Biomimetic Walking Robot Scorpion: Control and Modeling

Preprint: to appear in Robotics and Autonomous Systems journal (Special Issue: Best papers from SIRS00) Biomimetic Walking Robot Scorpion: Control and Modeling Bernhard Klaassen, Ralf Linnemann, Dirk Spenneberg, Frank Kirchner Fraunhofer Institut Autonome intelligente Systeme (AiS) D-53754 Sankt Augustin, Germany Abstract: We present the biomimetic control scheme for the walking robot SCORPION. We used a concept of Basic Motion Patterns, which can be combined in a very flexible manner. In addition our modeling and simulation approach is described, which has been done based on the ADAMS(TM) simulator. Especially the motion patterns of real scorpions were analyzed and used for walking patterns and acceleration of the robot. Introduction In the SCORPION project (sponsored by DARPA Grant No. N004-99--0483) we are developing a biomimetic eight-legged walking robot (see picture on next page). Since our ambulation control approach is also suitable for the more widely studied hexapods, we also built up a six-legged robot which is equipped with the same electronic and mechanical parts as the eight-legged version. The length of the eight-legged robot is 65 cm and the six-legged one is 5 cm long. The other dimensions are shown in fig... The weight of the fully equipped robots( including 3.8 Ah accumulators, communication equipment and sensors) is 9.8 kg for the six-legged and.5 kg for the eight-legged robot. The most challenging parts of a walking robot are the legs. The leg presented here provides 3 degrees of freedom. We feel confident that 3 degrees of freedom is the minimum needed in a flexible outdoor-capable walking robot, for example it provides the possibility to walk omnidirectional in narrow environments. The leg consist of a thoracical joint for protraction and retraction, a basalar joint for elevation and depression and a distal joint for extension and flexion of the leg (see fig..). The joints are actuated by standard 6Watt 4V DC-Motors with high gear transmission ratio for sufficient lifting capacity. Fig.. Schematic front view of the SCORPION walking robot

Robot construction requires frequent design changes, and experiments tend to stress the often touchy hardware. Therefore a parametric robot model is well suited for design optimization and virtual motion experiments, especially because simulations always deliver a full set of observables. We were able to construct a physical model of our robot for simulation in ADAMS TM and added a programmable interface for C-routines, which form the motion control for the simulation[4]. The paper is organized as follows: In the second section we describe the biomimetic control approach making use of so-called Basic Motion Patterns. The third section describes the aspects of modeling and simulation especially for walking patterns and acceleration. Fig..: Eight-legged walking robot SCORPION during a climbing test on the DARPA test site in San Antonio, Texas The Biomimetic Control Approach Many approaches to leg based walking already exists [,3,5,8,9,0]. Most of them are biological inspired. The here presented ambulation control approach combines two biological control principles, the Central Pattern Generator (CPG) and the Reflex. Whereas a Central Pattern Generator is able to produce rhythmic motion without the need of sensory feedback [,7], reflexes are based on the sensor-motor-feedback. It is assumed that the by the CPGs produced motion patterns are not learned or adapted by the animal but represent a set of low-level locomotion mechanisms specific for the species. Applied to a robotic system this implies, that is possible to a-priori define a set of Basic Motion Patterns (BMPs), which can be produced without the need of sensory feedback. A well known locomotion approach using only reflex systems is the ''Walk Net'' []. It is based on the assumption that only local sensory feedback at the legs and a coupling between the control of neighbored legs is sufficient for stable walking. A robot control concept which is based on CPGs is the ambulation controller [3]. To control the CPGs it uses a command neuron [4] like approach. Here the motions for lateral left, lateral right, forward and backward walking are implemented as finite state machines. The control to execute one of these finite state machines is done by a command neuron like structure. The ambulation control approach presented here also uses a CPG model, but in contrast to the command neuron approach it uses combinable ``Basic Motion Patterns'' (BMPs). By combinable we mean, that first it is possible that more than one BMP is stimulated at the same time. Second, each BMP can be activated with different strength. Third different behaviors can take simultaneously influence on the activation of a BMP. And finally the observable movement is the result of a overlaying process applied to all activated Basic Motion Patterns.

A Basic Motion Pattern(BMP) describes a trajectory of the leg in the joint angle space. For a pure forward movement this means, that the trajectory of the corresponding BMP describes a swing motion followed by a stance motion. In the perspective of behavior based software control the idea of using structures which are in function equal to the command neuron idea, is related to the subsumption architecture and its finite state representations [3]. Whereas the idea of combinable BMPs is closer related to the neural assembly theory [7]. This means that dynamically changing groups of cells (more than one) are responsible for the activity and kind of observed behavior. From the behavior based control perspective the analogue to a neuronal ensemble is a behavior ensemble. In the software developers view this can be related to the concepts of the Process Description Language [4] where the overall system behavior emerges from the massive parallelism of normally more then one behavior system. As mentioned above in our approach we combine both concepts, the CPGs configured by Basic Motion Patterns and the Reflexes. The CPGs control the leg under normal circumstances. By normal we mean, that no exceptions, like an obstacle blocking the path of a leg, during the walking occur. The reflexes are only activated by such exceptions and are used to deal with them, e.g. a reflex, which lifts the leg upward to overcome a detected obstacle. The Idea of Implementation The behavioral level has two ways to control each leg (see fig..). The first one is the posture control, which is mainly used to change the position of the leg while walking, e.g. to stretch/compress the leg in order to walk in a higher/lower position. Fig..: Scheme of the Locomotion Control Approach This is done by taking an additional influence on the nominal joint angle values, which are fed to the motor controllers. The second part (the CPG) produces the rhythmic motion. A CPG is modeled as a system which consists of a multitude of basic motion patterns. A BMP describes a rhythmic trajectory of the leg in the joint angle space. In a first approach splined squared sinusoids were used to describe the BMPs. These sinusoids are alterable in the amplitude, the frequency and the phase. These BMPs are combinable in the sense, that they can be simultaneously and differently strong stimulated by the behaviors (e.g. obstacle avoidance) at the A swing consist of protraction of the leg while it is first elevated and then depressed. A stance consist of retraction and ongoing low depression.

behavioral level. This is shown at the top of fig... The CPG produces a Desired Pattern by overlaying all stimulated BMPs, e.g. if a pure forward BMP and a pure lateral walking BMP are both evenly strong stimulated the result is a diagonal walking pattern. By varying the strength every intermediate state between pure forward walking and pure lateral walking can be achieved. If the higher behavioral level changes the stimulation of the BMPs, consequently a new pattern (from the behavioral level the Desired Pattern ) is produced. This pattern can not be fed directly to the motor controller, but goes through a fading process with the Previous Pattern to result in a smooth pattern transition. The Previous Pattern is blended out and the new Desired Pattern is faded in. So the Present Pattern is a combination of the Previous Pattern and the Desired Pattern. The current angle values from the Present Pattern are then added to the values given by the posture control. The sum is fed to the motor controllers (see bottom of fig..). The motor controllers are based on a motor model and a proportional controller to compute the correct pulse width modulated motor signals. To achieve this the actual measured motor current and voltage are taken into account. Furthermore the error between the angle of the present motion pattern and the angle measured by motor encoders is looped back into the motor controller. On this level of control also a set of reflexes is implemented. The reflexes are meant to deal locally with environmentally induced events, such as an obstacle blocking the path of the leg. They are triggered by the measured joint current and the looped back angular displacement error. For example, if the current at one joint raises up very fast and also a significant angle error is detected at the upper (coxa) joint, which moves the leg forward or backward, it can be assumed a obstacle is in the way. So a reflex is triggered, which moves the leg upward (via the femur and tibia joint) as fast as possible. These reflexes override for a short time period the output of the motor controller. The reaction time is at a centisecond. The above presented low-level motion production is controlled and modulated by a behavioral level, which stimulates the BMPs for the CPG of each leg. Here also the phase shifting between the legs are realized to perform a movement as shown in fig. 3..The control approach was successfully tested in real world environment with different terrain covered with grass and sand, obstacles like 5cm high rocks or pipes and acclivities up to 30%. More detailed information and data about the implementation of the control idea, the performed tests and the SCORPION robot can be found in [8,9]. 3 Modeling and Simulation The mechanical model of the walking robot Scorpion in ADAMS TM consists of 43 rigid parts which are coupled by 4 joints. It describes the mechanical features of the robot and is based on three assumptions:. The robot model consists of three scalable body parts and eight homogenous legs. Each leg is movable by three active joints.. Lateral and longitudinal symmetry of the robot. 3. A leg consists of a link firmly attached to the body which houses the horizontal joint. This joint rotates a hip which houses the first vertical joint. The vertical joint rotates the thigh. Thigh and shank are coupled by another vertical joint. A passive joint serves as ankle between foot and shank. A set of about 70 design variables allows instant modification of each and every aspect (Fig. 3.): geometry and shape, mass and inertia of each part, individual position and orientation of leg pairs, posture, individual scope of a joint, and in case of ground contact reaction forces and friction. Fig. 3.: One model, three different designs in shape, posture and leg orientation

The skeleton of the model design points for the position and tripod markers for the orientation of objects contains the entire geometrical information in parameterized form. Every object is linked to at least one design point or one marker. The design points and tripod markers are chained; changing one of them affects the entire set. The objects themselves contain additional design parameters regarding their shape. Thus the entire model is adapted automatically when one parameter is altered. It is implemented in the ADAMS TM package (normally used in vehicle simulation) which we have tailored for walking machines. Especially for the walking patterns we introduced a C-interface for easier description of motions. Motion Patterns The gait of living scorpions is almost always an alternating tetrapod scheme (Fig. 3., left). Legs within a tetrapod, beginning with the posterior leg, step in an anteriorly directed order, with each leg lagging the preceding one by ten percent of the total cycle (phase). The other tetrapod commences the wave of promotions when the first one is half way through its cycle []. A cycle consists of a leg promotion period (swing) and a leg remotion period (stance). Phase, swing, and stance are the parameters of the robot s motion pattern (Fig. 3., right) together with the step size of a leg. Fig. 3.: Tetrapod walking gait of real scorpions (left) and an according motion pattern beginning from the start position (right). Vertical lines reveal how many legs are touching the ground at given times. Bowerman reports a linear change of the promotion period T as well as the remotion period T with the stride frequency []. The slope is about 0. in case of promotions (m ) and about 0.8 in case of remotions (m ). This relation allows to express one parameter by the other: Swing and stance period are coupled and can not change independently. Their ratio is a functions of the stride frequency. According to the biomimetic approach the patterns are transferred to the model of the robot. For the inverse dynamics simulations a sine function is applied to the horizontal hip joints to avoid too abrupt accelerations (Fig. 3.3, left). The function f(t) for leg L4 is repeated by the other legs (g(t)) after a portion of a cycle. f ( t) = A sin A sin ( π t T π ) 0 MOD( t, T + T ) ( π ( t T ) T + π ) T MOD( t, T + T ) π T π T + T (4) The phase ϕ between two legs remains constant independent of the velocity []: g ( t) A sin = A sin ( π t T π + ϕ ) 0 MOD( t, T + T ) ( π ( t T ) T + π + ϕ ) T MOD( t, T + T ) π T π T + T (5)

The coupling of swing and stance has interesting consequences for the motion control. With m +m = and b =-b - derived from () and () - a set of only five parameters (e.g. T, m, b, ϕ, step size) is sufficient to describe all potential states of motion. Furthermore it allows smooth transitions in velocity without loss of coordination or change of the gait. swing stance Fig. 3.3: A tetrapod group of horizontal joints for swing/stance=3/5 and for ϕ=0. (left) And an example for joint coordination during a stance (horizontal angle is downscaled by 3:). To avoid disturbing shaking of the walking robot, all three joints of a leg should only contribute to the forward motion of the body and not to an up/down or left/right shift. During each stance the lateral distance between body and foot and the height of the body above the ground should remain constant (Fig. 3.4, left) as for the scorpion Hadrurus arizonensis [6]. Therefore the two angles for a vertical hip joint resp. for a knee joint are expressed as functions of the horizontal hip angle (Fig. 3.3, right). The equations for this behavior are lengthy and complex [3], but the solution is unequivocal and easy to compute. It takes into account the initial posture and the actual parameter configuration (Fig. 3.4, middle and right). Fig. 3.4: left: phases during a stance in front view (leftmost) and top view. Thigh (green) and shank (blue) are bent to sustain body height H and foot distance s according to the horizontal joint. Middle and right lead to s=cos(h)*(l*cos(v)+l*sin(v+k)) and H=-L*sin(v)+L*cos(k+v). Resolving these equations to sin(k+v) and cos(k+v) leads to solutions for the vertical joint angles v and k. The model was simulated on a flat floor with a first set of design parameters to test its general practicability. The body was constructed as a box, and all the legs had an initial M-shape posture perpendicular to the sides of the body. Other parameters were length of thigh=36 mm, length of shank=37 mm, swing=.5s, stance=.5s, phase=0. Accelerated Motion Preliminary studies were conducted with a rudimentary implementation of the algorithm for accelerations. The rotational motion of the joints is transferred to the forward motion of the robot. The acceleration of forward motion is rather constant during the entire simulation (rising line in fig. 3.5, left). There is some rolling during the forward motion, which abruptly disappears after two third of the simulation (waving line in fig. 3.5, left). During this rolling there is some deviation of the forward direction of about 0 degrees (fig. 3.6). At the same point the velocity stops showing the undulation pattern and its slope increases. Later an oscillation becomes visible with growing amplitude (fig. 3.5, right). The swing/stance ratio is 3:5 at the begin of the

simulation, it is about : when the undulation disappears and it is above 5: at the end. The ratio expresses how many legs are with (respectively without) ground contact. At the end of the simulation there are only two or three feet stancing simultaneously. It is a well known fact that the minimum number for stable motions is three feet [], and the increasing periods of instability could be the source of the oscillation. The slide of the feet increases considerably during the accelerated motion of Scorpion (fig. 3.6). This effect contributes to unstable periods of motions and it decreases the efficiency. Fig. 3.5: Motion and velocity of the model during a constant acceleration Fig. 3.6: Trace of the center of mass and of foot L It should be noted that the slight deviation in the walking direction is completely due to sliding effects which are far from being predicted precisely. It just shows that such shifts can occur in an unforeseen way and that, of course, a control mechanism has to be added using e.g. a compass or other direction-sensitive devices. We have shown that the task of acceleration is not a trivial one for eight-legged robots. Especially for fast running of walking machines there is much work to be done on optimization of the walking patterns. The investigation of real scorpion data yields many ideas for robotic locomotion. It is quite interesting to observe living scorpions running on high speed (compared to their size) and we will need a lot of future work on this topic to mimic their skills. We have identified stable and instable regions of walking speed and found a robust acceleration scheme for eight-legged walking robots. But in the simulation we could handle much higher forces than our real motors can deliver. So we will have to add elasticity (like springs) to end up with a real dynamic walking or even running.

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