Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> A set of van der Pol oscillators is arranged in a network in which each oscillator is coupled to each other oscillator. Through the selection of coupling coefficients, the network is made to appear as a ring and as a chain of coupled oscillators. Each oscillator is provided with amplitude, frequency, and offset parameters which have analytically indeterminable effects on the output waves. These systems are simulated on the digital computer in order to study the amplitude, frequency, offset, and phase relationships of the waves versus parameter changes. Based on the simulations, systems of coupled oscillators are configured so that they exhibit stable patterns of signals which can be used to model the central pattern generator (CPG) of living organisms. Using a simple biped as an example locomotory system, the CPG model generates control signals for simulated walking and jumping maneuvers. It is shown that with parameter adjustments, as guided by the simulations, the model can be made to generate kinematic trajectories which closely resemble those for the human walking gait. Further-more, minor tuning of these parameters along with some algebraic sign changes of coupling coefficients can effect a transition in the trajectories to those of a two-legged hopping gait. The generalized CPG model is shown to be versatile enough that it can also generate various n-legged gaits and spinal undulatory motions, as in the swimming motions of a fish. <s> BIB001 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> This paper considers a synthesis approach to autonomous distributed systems in which the functional order of the entire system is generated by cooperative interaction among its subsystems, each of which has the autonomy to control a part of the state of the system, and its application to pattern generators of animal locomotion. First, biological locomotory rhythms and their generators, and gait patterns of quadrupeds, are reviewed briefly. Then, a design principle for autonomous coordination of many oscillators is proposed. Using these results, a gait pattern generator is synthesized. Finally, it is shown using computer simulations that the proposed systems generate desirable patterns. <s> BIB002 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> We present a neural network model inspired from both behavioral and neurophysiological data on insect locomotion. The model consists of a central rhythmic pattern generator and a sensory motor network. We show that it exhibits various behavioral properties observed in several insect species: it produces a continuum of stable gaits ranging from metachronal to tripod; the changes in the duration of protraction retraction phases for various walking speeds follow closely the behavorial data; the network is insensitive to the initial position of the legs, in that it can achieve rapidly a coherent phase relationship regardless of the initial conditions. In addition, this transient property also extends to situations where rapid changes occur in the walking speed; the network can reorganize its phase rapidly during fast accelerations as well as fast decelerations. <s> BIB003 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> This paper presents how neural swimming controllers for a simulated lamprey can be developed using evolutionary algorithms. A genetic algorithm is used for evolving the architecture of a connectionist model which determines the muscular activity of a simulated body in interaction with water. This work is inspired by the biological model developed by Ekeberg which repro duces the central pattern generator observed in the real lamprey (Ekeberg, 1993). In evolving artificial controllers, we demonstrate that a genetic algorithm can be an interesting design tech nique for neural controllers and that there exist alternative solutions to the biological connectiv ity. A variety of neural controllers are evolved which can produce the pattern of oscillations necessary for swimming. These patterns can be modulated through the external excitation ap plied to the network in order to vary the speed and the direction of swimming. The best evolved controllers cover larger ranges of frequencies, phase lags and speeds of s... <s> BIB004 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Recently, the field of humanoid robotics attracts more and more interest and the research on humanoid locomotion based on central pattern generators (CPG) reveals many challenging aspects. This paper describes the design of CPG for stable humanoid bipedal locomotion using an evolutionary approach. In this research, each joint of the humanoid is driven by a neuron that consists of two coupled neural oscillators, and corresponding joint's neurons are connected by strength weight. To achieve natural and robust walking pattern, an evolutionary-based multi-objective optimization algorithm is used to solve the weight optimization problem. The fitness functions are formulated based on zero moment point (ZMP), global attitude of the robot and the walking speed. In the algorithms, real value coding and tournament selection are applied, the crossover and mutation operators are chosen as heuristic crossover and boundary mutation respectively. Following evolving, the robot is able to walking in the given environment and a simulation shows the result. <s> BIB005 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In this paper, we develop a simple bipedal locomotion algorithm based on biological concepts. The algorithm utilized a central pattern generator (CPG) composed of four coupled neural oscillators (NO) to generate control signal for the bipedal robot. Feedbacks from the robot dynamics and the environment are used to update the CPG online. Our algorithm is then tested on a seven link model of bipedal robot. Simulation results suggest the proposed CPG can generate a smooth and continuous walking pattern for the robot. <s> BIB006 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> A challenging task that must be accomplished for every legged robot is creating the walking and running behaviors needed for it to move. In this paper we describe our system for autonomously evolving dynamic gaits on two of Sony's quadruped robots. Our evolutionary algorithm runs on board the robot and uses the robot's sensors to compute the quality of a gait without assistance from the experimenter. First, we show the evolution of a pace and trot gait on the OPEN-R prototype robot. With the fastest gait, the robot moves at over 10 m/min, which is more than forty body-lengths/min. While these first gaits are somewhat sensitive to the robot and environment in which they are evolved, we then show the evolution of robust dynamic gaits, one of which is used on the ERS-110, the first consumer version of AIBO. <s> BIB007 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Inspired by the efficient method of locomotion of the rattlesnake Crotalus cerastes, the objective of this work is automatic design through genetic programming (GP) of the fastest possible (sidewinding) locomotion of simulated limbless, wheelless snake-like robot (Snakebot). The realism of simulation is ensured by employing the Open Dynamics Engine (ODE), which facilitates implementation of all physical forces, resulting from the actuators, joints constrains, frictions, gravity, and collisions. Reduction of the search space of the GP is achieved by representation of Snakebot as a system comprising identical morphological segments and by automatic definition of code fragments, shared among (and expressing the correlation between) the evolved dynamics of the vertical and horizontal turning angles of the actuators of Snakebot. Empirically obtained results demonstrate the emergence of sidewinding locomotion from relatively simple motion patterns of morphological segments. Robustness of the sidewinding Snakebot, which is considered to be the ability to retain its velocity when situated in an unanticipated environment, is illustrated by the ease with which Snakebot overcomes various types of obstacles such as a pile of or burial under boxes, rugged terrain, and small walls. The ability of Snakebot to adapt to partial damage by gradually improving its velocity characteristics is discussed. Discovering compensatory locomotion traits, Snakebot recovers completely from single damage and recovers a major extent of its original velocity when more significant damage is inflicted. Exploring the opportunity for automatic design and adaptation of a simulated artifact, this work could be considered as a step toward building real Snakebots, which are able to perform robustly in difficult environments. <s> BIB008 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> We present a novel fish robot capable of swimming and crawling. The robot is driven by DC motors and has three actuated fins, with two pectoral fins and one caudal fin. It is loosely inspired from the boxfish. The control architecture of the robot is constructed around a central pattern generator (CPG) implemented as a system of coupled nonlinear oscillators, which, like its biological counterpart, can produce coordinated patterns of rhythmic activity while being modulated by simple control parameters. Using the CPG model, the robot is capable of performing and switching between a variety of different locomotor behaviors such as swimming forwards, swimming backwards, turning, rolling, moving upwards/downwards, and crawling. These behaviors are triggered and modulated by sensory input provided by light and water sensors. Results are presented demonstrating the agility of the robot, and interesting properties of a CPG-based control approach such as stability of the rhythmic patterns due to limit cycle behavior, and the production of smooth trajectories despite abrupt changes of control parameters <s> BIB009 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> The paper proposes an artificial central pattern generator (CPG) for bionic-robot joint control. The neural oscillator adopted to produce rhythmic pattern is specially designed from original sin-cosine oscillator model. An amplitude neural estimator consisted of two neurons is presented to provide sensor feedback to CPG control. The artificial CPG can adapt itself to the physical system parameters variety by rhythmic movement angular frequency modulation. <s> BIB010 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In this paper, we present our design and experiments on a planar biped robot under the control of a pure sensor-driven controller. This design has some special mechanical features, for example small curved feet allowing rolling action and a properly positioned center of mass, that facilitate fast walking through exploitation of the robot's natural dynamics. Our sensor-driven controller is built with biologically inspired sensor- and motor-neuron models, and does not employ any kind of position or trajectory tracking control algorithm. Instead, it allows our biped robot to exploit its own natural dynamics during critical stages of its walking gait cycle. Due to the interaction between the sensor-driven neuronal controller and the properly designed mechanics of the robot, the biped robot can realize stable dynamic walking gaits in a large domain of the neuronal parameters. In addition, this structure allows the use of a policy gradient reinforcement learning algorithm to tune the parameters of the sensor-driven controller in real-time, during walking. This way RunBot can reach a relative speed of 3.5 leg lengths per second after only a few minutes of online learning, which is faster than that of any other biped robot, and is also comparable to the fastest relative speed of human walking. <s> BIB011 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> We present a system of coupled nonlinear oscillators to be used as programmable central pattern generators, and apply it to control the locomotion of a humanoid robot. Central pattern generators are biological neural networks that can produce coordinated multidimensional rhythmic signals, under the control of simple input signals. They are found both in vertebrate and invertebrate animals for the control of locomotion. In this article, we present a novel system composed of coupled adaptive nonlinear oscillators that can learn arbitrary rhythmic signals in a supervised learning framework. Using adaptive rules implemented as differential equations, parameters such as intrinsic frequencies, amplitudes, and coupling weights are automatically adjusted to replicate a teaching signal. Once the teaching signal is removed, the trajectories remain embedded as the limit cycle of the dynamical system. An interesting aspect of this approach is that the learning is completely embedded into the dynamical system, and does not require external optimization algorithms. We use our system to encapsulate rhythmic trajectories for biped locomotion with a simulated humanoid robot, and demonstrate how it can be used to do online trajectory generation. The system can modulate the speed of locomotion, and even allow the reversal of direction (i.e. walking backwards). The integration of sensory feedback allows the online modulation of trajectories such as to increase the basin of stability of the gaits, and therefore the range of speeds that can be produced <s> BIB012 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Anthropomorphic walking for a simulated bipedal robot has been realized by means of artificial evolution of central pattern generator (CPG) networks. The approach has been investigated through full rigid-body dynamics simulations in 3D of a bipedal robot with 14 degrees of freedom. The half-center CPG model has been used as an oscillator unit, with interconnection paths between oscillators undergoing structural modifications using a genetic algorithm. In addition, the connection weights in a feedback network of predefined structure were evolved. Furthermore, a supporting structure was added to the robot in order to guide the evolutionary process towards natural, human-like gaits. Subsequently, this structure was removed, and the ability of the best evolved controller to generate a bipedal gait without the help of the supporting structure was verified. Stable, natural gait patterns were obtained, with a maximum walking speed of around 0.9 m/s. <s> BIB013 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In limbed animals, spinal neural circuits responsible for controlling muscular activities during walking are called central pattern generators (CPG). CPG networks display oscillatory activities that actuates individual or groups of muscles in a coordinated fashion so that the limbs of the animal are flexed and extended at the appropriate time and with the required velocity for the animal to efficiently traverse various types of terrain, and to recover from environmental perturbation. Typically, the CPG networks are constructed with many neurons, each of which has a number of control parameters. As the number of muscles increases, it is often impossible to manually, albeit intelligently, select the network parameters for a particular movement. Furthermore, it is virtually impossible to reconfigure the parameters on-line. This paper describes how genetic algorithms (GA) can be used for on-line (re)configuring of CPG networks for a bipedal robot. We show that the neuron parameters and connection weights/network topology of a canonical walking network can be reconfigured within a few of generations of the GA. The networks, constructed with integrate-and-fire-with-adaptation (IFA) neurons, are implemented with a microcontroller and can be reconfigured to vary walking speed from 0.5Hz to 3.5Hz. The phase relationship between the hips and knees can be arbitrarily set (to within 1 degree) and prescribed complex joint angle profiles are realized. This is a powerful approach to generating complex muscle synergies for robots with multiple joints and distributed actuators. <s> BIB014 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> There is evidence showing that animals have inherent rhythmic pattern generators called central pattern generator (CPG) that produce locomotion, respiration, heartbeat, and etc. Until now, the CPG has been widely used in robotic systems especially for locomotion. In this paper, we propose a gait adaptation method of biped robot for various terrains. The CPGs are used for creating desired joint angle of a biped robot. And a learning mechanism is realized with genetic algorithms (GAs) and Neural Network (NN). From an each terrain, the most suitable parameters of CPGs that can produce stable biped robot gait are founded by GAs. The parameter set founded by GAs and sensor data at that time are used for training the NN. After finishing training of the NN, the NN can be used for producing suitable parameters of the CPGs according to a sensor input. Finally the gait of the biped robot is changed according to environment. <s> BIB015 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Biological systems seem to have a simpler but more robust locomotion strategy than that of the existing biped walking controllers for humanoid robots. We show that a humanoid robot can step and walk using simple sinusoidal desired joint trajectories with their phase adjusted by a coupled oscillator model. We use the center-of-pressure location and velocity to detect the phase of the lateral robot dynamics. This phase information is used to modulate the desired joint trajectories. We do not explicitly use dynamical parameters of the humanoid robot. We hypothesize that a similar mechanism may exist in biological systems. We applied the proposed biologically inspired control strategy to our newly developed human-sized humanoid robot computational brain (CB) and a small size humanoid robot, enabling them to generate successful stepping and walking patterns. <s> BIB016 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> A control problem is studied for generating the locomotion pattern of a semi-looper type robot by applying central pattern generators (CPGs), in which such a robot can realize two-rhythm motion and green caterpillar locomotion depending on the condition of environment. After deriving the dynamical model with two links and one actuator, the simulation of the robot is conducted using a CPG consisting of one van der Pol (VDP) oscillator. A CPG network composed of two VDP oscillators is further constructed to realize four-rhythm motion with three links and two actuators. <s> BIB017 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Central pattern generators (CPGs) are becoming a popular model for the control of locomotion of legged robots. Biological CPGs are neural networks responsible for the generation of rhythmic movements, especially locomotion. In robotics, a systematic way of designing such CPGs as artificial neural networks or systems of coupled oscillators with sensory feedback inclusion is still missing. In this contribution, we present a way of designing CPGs with coupled oscillators in which we can independently control the ascending and descending phases of the oscillations (i.e. the swing and stance phases of the limbs). Using insights from dynamical system theory, we construct generic networks of oscillators able to generate several gaits under simple parameter changes. Then we introduce a systematic way of adding sensory feedback from touch sensors in the CPG such that the controller is strongly coupled with the mechanical system it controls. Finally we control three different simulated robots (iCub, Aibo and Ghostdog) using the same controller to show the effectiveness of the approach. Our simulations prove the importance of independent control of swing and stance duration. The strong mutual coupling between the CPG and the robot allows for more robust locomotion, even under non precise parameters and non-flat environment. <s> BIB018 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In this study, we examine, for a six-link snake robot, how an optimal gait might change as a function of the snake- surface interaction model and how the overall locomotion performance changes under nonoptimal conditions such as joint failure. Simulations are evaluated for three different types of friction models, and it is shown that the gait parameters for serpentine motion are very dependant on the frictional model if minimum power expenditure is desired for a given velocity. Experimental investigations then motivate a surface interaction model not commonly used in snake locomotion studies. Using this new model, simulation results are compared to experiments for nominal and nonnominal locomotion cases including actuator faults. It is shown that this model quite accurately predicts locomotion velocities and link profiles, but that the accuracy of these predictions degrades severely at speeds where actuator dynamics become significant. <s> BIB019 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> We present a new quadruped robot, ldquoCheetahrdquo, featuring three-segment pantographic legs with passive compliant knee joints. Each leg has two degrees of freedom - knee and hip joint can be actuated using proximal mounted RC servo motors, force transmission to the knee is achieved by means of a bowden cable mechanism. Simple electronics to command the actuators from a desktop computer have been designed in order to test the robot. A Central Pattern Generator (CPG) network has been implemented to generate different gaits. A parameter space search was performed and tested on the robot to optimize forward velocity. <s> BIB020 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> The generation of trajectories for a biped robot is a problem which has been largely studied for several years, and many satisfying offline solutions exist for steady-state walking in absence of disturbances. The question is a little more complex when the generation of the desired trajectories of joints or links has to be achieved or adapted online, i.e. in real time, for example when it is wished to strongly synchronize these trajectories with an external motion. This is precisely the problem addressed in this paper. Indeed, we consider the case where the ''master'' motion is measured by a position sensor embedded on a human leg. We propose a method to synchronize the motion of a robot or of other device with respect to the output signal of the sensor. The main goal is to estimate as accurately as possible the current phase along the gait cycle. We use for that purpose a model based on a nonlinear oscillator, which we associate an observer. Introducing the sensor output in the observer allows us to compute the oscillator phase and to generate a synchronized multilinks trajectory, at a very low computational cost. The paper also presents evaluation results in terms of robustness against parameter estimation errors and velocity changes in the input. <s> BIB021 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Biped robot with heterogeneous legs (BRHL) is a novel robot model, which consists of an artificial leg and an intelligent bionic leg. The artificial leg is used to simulate the amputeepsilas healthy leg and the bionic leg works as the intelligent artificial limb. To describe the present gait of the healthy leg and make intelligent bionic leg follow the walking of artificial leg in all phases is the target of BRHLpsilas research. So gait planning of artificial leg is the emphasis of BRHLpsilas research. This paper uses the model of central pattern generator (CPG) in the research of artificial legpsilas gait planning from the point of biology. To obtain natural and robust walking pattern, genetic algorithm is used to optimize parameters of the CPG network model and the fitness function is formulated based on zero moment point (ZMP). Simulation results testify the feasibility of this method. <s> BIB022 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In this paper we describe a learning framework for a central pattern generator (CPG)-based biped locomotion controller using a policy gradient method. Our goals in this study are to achieve CPG-based biped walking with a 3D hardware humanoid and to develop an efficient learning algorithm with CPG by reducing the dimensionality of the state space used for learning. We demonstrate that an appropriate feedback controller can be acquired within a few thousand trials by numerical simulations and the controller obtained in numerical simulation achieves stable walking with a physical robot in the real world. Numerical simulations and hardware experiments evaluate the walking velocity and stability. The results suggest that the learning algorithm is capable of adapting to environmental changes. Furthermore, we present an online learning scheme with an initial policy for a hardware robot to improve the controller within 200 iterations. <s> BIB023 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> The objective of the work presented here is to develop a low cost active above knee prosthetic device exploiting bipedal robotics technology which will work utilizing the available biological motor control circuit properly integrated with a Central Pattern Generator (CPG) based control scheme. The approach is completely different from the existing Active Prosthetic devices, designed primarily as standalone systems utilizing multiple sensors and embedded rigid control schemes. In this research, first we designed a fuzzy logic based methodology for offering suitable gait pattern for an amputee, followed by formulating a suitable algorithm for designing a CPG, based on Rayleigh's oscillator. An indigenous probe, Humanoid Gait Oscillator Detector (HGOD) has been designed for capturing gait patterns from various individuals of different height, weight and age. These data are used to design a Fuzzy inference system which generates most suitable gait pattern for an amputee. The output of the Fuzzy inference system is used for designing a CPG best suitable for the amputee. We then developed a CPG based control scheme for calculating the damping profile in real time for maneuvering a prosthetic device called AMAL (Adaptive Modular Active Leg). Also a number of simulation results are presented which show the stable behavior of knee and hip angles and determine the stable limit cycles of the network. <s> BIB024 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> Central pattern generators (CPGs) inspired from neural system of animal are widely used for the control of locomotion in robots. The objective of this paper is to modeling a CPG-network formed by a set of mutually coupled Van Der Pol (VDP) oscillators to generating rhythmic movement patterns for multi-joint robot. Firstly, a VDP-CPG network is made up by four coupled VDP oscillators, which can produce multiple phase-locked oscillation patterns that correspond to the four basic quadrupedal gaits. Then the gait transitions between the different gaits are generated by altering the internal oscillator parameters. At last, we use VDP-CPG network to produce the joints trajectories for AIBO to control the locomotion. The simulation and experimental results demonstrate that the designed VDP-CPG network is effective to control the quadruped locomotion. <s> BIB025 </s> Intelligent Approaches in Locomotion - A Review <s> Parameter selection <s> In this paper, we propose a new CPG model and hebbian learning rule for the CPG. The output of the proposed CPG is determined by only phase differences of synchronization of component oscillators. A phase synchronization can be regarded as an adaptive behavior to an environment, so the CPG has an adaptavility despite of only simple connections to the environment. We also propose a motion learning rule for the proposed CPG. Since the rule is described by only simple signal processing, so that it can be realized by electric circuits easily, it will be able to be used efficiently for high degree of freedom robots. <s> BIB026
In general, the oscillator constants and coupling weights of the CPG need specifying. At the simplest level, manual specification can be used, as discussed in BIB016 , BIB024 , BIB009 , BIB017 , BIB006 - BIB002 , BIB001 , BIB018 ,  , BIB025 , BIB003 ,  , BIB010 . Although this approach is unlikely to be optimal for any particular criterion, it may be sufficient to give good results. It allows solutions to be determined with few trials and is therefore appropriate for implementing directly in hardware. By analysing gait characteristics common to several animals of a type similar to the target system, variables such as phase differences can be determined. For oscillator types where there is good parameter separation, frequency and amplitude components can again be specified by observing or making logical arguments and conclusions. Parameter optimisation criteria include minimising energy expenditure BIB019 , maximising speed BIB011 , BIB020 , BIB007 , matching a control speed BIB026 , reference tracking BIB012 , BIB021 ,  , BIB014 , maximising stability BIB022 , BIB023 , BIB005 , and producing walking in an unconstrained system BIB015 , BIB013 . The implemented optimisation techniques vary from exhaustive search BIB019 , to hill climbing BIB020 , policy gradient search BIB011 , actor/critic BIB023 , sequential quadratic programming BIB021 , Hebbian style learning rules BIB026 , integrated oscillator learning terms BIB012 , and GAs BIB022 , BIB004 , BIB005 - BIB007 . The exhaustive search, hill climbing and sequential quadratic programming offer straight forward approaches but are limited in their application. The learning rules/terms provide real time error correction or reference tracking, and are therefore possibly appropriate for direct hardware implementation. The gradient and actor/critic searches are used to speed up optimisation, while the GA are used to fully explore and exploit the search space and possibly find global optimal solutions, but require more computation. Multi staged optimisation has been used to simplify the complex process  , BIB014 . For example, in  a GA was used to find parameters for the hip joints first, then all joints in the left leg, the whole lower body, the upper body, and then finally, the whole body (which had 271 parameters). The optimized fitness functions can include multiple components BIB005 , BIB007 . In BIB005 , stability, pose angle and step length were optimized in order to find good solutions for stability, form and speed. Using outcome measures to produce walking in an unconstrained system can be difficult. The optimisation process needs to find a workable solution from a large solution space. Using travelled distance as a fitness function was successful in BIB015 when combined with analysing final height, to detect possible falling, and average step length. In BIB013 , the authors initially failed to produce a walking gait with the outcome measures of travelled distance, frequency of foot strikes, and uprightness. They presented a theory that control systems in nature may have co-evolved with the structure of the physical system. With this in mind, they added support structures to the biped that allowed it to evolve effective gaits without the risk of falling down. Although not investigated, the authors suggested that the supports could then be removed and optimisation continued. A somewhat different approach was demonstrated in BIB008 , where a genetic programming algorithm was employed to construct a sinusoidal system, producing optimal side winding locomotion for a snake model. The function set of the GP algorithm consisted of trigonometric and basic arithmetic functions, and the fitness function was the distance travelled in a set time.