Adaptive control for insect leg position: controller properties depend on substrate compliance

This paper concentrates on the system that controls the femur-tibia joint in the legs of the stick insect, Carausius morosus. Earlier investigations have shown that this joint is subject to a mixture of proportional and differential control whereby the differential part plays a prominent role. Experiments presented here suggest another interpretation: single legs of a stick insect were systematically perturbed using devices of different compliance and compensatory forces and movements monitored. When the compliance is high (soft spring), forces are generated that return the leg close to its original position. When the compliance is low (stiff spring), larger forces are generated but sustained changes in position occur that are proportional to the force that is applied. Selective ablation of leg sense organs showed that the leg did not maintain its position after elimination of afferents of the femoral chordotonal organ. Ablation of leg campaniform sensilla had no effect. These data support the idea that different control strategies are used, depending upon substrate compliance. In particular, what we and other authors have called a differential controller, is now considered as an integral controller that "intelligently gives up" when the correlation between motor output and movement of the leg is low.

Mechanisms of stick insect locomotion in a gap-crossing paradigm

Locomotion of stick insects climbing over gaps of more than twice their step length has proved to be a useful paradigm to investigate how locomotor behaviour is adapted to external conditions. In this study, swing amplitudes and extreme positions of single steps from gap-crossing sequences have been analysed and compared to corresponding parameters of undisturbed walking. We show that adaptations of the basic mechanisms concern movements of single legs as well as the coordination between the legs. Slowing down of stance velocity, searching movements of legs in protraction and the generation of short steps are crucial prerequisites in the gap-crossing task. The rules of leg coordination described for stick insect walking seem to be modified, and load on the supporting legs is assumed to have a major effect on coordination especially in slow walking. Stepping into the gap with a front leg and antennal contact with the far edge of the gap provide information, as both events influence the following leg movements, whereas antennal "non-contact" seems not to contain information. Integration of these results into the model of the walking controller can improve our understanding of insect locomotion in highly irregular environments.

A recurrent network for landmark-based navigation

A new type of network is proposed that can be applied to landmark navigation. It solves the guidance task, that is, it finds a nonvisually marked location using knowledge concerning its spatial relation to other, visible landmarks. The path to the searched location is not disturbed if a landmark is not visible for some time. The network can also describe findings obtained by experiments with insects and rodents, where the position of the landmarks has been changed after training. In this net, recognition does not occur by searching for a match between a pattern seen and the same pattern being stored but by searching for a match between a pattern seen with a prediction calculated from different data. A simple extension allows a unique match of the landmarks seen with the items stored in memory. With this extension a recognition of the individual landmark is not necessary. A specific output unit of the network can be interpreted in such a way as to show properties of place cells found in vertebrates and the function of the network proposed here as to determine the input to a place cell. The model can explain the observation that a given place cell can also be active when the animal moves in a different environment. An extension is discussed of how the network could be exploited for recognition-triggered response that allows animals to follow fixed routes.

The functional sense of central oscillations in walking

Rhythmic motor output is generally assumed to be produced by central pattern generators or, more specific, central oscillators, the rhythmic output of which can be entrained and modulated by sensory input and descending control. In the case of locomotor systems, the output of the central system, i.e., the output obtained after deafferentation of sensory feedback, shows many of the temporal characteristics of real movements. Therefore the term fictive locomotion has been coined. This article concentrates on a specific locomotor behavior, namely walking; in particular walking in invertebrates. In contrast to the traditional view, an alternative hypothesis is formulated to interpret the functional sense of these central oscillations which have been found in many cases. It is argued that the basic function of the underlying circuit is to avoid cocontraction of antagonistic muscles. Such a system operates best with an inherent period just above the maximum period observed in real walking. The circuit discussed in this article (Fig. 2) shows several properties in common with results described as "fictive walking". It furthermore could explain a number of properties observed in animals walking in different situations. According to this hypothesis, the oscillations found after deafferentation are side effects occurring in specific artificial situations. If, however, a parameter called central excitation is large enough, the system can act as a central oscillator that overrides the sensory input completely.

Two kinds of body representation are used to control hand movements following tactile stimulation

The task of reaching with a hand toward a target given in space is generally described as an ill-posed problem. It is often assumed that some kind of internal body model is required to solve this problem. This article provides information concerning the nature of this representation. Experiments were carried out in which blindfolded subjects were stimulated mechanically at one of eight possible stimulation sites on the legs and then asked to move one hand as quickly as possible to the stimulated site. In nine different postures of legs and hands, the frequency was recorded of the use of either hand. In addition, reaction times (RT) were measured and in two choice reaction tasks RTs were measured for different conditions (morphologically compatible vs morphologically incompatible, hands parallel vs hands crossed): The results support the hypothesis that the representation of the body is based on at least two systems, one which provides spatial information concerning the body position and a second one which is based on a morphological representation. According to this hypothesis, our results could be described by the following schema. Following the application of the stimulus, two processes were started in parallel. One concerned the activation of the spatial representation of body position, including the position of stimulus site and the possible response sites. This was more difficult, i.e., took more time, when the hands were crossed. Within this spatial representation, the distances between stimulus site and response sites were determined, and it was found that the smaller the distance, the more strongly the hands were activated. Simultaneously, in a second process the response site which was morphologically ipsilateral to the stimulus was excited. This schema could explain our results: In the behavioral experiments that hand which was most strongly excited, and which therefore exceeded a threshold sooner, won the decision and showed smaller RT values. In the choice reaction experiments, the winning hand was compared with the externally given task. The more strongly, according to the given task, the wrong hand was excited, the longer was the RT of the response.

A biologically inspired controller for hexapod walking: simple solutions by exploiting physical properties

The locomotor system of slowly walking insects is well suited for coping with highly irregular terrain and therefore might represent a paragon for an artificial six-legged walking machine. Our investigations of the stick insect Carausius morosus indicate that these animals gain their adaptivity and flexibility mainly from the extremely decentralized organization of the control system that generates the leg movements. Neither the movement of a single leg nor the coordination of all six legs (i.e., the gait) appears to be centrally pre-programmed. Thus, instead of using a single, central controller with global knowledge, each leg appears to possess its own controller with only procedural knowledge for the generation of the leg's movement. This is possible because exploiting the physical properties avoids the need for complete information on the geometry of the system that would be a prerequisite for explicitly solving the problems. Hence, production of the gait is an emergent property of the whole system, in which each of the six single-leg controllers obeys a few simple and local rules in processing state-dependent information about its neighbors.

Load-regulating mechanisms in gait and posture: comparative aspects

How is load sensed by receptors, and how is this sensory information used to guide locomotion? Many insights in this domain have evolved from comparative studies since it has been realized that basic principles concerning load sensing and regulation can be found in a wide variety of animals, both vertebrate and invertebrate. Feedback about load is not only derived from specific load receptors but also from other types of receptors that previously were thought to have other functions. In the central nervous system of many species, a convergence is found between specific and nonspecific load receptors. Furthermore, feedback from load receptors onto central circuits involved in the generation of rhythmic locomotor output is commonly found. During the stance phase, afferent activity from various load detectors can activate the extensor part in such circuits, thereby providing reinforcing force feedback. At the same time, the flexion is suppressed. The functional role of this arrangement is that activity in antigravity muscles is promoted while the onset of the next flexion is delayed as long as the limb is loaded. This type of reinforcing force feedback is present during gait but absent in the immoble resting animal.

Simulation of complex movements using artificial neural networks

A simulated network for controlling a six-legged, insect-like walking system is proposed. The network contains internal recurrent connections, but important recurrent connections utilize the loop through the environment. This approach leads to a subnet for controlling the three joints of a leg during its swing which is arguably the simplest possible solution. The task for the stance subnet appears more difficult because the movements of a larger and varying number of joints (9-18: three for each leg in stance) have to be controlled such that each leg contributes efficiently to support and propulsion and legs do not work at cross purposes. Already inherently non-linear, this task is further complicated by four factors: 1) the combination of legs in stance varies continuously. 2) during curve walking, legs must move at different speeds, 3) on compliant substrates, the speed of the individual legs may vary unpredictably, and 4) the geometry of the system may vary through growth and injury or due to non-rigid suspension of the joints. This task appears to require some kind of "motor intelligence". We show that an extremely decentralized, simple controller, based on a combination of negative and positive feedback at the joint level, copes with all these problems by exploiting the physical properties of the system.

Curve walking in crayfish

Curve walking of crayfish Astacus leptodactylus was investigated by exploiting their optomotor response. The animal walked while spatially fixed on a motor-driven treadmill and turning behaviour was induced by an optical stimulus, a pattern consisting of vertical stripes moving in a horizontal direction. In this open-loop situation, the crayfish maintains the same step frequency for the legs on both sides of the body for low and intermediate turning speeds, but increases the step amplitude of the outer legs 2, 3 and 4 by shifting the posterior extreme position (PEP) of these legs in a posterior direction and reduces the step amplitude of inner leg 5 by shifting the PEP of this leg in an anterior direction. Furthermore, the main movement direction of the legs can change relative to the body. This was observed for outer leg 5 and also, at higher turning speeds, for outer leg 2. As coordinating influences between contra- and ipsilateral legs were found directly to influence only the anterior extreme position of the legs, these results indicate that the mechanisms controlling curve walking may be different from those controlling normal leg coordination.

A fast, three-layer neural network for path finding

A path-planning algorithm is proposed to find a path based on local rules applied to a three-layer artificial neural network. Each layer consists of two-dimensionally arranged neurons with recurrent connections within a limited neighbourhood. The output of one layer determines the weights of the connections in the next layer. In principle, the method is based on a diffusion process, but is modified such that it does not suffer from several drawbacks involved in this algorithm. By application of a nonlinear transformation in layer 2, the diffusion front has the qualitative properties of a propagation wave. Therefore, limited resolution of the units is not critical, in contrast to classical diffusion algorithms. Furthermore, the algorithm generally does not suffer from the superposition of diffusion gradients when several paths are possible. The diffusion takes place in a space covered with 'obstacle potentials' which decrease the velocity of the diffusion front. In this way the path can maintain an adjustable safety margin in relation to the obstacles, for example, to cope with problems of incomplete knowledge of the obstacle's position. The algorithm thus combines the advantages of the diffusion algorithm, namely avoidance of local minima, of wave propagation, i.e. coping with limited resolution, and the potential field approach, i.e. maintaining a safety margin in relation to obstacles. The distributed architecture also allows for 'spatial interpolation' between the units (coarse coding), thereby providing smooth path forms. A comparison with paths developed by human subjects shows some similarity on the qualitative level, but there are also obvious differences.

A modular artificial neural net for controlling a six-legged walking system

A system that controls the leg movement of an animal or a robot walking over irregular ground has to ensure stable support for the body and at the same time propel it forward. To do so, it has to react adaptively to unpredictable features of the environment. As part of our study of the underlying mechanisms, we present here a model for the control of the leg movement of a 6-legged walking system. The model is based on biological data obtained from the stick insect. It represents a combined treatment of realistic kinematics and biologically motivated, adaptive gait generation. The model extends a previous algorithmic model by substituting simple networks of artificial neurons for the algorithms previously used to control leg state and interleg coordination. Each system controlling an individual leg consists of three subnets. A hierarchically superior net contains two sensory and two 'premotor' units; it rhythmically suppresses the output of one or the other of the two subordinate nets. These are continuously active. They might be called the 'swing module' and the 'stance module' because they are responsible for controlling the swing (return stroke) and the stance (power stroke) movements, respectively. The swing module consists of three motor units and seven sensory units. It can produce appropriate return stroke movements for a broad range of initial and final positions, can cope with mechanical disturbances of the leg movement, and is able to react to an obstacle which hinders the normal performance of the swing movement. The complete model is able to walk at different speeds over irregular surfaces. The control system rapidly reestablishes a stable gait when the movement of the legs is disturbed.

Control of Three- and Four-Joint Arm Movement: Strategies for a Manipulator With Redundant Degrees of Freedom

Control of arm movements when the number of joints exceeds the degrees of freedom necessary for the task requires a strategy for selecting specific arm configurations out of an infinite number of possibilities. This report reviews strategies used by human subjects to control the shoulder, elbow, and wrist (three degrees of freedom) while moving a pointer to positions in a horizontal plane (two degrees of freedom). Analysis of final arm configurations assumed when the pointer was at the target showed the following: (a) Final arm configurations were virtually independent of the configuration at the start of the pointing movement, (b) subjects avoided configurations subjectively felt to be uncomfortable (e.g., those with extreme flexion or extension of the wrist), and (c) the results could be simulated by assigning hypothetical cost functions to each joint and selecting the arm configuration that minimized the sum of the costs. The fitted cost functions qualitatively agreed with psychophysically determined comfort; they appeared to depend on joint angle and on muscular effort. Simple neural networks can learn implicit representations of these cost functions and use them to specify final arm configurations. The minimum cost principle can be extended to movements that use the fingers as a fourth movable segment. For this condition, however, experiments showed that final configurations of the arm depended upon initial configurations. Analysis of movement trajectories for arms with three degrees of freedom led to a control model in which the minimum cost principle is augmented by a mechanism that distributes required joint movements economically among the three joints and a mechanism that implements a degree of mass-spring control.

CONTROL OF BODY HEIGHT IN A STICK INSECT WALKING ON A TREADWHEEL

The properties of the system that controls the distance between body and ground was investigated in the stick insect Carausius morosus. The insect walked on a lightweight double treadwheel under open-loop or closed-loop conditions. The open-loop investigations show that the dynamic behaviour of the height-control system in the walking animal can be described in terms of a simple proportional system with negligible dynamic properties, and it is therefore much simpler than the height-control system in the standing animal. Under open-loop conditions, we found no coupling between contralateral or ipsilateral legs. This agrees with the findings on standing animals. The force- height characteristic shows two ranges, in each of which the system exhibits a linear relationship but a different slope. Under closed-loop conditions, the force-height characteristic shows the same two linear ranges, but the slopes are greater than under open-loop conditions. Because the height controller of each leg can be considered to act like a spring, this result means that under closed-loop conditions the controller is stiffer than it is under open-loop conditions.

Coordination of the legs of a slow-walking cat

On the basis of behavioural studies the influences that coordinate the movement of the legs of a slowly walking cat have been investigated. The recording method applied here allows for the measurement of forward and backward movement of the legs which are called swing and stance movements, respectively. Influences between contralateral legs, i.e. both front legs or both hind legs, are stronger than those occurring between ipsilateral legs, i.e. front and hind leg of the same side. Influences which coordinate the front legs seem to be of the same kind as those for the hind legs. These influences are symmetrical, which means that the same type of influence acts from right to left leg and in the reverse direction. Two types of influences are described for contralateral legs: 1. When the influencing leg performs a swing movement, the influenced leg is prevented from starting a swing movement. 2. When the influencing leg performs a stance movement, the probability that the influenced leg starts a swing movement increases as the influencing leg moves backwards during its stance movement. In contrast to contralateral coupling, the ipsilateral influences are symmetric, i.e. a different influence acts from front to hind leg than does in the reverse direction. The front leg is influenced to start a swing when both legs have approached each other to a given value. The hind leg is influenced to start a stance movement after the front leg has begun its swing.

What mechanisms coordinate leg movement in walking arthropods?

The construction of artificial walking machines has been a challenging task for engineers for several centuries. Advances in computer technology have stimulated this research in the past two decades, and enormous progress has been made, particularly in recent years. Nevertheless, in comparing the walk of a six-legged robot with the walk of an insect, the immense differences are immediately obvious. The walking of an animal is much more versatile, and seems to be more effective and elegant. Thus it is useful to consider the corresponding biological mechanisms in order to apply these or similar mechanisms to the control of walking legs in machines. Until recently, little information on this paper summarizes recent developments.

Coactivating Influences Between Neighbouring Legs in Walking Insects

When the movement of one leg of a walking stick insect is interrupted during the power stroke, the force developed by other legs is increased. This effect is shown to occur between all orthogonal nearest-neighbour legs except for the two hind legs. Such effects do not occur between diagonal or next nearest-neighbour pairs. The possible function of these ‘coactivating’ influences is assumed to be to enable the animal to increase the total force propelling the body.