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Muscular hydrostats are organs composed entirely of packed arrays of incompressible muscles and lacking any skeletal support. Found in both vertebrates and invertebrates, they are of great interest for comparative biomechanics from engineering and evolutionary perspectives. The arms of cephalopods (e.g. octopus and squid) are particularly interesting muscular hydrostats because of their flexibility and ability to generate complex behaviors exploiting elaborate nervous systems. Several lines of evidence from octopus studies point to the use of both brain and arm-embedded motor control strategies that have evolved to simplify the complexities associated with the control of flexible and hyper-redundant limbs and bodies. Here, we review earlier and more recent experimental studies on octopus arm biomechanics and neural motor control. We review several dynamic models used to predict the kinematic characteristics of several basic motion primitives, noting the shortcomings of the current models in accounting for behavioral observations. We also discuss the significance of impedance (stiffness and viscosity) in controlling the octopus's motor behavior. These factors are considered in light of several new models of muscle biomechanics that could be used in future research to gain a better understanding of motor control in the octopus. There is also a need for updated models that encompass stiffness and viscosity for designing and controlling soft robotic arms. The field of soft robotics has boomed over the past 15 years and would benefit significantly from further progress in biomechanical and motor control studies on octopus and other muscular hydrostats.

The inverse kinematics problem deals with the question of how the nervous system coordinates movement to resolve redundancy, such as in the case of arm reaching movements where more degrees of freedom are available at the joint versus hand level. In particular, this work focuses on determining which coordinate frames can best represent human movements, allowing the motor system to solve the inverse kinematics problem in the presence of kinematic redundancies. In particular, in this work we used a multi-dimensional sparse source separation method called FADA to derive sets of basis functions (here called sources) for both the task and joint spaces, with joint space being represented in terms of either the absolute or anatomical joint angles. We assessed the similarities between the joint and task sources in each of these joint representations. We found that the time-dependent profiles of the absolute reference frame’s sources show greater similarity to those of the corresponding sources in the task space. This result was found to be statistically significant. Hence, our analysis suggests that the nervous system represents multi-joint arm movements using a limited number of basis functions, to allow for simple transformations between task and joint spaces. Importantly, joint space seems to be represented in terms of an absolute reference frame to achieve successful performance and simplify inverse kinematics transformations in the face of the existing kinematic redundancies. Further studies will be needed to determine the generalizability of this finding and its implications for neural control of movement.

During evolution, living systems, actively interacting with their environment, developed the ability, through sensorimotor contingencies, to construct functional spaces shaping their perception and their movements. These geometries were modularly embedded in specific functional neuro-architectures. In particular, human movements were shown to obey several empirical laws, such as the 2/3 power law, isochrony, or jerk minimization principles, which constrain and adapt motor planning and execution. Outstandingly, such laws can be deduced from a combination of Euclidean, affine, and equi-affine geometries, whose neural correlates have been partly detected in several brain areas including the cerebellum and the basal ganglia. Reviving Pellionisz and Llinas general hypothesis regarding the cerebrum and the cerebellum as geometric machines, we speculate that the cerebellum should be involved in implementing and/or selecting task-specific geometries for motor and cognitive skills. More precisely, the cerebellum is assumed to compute forward internal models to help specific cortical and subcortical regions to select appropriate geometries among, at least, Euclidean and affine geometries. We emphasize that the geometrical role of the cerebellum deserves a renewal of interest, which may provide a better understanding of its specific contributions to motor and associative (cognitive) functions.

The art of conducting involves a formal set of gestures, designed to convey musical meaning through movement. Interestingly, this relatively simple collection of gestures enables the conductor to communicate highly complex musical messages to the ensemble, indicating a non-trivial interaction between movement kinematics and sound. The following book chapter discusses this phenomenon. We first introduce movement-to-sound cross-modal mapping, surveying behavioral and neurophysiological research suggesting how spatio-kinetic features may be “translated” into aspects of musical rhythm, loudness and pitch. This is followed by a detailed discussion of the kinematics of right-hand gestures in conducting and their musical meanings. The kinematic correlates of expressive conducting are discussed by introducing some of the basic principles governing human movement generation. These principles include the wish to maximize motion smoothness, captured by the “minimum jerk” model, and the isochrony principle governing motor timing. Notwithstanding the considerable work that has already been invested in analyzing music conducting, many of the secrets underlying musical conducting still remain to be unraveled. This can only be achieved through a multidisciplinary approach, involving a variety of research disciplines, such as social psychology, computational motor control, musicology, mechanics, acoustics, as well as cross-modal sound-to-movement mapping.

Many motor behavioral studies have aimed at inquiring what general principles underlie movement generation during multi-joint movements. Careful analysis of the observed behavior has led to the formulation of several kinematic laws of motion describing the invariant geometric, kinematic, and timing patterns of the upper limb and full-body movements. Similar kinematic laws of motion also characterize motion perception by the brain. Different theoretical approaches aimed at investigating the origins of these kinematic laws of motion, and the observed geometrical and temporal invariants describing motion production and perception have been developed. These included optimization theory and differential geometry models, both types of models aiming at accounting for the tight coupling existing between spatial and temporal features of natural movements. The proposed geometrical models assume that a mixture of several Euclidean and non-Euclidean space-time geometries subserve motion production and perception. This theory has enabled us also to examine the issues associated with motor compositionality—namely, how the brain constructs complex movements by composing together elementary motor primitives. Here I will also describe the possibilities offered by the unraveled motion production and perception principles for guiding research and scholarly studies concerning the expression of brain space-time geometries in movement and the arts. Open questions are how artists might be utilizing similar principles in different artistic domains, whether such principles are shared among different creative modalities, and whether they may also underlie esthetic judgments and emotional expressions in the arts.

A complex action can be described as the composition of a set of elementary movements. While both kinematic and dynamic elements have been proposed to compose complex actions, the structure of movement decomposition and its neural representation remain unknown. Here, we examined movement decomposition by modeling the temporal dynamics of neural populations in the primary motor cortex of macaque monkeys performing forelimb reaching movements. Using a hidden Markov model, we found that global transitions in the neural population activity are associated with a consistent segmentation of the behavioral output into acceleration and deceleration epochs with directional selectivity. Single cells exhibited modulation of firing rates between the kinematic epochs, with abrupt changes in spiking activity timed with the identified transitions. These results reveal distinct encoding of acceleration and deceleration phases at the level of M1, and point to a specific pattern of movement decomposition that arises from the underlying neural activity. A similar approach can be used to probe the structure of movement decomposition in different brain regions, possibly controlling different temporal scales, to reveal the hierarchical structure of movement composition.

Here we review recent studies of the cortical circuits subserving the control of posture and movement. This topic is addressed from neurophysiological and evolutionary perspectives describing recent advancements achieved through experimental studies in humans and non-human primates. We also describe current debates and controversies concerning motor mapping within the motor cortex and the different computational approaches aimed at resolving the mystery around motor representations and computations. In recent years there is growing interest in the possibly modular organization of motor representations and dynamical processes and the potential of such studies to provide new clues into motor information processing. Hence this review focuses on motor modularity, highlighting the new research directions inspired by empirical findings and theoretical models developed within the last several years.

The complex motion abilities of the Octopus vulgaris have been an intriguing research topic for biologists and roboticists alike. Various studies have been conducted on the underlying control architectures employed by these high dimensional biological organisms. Researchers have attempted to replicate these architectures on robotic systems. Contrary to previous approaches, this study focuses on a robotic system, which is only morphologically similar to the Octopus vulgaris, and how it would behave under different control policies. This sheds light on the underlying optimality principles that these biological systems employ. Open loop control policies are obtained through a trajectory optimization method on a learned forward dynamic model. The motion patterns emerging from variations in morphology and environment were then derived to study the role of the body and environment. Results show that for the specific case of dynamic reaching with a soft appendage, the invariance in motion profile is a fundamental constraint imposed by the morphology and environment, independent from the controller. This suggests how morphological design can simplify stable control even for highly dimensional nonlinear dynamical systems and can provide insights into design of new soft robotic mechanisms.

In 1954, Penfield and Jasper's findings based on electric stimulation of epileptic patients led them to hypothesize that a sensory representation of the body should be found in the precuneus. They termed this representation the “supplementary sensory” area and emphasized that the exact form of this homunculus could not be specified on the basis of their results. In the decades that followed, their prediction was neglected. The precuneus was found to be involved in numerous motor, cognitive and visual processes, but no work was done on its somatotopic organization. Here, we used a periodic experimental design in which 16 human subjects (eight women) moved 20 body parts to investigate the possible body part topography of the precuneus. We found an anterior-to-posterior, dorsal-to-ventral, toes-to-tongue gradient in a mirror orientation to the SMA. When inspecting body-part-specific functional connectivity, we found differential connectivity patterns for the different body parts to the primary and secondary motor areas and parietal and visual areas, and a shared connectivity to the extrastriate body area, another topographically organized area. We suggest that a whole-body gradient can be found in the precuneus and is connected to multiple brain areas with different connectivity for different body parts. Its exact role and relations to the other known functions of the precuneus such as self-processing, motor imagery, reaching, visuomotor and other body–mind functions should be investigated.SIGNIFICANCE STATEMENTUsing fMRI, as well as sensitive spectral analysis, we found a new homunculus in the precuneus: an anterior-to-posterior, dorsal-to-ventral, toes-to-tongue somatotopic gradient in a mirror orientation to the SMA. When inspecting body-part-specific functional connectivity, we found differential connectivity patterns for the different body parts to the primary and secondary motor areas, parietal and visual areas, and a shared connectivity to the extrastriate body area, another topographically organized area. We suggest that a whole-body gradient can be found in the precuneus and is connected to multiple brain areas in a body-part-specific manner.