Thomas Kindermann

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.

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.

Behavior and adaptability of a six-legged walking system with highly distributed control

A situated, moderately complex kinematic system—here an 18-degree-of-freedom six-legged walking system—can show a variety of behaviors, even when controlled by a relatively simple controller. Therefore, a detailed quantitative study of the behavior of such a system is necessary to achieve an understanding of its properties. This “artificial ethology” is applied to a controller with a decentralized structure that uses essential design characteristics of its biological model, the stick insect. The system takes advantage of recurrent connections that establish a loop through the environment. Despite its completely reactive nature, the system can adapt to unpredictable external conditions with no need for specific reprogramming. Leg trajectories are always adapted such that mechanical stress is reduced. This even holds true for special situations like, for example, walking over obstacles, stumbling, or walking with partially or totally amputated legs. Similarities and important discrepancies between the models behavior and the walking behavior of stick insects are discussed.

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.

Control of Walking in the Stick Insect: From Behavior and Physiology to Modeling

Classical engineering approaches to controlling a hexapod walker typically involve a central control instance that implements an abstract optimal gait pattern and relies on additional optimization criteria to generate reference signals for servocontrollers at all the joints. In contrast, the gait of the slow-walking stick insect apparently emerges from an extremely decentralized architecture with separate step pattern generators for each leg, a strong dependence on sensory feedback, and multiple, in part redundant, primarily local interactions among the step pattern generators. Thus, stepping and step coordination do not reflect an explicit specification based on a global optimization using a representation of the system and its environment; instead they emerge from a distributed system and from the complex interaction with the environment. A similarly decentralized control at the level of single leg joints also may explain the control of leg dynamics. Simulations show that negative feedback for control of body height and walking direction combined with positive feedback for generation of propulsion produce a simple, extremely decentralized system that can handle a wide variety of changes in the walking system and its environment. Thus, there is no need for a central controller implementing global optimization. Furthermore, physiological results indicate that the nervous system uses approximate algorithms to achieve the desired behavioral output rather than an explicit, exact solution of the problem. Simulations and implementation of these design principles are being used to test their utility for controlling six-legged walking machines.

High-Pass Filtered Positive Feedback. Decentralized Control of Cooperation

In a multilegged walking system, the legs, when in stance mode, have to cooperate to propel and support the body and, at the same time, to avoid unwanted forces across the body. As a simple method to control the joint movement, we propose to use local high-pass filtered positive feedback. This does not only make redundant the determination of equations for coordinate transformation, but is also robust against all kinds of geometrical changes within the mechanical system as, for example, changes in leg segment length, bending of segments, changes in orientation of the rotational axes (by accident or because the suspension is soft by design), or addition of further joints. This simplification is possible because, instead of applying abstract, explicit computation, the physical properties of the world are exploited. It permits extreme decentralization, namely control on the joint level, and therefore allows very fast computation. In order to provide height control of the body, one leg joint is subjected to a negative feedback controller.

MMC – a new numerical approach to the kinematics of complex manipulators

Abstract A numerical approach (MMC-model; MMC – mean of multiple computations) is proposed for solving the kinematics of manipulators of nearly arbitrary configuration. It is applicable to serial, parallel and hybrid-chain-manipulators (HCMs). Even changing configurations of the manipulator are possible, because the structural analysis of the current manipulator configuration is done automatically. This approach does not make a strict distinction between the direct and inverse kinematics, but solves both tasks as well as mixed control tasks in a single model. With a slight modification over-constrained problems can also be solved. These properties make the model especially suitable for the simulation of reconfigurable HCMs. The advantages of the MMC-model arise from splitting the structural analysis into two parts. The first, linear part performs the topological analysis without any constraints. Only this part performs the numerical approximation. The second, generally non-linear part adds the constraints and thus allows versatile control of the movement without changing the equations of the approximation procedure in the first part. After a general description of the model we present a hexapod walking system as a complex application of a HCM.

WalkNet — a Decentralized Architecture for the Control of Walking Behaviour Based on Insect Studies

A network model for controlling a six-legged, insect-like walking system is described, which is based as far as possible on data obtained from biological experiments. The network contains internal recurrent connections, but important recurrent connections utilize the loop through the environment. This approach leads to a modular structure, WalkNet, consisting of several subnets. One subnet controls 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 have to be controlled such that each leg contributes efficiently to support and propulsion and legs do not work at cross purposes, i.e. do not produce interaction forces. 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.

A Simple Neural Network for the Control of a Six-Legged Walking System

All behaving systems—whether living or artificial—can be placed along a continuum spanning three types. One type comprises strictly sensory or data-driven, feedforward systems, such as simple reflex machines. The extant input determines the output. Although the internal state of such systems might be changed by learning, the system at any moment can be regarded as having a static world model. The other two types of systems have a form of world model that can be used to make predictions concerning future states of the world. Two levels may be distinguished. One is the type of system possessing an internal world model which is “manipulable” in the sense that the internal world model can be cut off from the sensory input and the motor output and then used to mentally “play” with different possibilities. Such a model could be used for thinking, for reflecting and—when connected to a value system—for decision making.

Simulation of complex movements using artificial neural networks.

Abstract 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 leg 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.