Multibody bionic systems modeling - The puppet master approach

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/254042391 Multibody bionic systems modeling - The puppet master approach Article · May 2012 DOI: 10.1109/CarpathianCC.2012.6228673 CITATIONS READS 0 37 3 authors: Janusz Kowal Wojciech Lepiarz 15 PUBLICATIONS 32 CITATIONS 6 PUBLICATIONS 3 CITATIONS AGH University of Science and Technology in … SEE PROFILE AGH University of Science and Technology in … SEE PROFILE Andrzej Sioma AGH University of Science and Technology in … 100 PUBLICATIONS 111 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Active suspensions of the high mobility multipurpose wheeled vehicles View project All content following this page was uploaded by Andrzej Sioma on 30 September 2014. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately. Multibody bionic systems modeling The Puppet Master Approach Janusz Kowal, Wojciech Lepiarz, Andrzej Sioma AGH – University of Science and Technology Faculty of Mechanical Engineering and Robotics, Department of Process Control Krakow, Poland [email protected], [email protected], [email protected] Abstract— In this study, the puppet master approach to solve the kinematics of complex multi-body systems is introduced. The puppet master approach is shown in comparison with traditional analytical one. The method is used to solve multi-body systems of bio-inspired concept prototypes. In these examples the strong and weak sides of this approach are shown. The puppet master approach can be used to rapidly evaluate and compare different concept prototypes. Keywords: multibody dynamics; bionics; biomimetics; process control; modeling and simulation; virtual prototyping I. INTRODUCTION The analysis of gait kinematics and dynamics is, in most cases, a complex and time-consuming task [8]. Furthermore, time is crucial in the early stages of prototype development, especially when there are many concept models that must be quickly evaluated and analyzed. The common method applied in robotics is the Inverse Kinematics (IK) method, which is used to calculate how a mechanism must move to achieve a certain position in space. However for mechanisms with many Degrees Of Freedom (DOF), IK is very complex and often gives more than one answer. Walking machines are an example of such mechanisms. On the other hand, the traditional approach (IK) always gives a full answer, i.e. every possible state of mechanism, but often this full answer is not needed, particularly in the early stages of design development. The method shown in this paper, called the Puppet Master Approach, enables finding the states of mechanism needed to move according to given algorithm. It uses MD Adams software to solve nonlinear and differential equations in order to find functions describing actuator or motor motion. It enables the quick and efficient implementation and evaluation of walking algorithms in virtual prototypes of walking robots. The method is intuitive and helpful in tasks, where the designer must compare many, even very different, concept models of walking machines. The method is shown on an example of a bio-inspired robot concept design. The walking algorithm is implemented in a given kinematic structure of a virtual prototype. It is then subject to a multi-body dynamic simulation, which verifies the walking algorithm, stability of motion and, if needed, gives formulas needed to control motors or actuators in the real prototype. Two main goals of the analysis are to verify a walking algorithm in virtual environment and to formulate motion functions, which may be implemented in a prototype’s control system. The walking algorithm and kinematic structure of the virtual prototype shown in this paper are inspired by the cockroach (Blaberus discoidalis). The Kinematic structure of the cockroach is a very good example - it is complex; after simplification it has 3 DOF on each of its six legs, which gives 18 DOF in total. Furthermore, it is described in literature [6], so this paper may focus on the Puppet Master Approach, instead of a traditional analysis of cockroach’s kinematic structure. II. A. Walking Algorithm In the early stages of walking machine prototype development one of the most important tasks is to implement a certain walking algorithm in a model of a walking robot. The designer must know, if the geometry of the robot enables it to move according to the walking algorithm and if the movement is stable, and where the core technical problems may lie in the future. The walking algorithm implemented in this example is inspired by the locomotion of an insect - Blaberus discoidalis. A single organism of this species was filmed. The captured video enabled the motion analysis of insect gait [1], [3]. Most six-legged insects walk according to the same movement algorithm [5][7]. They stand on 3 legs, while moving other 3 forward to make a step (Figure 1 A, B). Then, the legs that were lifted are put down and the other three are raised and moved to the front of the body (Figure 1 C, D). The movement algorithm is in fact very similar to human gait. We also stand on one leg, and move the other one forward to make a step. During the motion analysis of a cockroach 7 points were traced [4]. Six of them were the ends of insect legs, the seventh was the geometric center of insect’s body. Using the results of this analysis a simplified cockroach walking algorithm was developed. Financed as a part of research project N N502 337336 conducted by AGH University of Science and Technology 978-1-4577-1868-7/12/$26.00 ©2012 IEEE METHOD 388 B. The Kinematic Simulation The kinematic structure of the virtual prototype was also inspired by Blaberus discoidalis. Each leg is simplified to three parts linked together by rotational joints with 1 DOF, legs are linked to the body of a model also by a rotational joint with 1 DOF (Figure 2). All in all, the mechanism has 18 DOF (Figure 3). Each rotational joint in the virtual prototype represents a motor. The results of the kinematic analysis are 18 functions describing how angular displacements of rotational joints change in time. Figure 2. Kinematic structure of one of the legs, A, B and C are rotational joints with 1 DOF In the traditional approach, the forward and inverse kinematics would be calculated to find these functions. However, in the Puppet Master Approach mathematical formulation of the problem is different. When validating if certain mechanism will walk according to the chosen algorithm, solving IK is not needed. Instead, numerical methods for solving differential equations may be used to find how the analyzed virtual prototype moves in different conditions [2]. Figure 1. Frames illustrating cockroach’s gait, rectangle – geometric centre, circle – start leg position of step, cross – final leg position in step Figure 3. Virtual Prototype 2012 13th International Carpathian Control Conference (ICCC) 389 In the example MSC MD Adams was used to solve differential equations of motion. MD Adams uses a modified Newton-Rhapson algorithm to solve nonlinear equations, for more information see [9]. The software provided a sandbox, in which the virtual prototype could be tested. The whole idea of the Puppet Master Approach needs some kind of a virtual environment, in which models can be tested. The first step of the method is to constrain certain points in the mechanism in order to make it move according to the chosen walking algorithm. Similar to a puppet master, who attaches strings to certain parts of his puppet in order to control its movement. In the example, the total 7 points were constrained: six end points of legs and Center of Mass (CM) of the model’s body. All six DOF of CM were constrained. In the case of end points of legs only 3 DOF (translations) were constrained for each point. All in all, 24 functions were needed to fully describe the model’s walking algorithm. After constraining the model, transient kinematic simulation was performed to see if it moves according to a prescribed walking pattern. The duration of the simulation was 40 s with the step size of 4E-3 s. In this step it is possible to quickly refine the functions driving the 7 constrained points in order to make the mechanism move exactly like the designer intended. The results of this simulation are 18 functions describing the angular displacement of each rotational joint in time. The data are in discrete form. It is a set of 18 matrices, where the first column of each is time (s), the second one is angular displacement (rad) of a given kinematic pair. These data are then used in the next step of the method to drive the rotational joints in a dynamic simulation of the virtual prototype. C. The Dynamic Simulation The dynamic simulation is crucial in the Puppet Master Approach. It validates whether the walking algorithm is correct for a given kinematic structure, whether the movement of the model is stable, or even to determine the forces in the mechanism. In the dynamic simulation, the seven points earlier constrained in kinematic simulation are no longer driven. Instead, functions describing the angular displacement are applied to constraints on rotational joints. Furthermore, the gravity field is added and the mass of all elements is defined. A flat plane is added also as a ground on which the model can walk. 40 s and a step size of 4E-3 s. The resulting animation showed, that the walking algorithm is correct, and the model walks stably in a simulated environment. In most other cases however, dynamic simulation shows errors and flaws in the virtual prototype. They should be corrected and then a new kinematic and dynamic analysis should be performed until all the initial requirements, like stable movement, speed etc. are satisfied. The final results of the simulation include forces and torques in all of the joints, positions of mechanism’s elements. Every variable can be presented as a discrete function of time or another variable. Furthermore, functions computed during the kinematic simulation can be easily used in control programs of a real prototype of the analyzed walking machine. III. RESULTS AND DISCUSSION To validate dynamic simulation, comparison between position of CM of the body observed during kinematic simulation and the one computed in dynamic simulation was used. The results can be seen on Figure 4, Figure 5 and Figure 6 . On Figure 4, minor oscillations occur, but they are less than 2% body width. On Figure 5 a rapid fall can be seen at the start of the simulation. It is the result of the model falling to the ground placed 1.75 mm under it. Minor oscillations of CM position also occur along this axis. On Figure 6 Z translation of CM in time is shown, it illustrates a linear function. In dynamic simulation CM of the body moves along a very similar path to the ideal one. The maximum error equals 5%. During dynamic simulation the whole model moves almost perfectly, following the path defined in the ideal, kinematic simulation. The Puppet Master Approach was developed to improve the concept model validation process during the development of a walking machine prototype. The two main advantages of the Puppet Master Approach are intuitiveness and speed. It is faster than the traditional approach, especially in systems with many DOF and when validation of many different kinematic structures is needed. On the other hand, the results of this method are incomplete. Resulting functions show only how to control actuator displacement or velocity in order to move according to a chosen walking algorithm. Also, the implementation of sensors in the control algorithm is quite limited. The dynamic simulation was performed using GSTIFF integrator with I3 formulation [10, 11] with a total time equal Figure 4. Position of Center of Mass of the Body along X axis vs. time 390 2012 13th International Carpathian Control Conference (ICCC) Figure 5. Position of Center of Mass of the Body along Y axis vs. time Figure 6. Position of Center of Mass of the Body along Z axis vs. time IV. CONCLUSION The Puppet Master Approach is fast and intuitive. It is very useful in the early stages of the development of a new walking machine, especially when it has a complex kinematic structure. It is a tool that enables quick verification and comparison of many, even vastly different, concept models. It also includes complete dynamic analysis of the mechanism, which is needed to verify the walking algorithm. Furthermore, the Puppet Master Approach works very well with motion capture systems. The movement paths of points obtained by vision motion capture system can be easily implemented in multi-body models and used in the Puppet Master Approach. On the other hand, the results of the Puppet Master Approach are limited by initial constraints. The calculated displacement functions describe only a walking algorithm enforced on the model during kinematic simulation. The Puppet Master Approach should not be used in tasks, where the definition of all the possible states of kinematic structure is needed. It is possible to calculate all those kinematic states using the Puppet Master Approach for a discrete space, but such numerical analysis is less accurate and probably as time consuming as IK method. REFERENCES [1] J. Kowal, B. Karwat, A. Sioma, “The use of vision systems for building terrain maps for mobile robots,” Field robotics: proceedings of the 14th international conference on Climbing and walking robots and the support technologies for mobile machines, Paris, France, 6–8 September 2011, pp. 463-470 [2] A. Sioma, W. 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