favor of prospective information. Reaching is usually described as guided using relative distances of hand and target, but prospective information is usually temporal rather than spatial. We describe proportional rate control models that incorporate time dimensioned prospective information and show they remain stable in the face of delays. The use of time-dimensioned prospective information removes the need for internal models for stable behavior despite neural transmission delays and allows Gibson's approach to prevail.

Control of visually guided braking using constant-[Formula: see text] and proportional rate

This study investigated the optical information and control strategies used in visually guided braking. In such tasks, drivers exhibit two different braking behaviors: impulsive braking and continuously regulated braking. We designed two experiments involving a simulated braking task to investigate these two behaviors. Participants viewed computer displays simulating an approach along a linear path over a textured ground surface toward a set of road signs. The task was to use a joystick as a brake to stop as close as possible to the road signs. Our results showed that participants relied on a weak constant-[Formula: see text] strategy (Bingham 1995) when regulating the brake impulsively. They used discrete [Formula: see text] values as critical values and they regulated the brake so as not to let [Formula: see text] fall below these values. Our results also showed that proportional rate control (Anderson and Bingham 2010, 2011) is used in continuously regulated braking. Participants initiated braking at a certain proportional rate value and controlled braking so as to maintain that value constant during the approach. Proportional rate control is robust because the value can fluctuate within a range to yield good performance. We argue that proportional rate control unifies the information-based approach and affordance-based approach to visually guided braking.

Information and control strategy to solve the degrees-of-freedom problem for nested locomotion-to-reach

Locomoting-to-reach to a target is a common visuomotor approach behavior that consists of two nested component actions: locomotion and reaching. The information and control strategies that guide locomotion and reaching in isolation are well studied, but their interaction during locomoting-to-reach behavior has received little attention. We investigated the role of proportional rate control in unifying these components into one action. Individuals use this control strategy with hand-centric disparity-based τ information to guide seated reaching (Anderson and Bingham in Exp Brain Res 205:291-306. doi: 10.1007/s00221-010-2361-9 , 2010) and use it with sequential information to perform targeted locomotion to bring an outstretched arm and hand to a target; first with eye-centric τ information and then hand-centric τ information near the target (Anderson and Bingham in Exp Brain Res 214:631-644. doi: 10.1007/s00221-011-2865-y , 2011). In the current study, participants performed two tasks: locomoting to bring a rigidly outstretched arm and hand to a target (handout), and locomoting to initiate and guide a reach to a target (locomoting-to-reach). Movement trajectories were analyzed. Results show that participants used proportional rate control throughout both tasks, in the sequential manner that was found by Anderson and Bingham (Exp Brain Res 214:631-644. doi: 10.1007/s00221-011-2865-y , 2011). Individual differences were found in the moment at which this information switch occurred in the locomoting-to-reach task. Some participants appeared to switch to proportional rate control with hand-τ once the hand came into view and others switched once the reaching component was complete and the arm was fully outstretched. In the locomoting-to-reach task, participants consistently initiated reaches when eye-τ specified a time-to-contact of 1.0 s. Proportional rate control provides a solution to the degrees-of-freedom problem in the classic manner, by making multiple things one.