1、学位论文Robotics and Autonomous SystemsVolume 59, Issue 2, February 2011, Pages 1421501 Efficient force distribution and leg posture for a bio-inspired spider robot R. Vidoni, A. GasparettoShow moredoi:10.1016/j.robot.2010.10.001Get rights and content1.1 AbstractLegged walking and climbing robots have r
2、ecently achieved important results and developments, but they still need further improvement and study. As demonstrated by recent works, bio-mimesis can lead to important technical solutions in order to achieve efficient systems able to climb, walk, fly or swim (Saunders etal., 200636, Ayers, 200125
3、, Safak and Adams, 200226). In this paper, taking into account the anatomy and the adhesive and locomotion capabilities of the spider (i.e., an eight-legged system), we present on the one hand a study of the foot force and torque distribution in different operative and slope conditions and, on the o
4、ther hand, a posture evaluation by comparing different leg configurations in order to minimize the torque effort requirements.1.1.1.1 Research highlights We addressed the force and torque distribution for an eight-legged spider robot. We considered the anatomy and the adhesive and locomotion capabil
5、ities of the spider. The static problem is solved in all the working conditions. We evaluated different bio-mimetic postures from a minimum effort point of view. The C-shape posture allows a low effort and a torque diminution along the leg joints.1.2 Keywords Climbing spider robot; Legged mechanism;
6、 Bio-mimesis; Force distribution; Adhesion1.3 1. IntroductionMost of the vehicles that we are familiar with use wheels for their locomotion. They can achieve high speed and relatively small control complexity but, even with complex suspension systems, they present a lot of limitations in irregular a
7、nd rough terrains (e.g., hazardous environments and uneven ground). With legged systems, most of the difficulties can be overcome thanks to the flexibility and ground adaptation. Indeed, the opportunity to choose between different available solutions and to adapt and control the position of the cent
8、er of mass of the system allows avoiding slippage and overturns due to terrain irregularities. The costs that have to be paid are lower speed of locomotion and higher complexity of the control with respect to wheeled systems. However, bio-inspired locomotion controllers based on central pattern gene
9、rators (CPGs; see1), i.e., neural circuits capable of producing coordinated patterns of high-dimensional rhythmic output signals while receiving only simple input signals, and on reflexive controllers, i.e., Cruse control for the coordination of the legs2and3, are looking to fill the gap.Moreover, d
10、ue to the fact that the legs are independently controlled, legged systems have a large number of degrees of freedom (DOFs) to be coordinated in order to control the position, balance the forces (e.g., load, external forces) and consume as little energy as possible. Since the task of finding an optim
11、al force allocation should be done in real time, fast algorithms and control functions have to be used, as also when a body force command solution is not achievable and a new plan has to be formulated.Legged robots have a body and a number of articulated legs that start from it. Each of these kinema
12、tic chains can be viewed as a manipulator that acts like a limb and contributes to the overall position and equilibrium of the structure.In order to evaluate and create an effective legged robot, the idea is to draw inspiration from nature. In nature, different legged systems able to walk and climb
13、different surfaces with a low energetic consumption and high autonomy can be found. Indeed, safe attachment to and easy detachment from smooth substrates is a major feature of a diverse range of animal species. Attachment without using fluids, so-called dry adhesion, is exploited by geckos andEvarch
14、a arcuataspiders by means of fibrillar elements4,5,67.The adhesion force seems to be related to the approaching angle between the attaching elements and the surface: the maximum adhesion condition is reached when the angle is around 30; a sliding condition occurs when the angle is smaller, and detac
15、hment occurs when the angle is bigger89.In this work our attention is focused on a bio-mimetic spider robot.Starting from the kinematic model and simulator (Fig.1), which are the result of a previous biological and kinematic study1011, the static and quasi-static problems applied to the spider eight
16、-legged system in different slope conditions are solved.Fig.1.Kinematic model of the spider robot. Each leg is composed of three links and three joints (one universal and two revolute pairs;11).Figure optionsIn Section2, the analysis of the different theories and approaches related to the force and
17、torque foot distribution that can be found in literature12,13,14,15,16,17,18,19,20,21,22,2324are reviewed.3, the theory of the optimal force distribution is presented and extended in order to search for an effective result for the spider system in all working conditions (i.e., flat, vertical and inv
18、erted surfaces).4an analysis of the overall amount of torque that has to be applied for maintaining different configurations and a comparison between different bio-mimetic postures and conditions for the legs is made.Finally, concluding remarks and future work directions are presented in Section5.2.
19、 Legged robots: the force distribution problem (FDP)The complexity of light legged robots, such as six-legged and four-legged robots, is due to the different kinematic chains (i.e., legs) that during the locomotion have to develop two different actions: those that are in a rested condition have to s
20、upport and shift the body while balancing the forces; the legs in flight have to reach the future support position.Moreover, due to the existence of four actuated joints in each leg, as in11, the octopod model has a redundant actuation leading to more active joints than the number of robot degrees o
21、f freedom. Therefore, there are fewer force moment balance equations than unknown design variables, and the mathematical solution of these equations is not unique, due to the presence of a non-squared matrix. Looking at the real world, there are some physical constraints that have to be taken into a
22、ccount (i.e., the contact nature, friction, adhesion, torque limits) and that can be represented only through inequalities due to the nature of the contact.An effective approach is the one based on the distribution of forces that try to solve the so-calledforce distribution problem (FDP; see, e.g.,1
23、3). Each leg that touches and supports the body applies a certain force (fd) on the support point that is balanced by means of an (equal and opposite) reaction force (fr) of the substrate.fdis the distributed force because it represents the distributed component of the external forces and moments ap
24、plied on that leg. Hence, each leg can be considered as a manipulator anchored to the body that has to be able to generate on the tip of the last limb of the leg (i.e., the end-effector) anforce in order to create a static equilibrium. The geometry of the structure and the position of the legs produ
25、ce the distribution of forces and moments on the legs. Since the mathematical solution is not unique and the physical constraints are only inequalities, the FDP involves the optimization of the force for the legs. Then, the FDP can be formulated as a nonlinear constrained programming problem under n
26、onlinear equality and inequality constraints.In the literature, several approaches and algorithms have been proposed for solving and finding the optimal solution of the FDP for legged robots. There are four main methods that can be studied and evaluated for a real implementation of the control.1.Lin
27、ear-programming (LP) method14.2.Compact-dual LP (CDLP) method16.3.Quadratic programming (QP) method21.4.Analytical method22.In comparison with the existing literature, several original features of this work can be remarked upon.The spider is an eight-legged system, whereas usually six-legged and fou
28、r-legged robots are studied. No applications of the FDP problem for an eight-legged system have been found in the literature. As a consequence, at least four legs are in contact with the substrate in the support phase condition (i.e., four legs in contact and four legs in flight) and the hypothesis
29、adopted for six-legged robots in order to reduce the complexity of the system22cannot be applied.Moreover, the spider robotic system must be able to walk and climb on different slope conditions up to the inverted condition; hence, the adhesive capabilities have to be taken into account.Finally, in t
30、he model presented in this work, each spider leg has four DOFs while in the literature the number of DOFs of the eight-legged robots is usually three or less25,2627.Thus, the present study is more general with respect to all the other studies dealing with legged systems. In particular, not only the
31、friction force but also the adhesion forces have to be taken into account in order to simulate and control the system in the climbing phases.The artificial attaching systems developed until now28,29,3031do not reach the adhesive capabilities of the real ones, and usually degrade themselves with use; as a consequence, in order to evaluate and simulate an efficient model, the biological characteristics and adhesive capabilities of the spiderE. arcuata7will be u
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