The Riemannian Geometry Theory of Visually-Guided Movement Accounts for Afterimage Illusions and Size Constancy.

This discussion paper supplements our two theoretical contributions previously published in this journal on the geometric nature of visual space. We first show here how our Riemannian formulation explains the recent experimental finding (published in this special issue on size constancy) that, contrary to conclusions from past work, vergence does not affect perceived size. We then turn to afterimage experiments connected to that work.

A Riemannian Geometry Theory of Synergy Selection for Visually-Guided Movement.

Bringing together a Riemannian geometry account of visual space with a complementary account of human movement synergies we present a neurally-feasible computational formulation of visuomotor task performance. This cohesive geometric theory addresses inherent nonlinear complications underlying the match between a visual goal and an optimal action to achieve that goal: (i) the warped geometry of visual space causes the position, size, outline, curvature, velocity and acceleration of images to change with changes in the place and orientation of the head, (ii) the relationship between head place and body posture is ill-defined, and (iii) mass-inertia loads on muscles vary with body configuration and affect the planning of minimum-effort movement. We describe a partitioned visuospatial memory consisting of the warped posture-and-place-encoded images of the environment, including images of visible body parts.

A Riemannian Geometry Theory of Three-Dimensional Binocular Visual Perception.

We present a Riemannian geometry theory to examine the systematically warped geometry of perceived visual space attributable to the size-distance relationship of retinal images associated with the optics of the human eye. Starting with the notion of a vector field of retinal image features over cortical hypercolumns endowed with a metric compatible with that size-distance relationship, we use Riemannian geometry to construct a place-encoded theory of spatial representation within the human visual system. The theory draws on the concepts of geodesic spray fields, covariant derivatives, geodesics, Christoffel symbols, curvature tensors, vector bundles and fibre bundles to produce a neurally-feasible geometric theory of visuospatial memory.

A Riemannian geometry theory of human movement: The geodesic synergy hypothesis.

Mass-inertia loads on muscles change with posture and with changing mechanical interactions between the body and the environment. The nervous system must anticipate changing mass-inertia loads, especially during fast multi-joint coordinated movements. Riemannian geometry provides a mathematical framework for movement planning that takes these inertial interactions into account.

The BUMP model of response planning: intermittent predictive control accounts for 10 Hz physiological tremor.

Physiological tremor during movement is characterized by ∼10 Hz oscillation observed both in the electromyogram activity and in the velocity profile. We propose that this particular rhythm occurs as the direct consequence of a movement response planning system that acts as an intermittent predictive controller operating at discrete intervals of ∼100 ms. The BUMP model of response planning describes such a system.

On theory of motor synergies.

Recently Latash, Scholz, and Schöner (2007) proposed a new view of motor synergies which stresses the idea that the nervous system does not seek a unique solution to eliminate redundant degrees of freedom but rather uses redundant sets of elemental variables that each correct for errors in the other to achieve a performance goal. This is an attractive concept because the resulting flexibility in the synergy also provides for performance stability. But although Latash et al.

The BUMP model of response planning: variable horizon predictive control accounts for the speed-accuracy tradeoffs and velocity profiles of aimed movement.

The BUMP model is a comprehensive discrete-time computational model of response planning. Developed within the Adaptive Model Theory framework, it is based on intermittent optimal control. The theory posits a basic unit of motor production (BUMP) that is determined by a planning system that operates intermittently at fixed intervals of time.

Motor maps and synergies.

Consider the process of raising and lowering the arm in the sagittal plane. Different parts of different muscles operate over different sectors of the angular range. How and why does the nervous system implement this differential muscle activation according to joint angle? We contend that such control depends on the adaptive formation of motor maps.

Degrees of freedom and motor planning in purposive movement.

This paper presents empirical evidence suggesting that healthy humans can perform a two degree of freedom visuo-motor pursuit tracking task with the same response time delay as a one degree of freedom task. In contrast, the time delay of the response is influenced markedly by the nature of the motor synergy required to produce it. We suggest a conceptual account of this evidence based on adaptive model theory, which combines theories of intermittency from psychology and adaptive optimal control from engineering.

An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships.

A new view on visuomotor channels: the case of the disappearing dynamics.

A considerable body of kinematic data supports the proposal that independent visuomotor channels are involved in the control of the transport and grip components of reach and grasp. These channels are seen as having separate perceptual inputs, outputs and internal processing and are thought by some to correspond to independent neuroanatomical pathways. The idea that different groups of muscles and biomechanical structures can be controlled independently is attractive, but this kinematically-inspired hypothesis fails to take into account the complexity of the dynamic relationships and their interactions within the neuromusculoskeletal system.

A simulation study of the degrees of freedom of movement in reaching and grasping.

The question of independently controlled components in the act of reaching and grasping has attracted interest experimentally and theoretically. Data from 35 studies were recently found consistent with simulated kinematic finger and thumb trajectories optimised for minimum jerk. The present study closely reproduces those trajectories using a discrete-time model based on minimum acceleration.

Evidence for internal representation of a static nonlinearity in a visual tracking task.

A group of 24 participants was given over 3 h practice at a visual pursuit tracking task with a pronounced static nonlinearity between movement of the joystick and the resulting deflection of the response cursor. The aim was twofold: (1) to determine whether or not participants compensated for the nonlinearity and (2) to show that any such compensation involved the formation of an internal representation of the nonlinear relationship between movement of the joystick as sensed kinaesthetically and/or visually and movement of the response cursor as sensed visually. Results show that participants introduce partial compensation for the static nonlinearity.

Anisotropic tracking: evidence for automatic synergy formation in a bimanual task.

Investigation of interlimb synergy has become synonymous with the study of coordination dynamics and is largely confined to periodic movement. Based on a computational approach this paper demonstrates a method of investigating the formation of a novel synergy in the context of stochastic, spatially asymmetric movements. Nine right-handed participants performed a two degrees of freedom (2D) "etch-a-sketch" tracking task where the right hand controlled the horizontal position of the response cursor on the display while the left hand controlled the vertical position.