Holk Cruse

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.

Constraints for joint angle control of the human arm

The targeting movements of a human arm were examined when restricted to a horizontal plane. The three joints at shoulder, elbow, and wrist are allowed to move. Thus, the system is redundant and needs constraints. A model calculation using a simple form of constraint is found to describe the experimental results: a cost function is applied to each joint. The constraint consists in minimizing the sum of the costs of all three joints. The cost functions might be interpreted as to describing the energy cost necessary to move the joint and/or represent a mechanism which avoids singularities.

Walknet—a biologically inspired network to control six-legged walking

To investigate walking we perform experimental studies on animals in parallel with software and hardware simulations of the control structures and the body to be controlled. Therefore, the primary goal of our simulation studies is not so much to develop a technical device, but to develop a system which can be used as a scientific tool to study insect walking. To this end, the animat should copy essential properties of the animals. In this review, we will first describe the basic behavioral properties of hexapod walking, as the are known from stick insects. Then we describe a simple neural network called Walknet which exemplifies these properties and also shows some interesting emergent properties. The latter arise mainly from the use of the physical properties to simplify explicit calculations. The model is simple too, because it uses only static neuronal units. Finally, we present some new behavioral results.

On the cost functions for the control of the human arm movement

The aim of our investigation is to understand the mechanisms which control the movement of the human arm. The arm is here considered as a redundant system: the shoulder, elbow and wrist joints, which provide three degrees of freedom, combine to move the hand in a horizontal plane, i.e. a two dimensional space. Thus the system has one extra degree of freedom. Earlier investigations of the static situation led to the hypothesis that independent cost functions were attached to each of the three joints and that the configuration chosen for a given target position is that which provides the minimum total cost (Cruse 1986). The aim of the current investigation was to look for measurable values corresponding to the hypothetical cost functions. Experiments using pointers of different lengths attached to the hand showed that the strategy in choosing the joint angles are independent of the limb length. The muscle force necessary to reach a given angle is increased by a spring mounted across a joint. In this situation the angles of the loaded joint are changed for a given target point to give way to the force effect. This leads to the conclusion that the hypothetical cost functions are not independent of the physiological costs necessary to hold the joint at a given angle. The cost functions seem to depend on joint angle and on the force which is necessary to hold the joint in a given position. Cost functions are measured by psychophysical methods. The results showU-shaped curves which can be approximated by parabolas. The position of minimum cost (maximum comfort) for one joint showed no or weak dependency on the angles of the other joints. For each subject these “psychophysical” cost functions are compared with the hypothetical cost functions. The comparison showed reasonable agreement. This supports the assumption that the psychophysically measured “comfort functions” provide a measure for the hypothetical cost functions postulated to explain the targeting movements. Targeting experiments using a four joint arm which has two extra degrees of freedom showed a much larger scatter compared to the three joint arm. Nevertheless, the results still conform to the hypothesis that also in this case the minimum cost principle is applied to solve the redundancy problem. As the cost function for the whole arm shows a large minimum valley, quite a large range of arm positions is possible of about equal total costs. The scatter does not result from pure randomness but seems to be mainly produced by the fact that the angles at the end of the movement depend on the value of the joint angles at the beginning of the movement.

The function of the legs in the free walking stick insect,Carausius morosus

Summary1.The function of the legs of a free walking mature stick insect (Carausius morosus) is investigated in four different walking situations: walks on a horizontal path, walks on a horizontal plane, walks on a horizontal beam with the body hanging from the beam and walks up a vertical path.2.The geometrical data, which are necessary to describe the movement of the legs, are determined (Tables 1, 2, 3, 4; Figs. 2, 3, 4, 5).3.The forces, by which the leg of a free walking animal acts on the walking surface, are measured (Table 5). Typical results are shown in Figures 6, 7, 8, 9 for each walking situation. From these forces and the known geometrical relationships the torques, which are produced by the antagonistic muscle systems at each leg joint, can be calculated (Fig. 10). Those torques calculated for different typical leg positions are shown in Table 6, 7, 8, 9 for each walking situation.4.The results show that many things change depending upon the particular walking situation: the angular range in which the leg is moved (Table 2, Fig. 4), the activation and the kind of predominance of the antagonistic muscles (Table 6, 7, 8, 9), and especially the function of the single legs. Additionally, when looking at the direction of movement of a limb one cannot say which of the antagonistic muscles is predominating. Sometimes just the muscle opposite to the actual movement predominates (Table 7).5.For two walking situations the function of the legs can be demonstrated in a simple way. In a walk on the horizontal plane: the forelegs mainly have feeler function, the middlelegs have only supporting function, while the hindlegs have supporting as well as propulsive function. In a walk with the body hanging from the horizontal beam: forelegs and hindlegs are used mainly to support the body, while the middlelegs additionally provide the propulsive forces.6.In walking up the vertical path all legs provide support and propulsive forces. When walking on the horizontal path fore- and middlelegs on theone hand and hindlegs on the other form the static construction of a three centered arch (Fig. 11). In the same way when the insect walks hanging from the horizontal beam, a hanging three centered arch is assumed. The importance of this construction is discussed.

The Human Arm as a Redundant Manipulator: The Control of Path and Joint Angles

The movements studied involved moving the tip of a pointer attached to the hand from a given starting point to a given end point in a horizontal plane. Three joints — the shoulder, elbow and wrist —were free to move. Thus the system represented a redundant manipulator. The coordination of the movements of the three joints was recorded and analyzed. The study concerned how the joints are controlled during a movement. The results are used to evaluate several current hypotheses for motor control.Basically, the incremental changes are calculated so as to move the tip of the manipulator along a straight line in the workspace. The values of the individual joints seem to be determined as follows. Starting from the initial values the incremental changes in the three joint angles represent a compromise between two criteria: 1) the amount of the angular change should be about the same in the three joints, and 2) the angular changes should minimize the total cost of the arm position as determined by cost functions defined for each joint as a function of angle.By itself, this mechanism would produce strongly curved trajectories in joint space which could include additional acceleration and deceleration in a joint. These are reduced by the influence of a third criterion which fits with the mass-spring hypothesis. Thus the path is calculated as a compromise between a straight line in workspace and a straight line in joint space. The latter can produce curved paths in the workspace such as were actually found in the experiments.A model calculation shows that these hypotheses can qualitatively describe the experimental findings.

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.

A network model for the control of the movement of a redundant manipulator

In an earlier investigation (Cruse and Brüwer 1987) an algorithmic model was proposed which describes targeting movements of a human arm when restricted to a horizontal plane. As three joints at shoulder, elbow and wrist are allowed to move, the system is redundant. Two models are discussed here which replace this algorithmic model by a network model. Both networks solve the static problem, i.e. they provide the joint angles which the arm has to adopt in order to reach a given point in the workspace. In the first model the position of this point is given in the form ofx —y coordinates, the second model obtains this information by means of a retina-like input layer. The second model is expanded by a simple procedure to describe movements from a start to an end point. The results qualitatively correspond to those obtained from human subjects. The advantages of the network models in comparison to the algorithmic model are discussed.

Walking: a complex behavior controlled by simple networks

Understanding how behavior is controlled requires that modeling be combined with behavioral, electrophysiological, and neuroanatomical investigations. One problem in studying motor systems is that they have considerable autonomy; they are not driven solely by inputs. Choosing walking as the object of study is promising because it is a comparably simple and easy-to-elicit behavior, but it exhibits the special feature of most motor behavior—the interaction between central, autonomous components and peripheral, sensory influences. This article reviews the control of walking in stick insects, beginning with behavioral studies of single-leg control and the interleg coordinating mechanisms. These behavioral results are tested and supported by modeling the control system in an artificial neural network computer simulation and a six-legged robot. Supporting neurophysiological results also are considered. Together, the results indicate that the high flexibility and adaptability is based on a simple distributed control structure.

The control of the anterior extreme position of the hindleg of a walking insect, Carausius morosus

ABSTRACT. It is shown that the anterior extreme position of the hindleg of a walking insect is not fixed relative to the body but is determined by the position of the ipsilateral middleleg. This mechanism presumably helps the animal to find support for the hindleg when climbing on branches.