Optimal trajectory generation for biped robots walking up-and-down stairs

This paper proposes an optimal trajectory generation method for biped robots for walking up-and-down stairs using a Real-Coded Genetic Algorithm (RCGA). The RCGA is most effective in minimizing the total consumption energy of a multi-dof biped robot. Each joint angle trajectory is defined as a 4-th order polynomial of which the coefficients are chromosomes or design variables to approximate the walking gait. Constraints are divided into equalities and inequalities. First, equality constraints consist of initial conditions and repeatability conditions with respect to each joint angle and angular velocity at the start and end of a stride period. Next, inequality constraints include collision prevention conditions of a swing leg, singular prevention conditions, and stability conditions. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot model that consists of seven links in the sagittal plane. The optimal trajectory is more efficient than that generated by the Modified Gravity-Compensated Inverted Pendulum Mode (MGCIPM). And various trajectories generated by the proposed GA method are analyzed from the viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.     

Trajectory optimization with GA and control for quadruped robots

This paper proposes an optimal galloping trajectory, which costs low energy and guarantees the stability of the quadruped robot. In the realization of fast galloping, the trajectory design is important. For a galloping trajectory, we propose an elliptic leg trajectory, which provides simplified locomotion to complex galloping motions of animals. However, the elliptic trajectory, as an imitation of animal galloping motion, does not guarantee stability and minimal energy consumption. We propose optimization based on energy and stability using a genetic algorithm, which provides a robust and globally optimized solution to this multi-body, highly nonlinear dynamic system. To evaluate and verify the effectiveness of the proposed trajectory, a series of computer simulations were carried out. This paper was recommended for publication in revised form by Associate Editor Doo Yong Lee Jong Hyeon Park received the B.S. degree in mechanical engineering from Seoul National University, Seoul, Korea, in 1981 and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, in 1983 and 1991, respectively. Since 1992, he has been with the School of Mechanical Engineering at Hanyang University, Seoul, Korea, where he is currently a professor. He was a KOSEF (Korea Science and Engineering Foundation)-JSPS (Japan Society for the Promotion of Science) Visiting Researcher with Waseda University, Tokyo, Japan, in 1999, and a KOSEF-CNR (Consiglio Nazionale delle Ricerche) Visiting Researcher with Scuola Superiore Sant’Anna, Pisa, Italy, in 2000, a Visiting Scholar with MIT, Cambridge, USA, in 2002–2003. He was also associated with Brooks Automation Inc., Chelmsford, MA, in 1991–1992 and 2001–2002. His research interests include biped robots, robot dynamics and control, haptics, and bio-robots. He is a member of the IEEE (Institute of Electrical and Electronics Engineers), KSME (Korea Society of Mechanical Engineers), ICROS (Institute of Control, Robotics and Systems), KROS (Korea Robotics Society), KSAE (Korean Society of Automotive Engineers), KSPE (Korean Society of Precision Engineering) and KSEE (Korean Society for Engineering Education).     

The effects of ground compliance on flexible planar passive biped dynamic walking

Journal of Mechanical Science and Technology - Passive biped dynamic walking exhibits humanoid gait. Many efforts have been made to implement a flexible and anthropomorphic passive model. However,...     

考虑参数不确定性和外界干扰的移动机器人轨迹跟踪控制

针对具有参数不确定性和外界干扰的移动机器人轨迹跟踪问题,提出一种运动学跟踪控制器和动力学跟踪控制器相结合的控制方法。基于反演方法,应用自适应控制技术设计速度控制率的同时,对运动学模型中的未知参数进行了估计。在此基础上,引入动力学回归矩阵和单层神经网络以使机器人实际速度接近理论速度,并减弱系统参数不确定和外界干扰对于跟踪控制效果的影响。设计过程中,根据Lyapunov稳定性定律和Barbalat引理对控制系统的稳定性和收敛性进行了分析。对于典型曲线的仿真结果表明了所提出控制方法的有效性。     

Dynamic stair walking of biped humanoid robots

Biped humanoid robots are expected to move around human-centered setting that includes stairs as a major terrain. Reportedly, however, only few of them can walk up and down stairways as of now. Making it worse, even the successful ones carry out such motions either barely in terms of speed or fast enough but in an undisclosed technical manner. In this context, a dynamic gait pattern is proposed anew suitable for stair walks along with a transient pattern and verified by means of a multi-body dynamics analysis software.     

Trajectory generation to suppress oscillations in under-constrained cable-driven parallel robots

Cable-driven parallel robots (CDPRs) have many advantages over conventional link-based robot manipulators in terms of acceleration due to their low inertia. This paper concerns about under-constrained CDPRs, which have a less number of cables than six, often used favorably due to their simpler structures. Since a smaller number of cables than 6 are employed, however, their payloads have extra degrees of motion freedom and exhibit swaying motions or oscillation. In this paper, a scheme to suppress unwanted oscillatory motions of the payload of a 4-cable-driven CDPR based on a Zero-vibration (ZV) input-shaping scheme is proposed. In this method, a motion in the 3-dimensional space is projected onto the independent motions on two vertical planes perpendicular to each other. On each of the vertical plane, the natural frequency of the CDPR is computed based on a 2-cable-driven planar CDPR model. The precise dynamic model of a planar CDPR is obtained in order to find the natural frequency, which depends on the payload position. The advantage of the proposed scheme is that it is possible to generate an oscillation-free trajectory based on a ZV input-shaping scheme despite the complexity in the dynamics of the CDPR and the difficulty in computing the natural frequencies of the CDPR, which is required in any ZV input-shaping scheme. To verify the effectiveness of the proposed method, a series of computer simulations and experiments were conducted for 3- dimensional motions with a 4-cable-driven CDPR. Their results showed that the motions of the CDPR with the proposed method exhibited a significant reduction in oscillations of the payload. However, when the payload moves near the edges of its workspace, the improvement in oscillation reduction diminished as expected due to the errors in model projection.

     

Analysis of the dynamic stress of planar flexible-links parallel robots

This paper presents a method for the dynamic stress analysis of planar parallel robots with flexible links and a rigid moving platform. The finite element-based dynamic model of flexible parallel robots is proposed. The relation between elastic deformations and elastic displacements of the flexible links is investigated, considering the coupling effects of elastic motion and rigid motion. The elastic deformations of links are calculated. Considering the effects of bending-shearing strain and tensile-compression strain, the dynamic stress of the links and its position are derived by using the Kineto-Elastodynamics theory and the Timoshenko beam theory. Due to the flexibility of the links, the dynamic stresses are well illustrated through numerical simulation. Compared with the results of the finite element software SAMCEF, the numerical simulation results show the good coherence and advantages of the analysis method. The dynamic stress analysis is demonstrated to have a significant impact on the analysis, design and control of flexible parallel robots.     

Energy efficient walking control for biped robots using interval type-2 fuzzy logic systems and optimized iteration algorithm

An energy efficient approach is proposed for the walking control of bipedal robots. To compensate the ZMP error caused by model uncertainties and external disturbances, we design a new walking controller in this paper. Different from currently available control schemes for cancelling ZMP error, our newly proposed one additionally incorporates a fuzzy logic systems(FLSs) mechanism and an iterative mechanism. By employing FLSs to deduce Center of Mass(CoM) correction according to ZMP error and designing iterative mechanism to compute the optimal joint position, the newly proposed controller exhibits an excellent performance. To tackle the control difficulties arising from physical constraints of actuators and hard-to-stabilization of biped robot, an optimized control algorithm is included in the iterative mechanism to guarantee the convergence to the optimal solution. Moreover, the interval type-2 FLSs are adopted to handle the uncertainties. Finally, the experiment results are provided to validate the proposed control scheme.     

Static balancing of planar articulated robots

Static balancing for a manipulator’s weight is necessary in terms of energy saving and performance improvement. This paper proposes a method to design balancing devices for articulated robots in industry, based on robotic dynamics. Full design details for the balancing system using springs are presented from two aspects: One is the optimization for the position of the balancing system; the other is the design of the spring parameters. As examples, two feasible balancing devices are proposed, based on different robotic structures: The first solution consists of linkages and springs; the other consists of pulleys, cross mechanisms and (hydro-) pneumatic springs. Then the two solutions are compared. Pneumatic, hydro-pneumatic and mechanical springs are discussed and their parameters are decided according to the requirements of torque compensation. Numerical results show that with the proper design using the methodology presented in this paper, an articulated robot can be statically balanced perfectly in all configurations. This paper therefore provides a design method of the balancing system for other similar structures.     

载人两足步行机器人研究现状及其关键技术

鉴于在诸如医疗、福利等众多领域广泛的应用前景,载人两足步行机器人的研发逐渐成为机器人学领域的一个新的热点。介绍了目前载人两足步行机器人的研究现状和相关成果。然后,对该研究的关键内容——步态稳定控制、安全保护和减震系统等作了介绍和分析。     

Dynamic modeling of flexible-links planar parallel robots

This paper presents a finite element-based method for dynamic modeling of parallel robots with flexible links and rigid moving platform. The elastic displacements of flexible links are investigated while considering the coupling effects between links due to the structural flexibility. The kinematic constraint conditions and dynamic constraint conditions for elastic displacements are presented. Considering the effects of distributed mass, lumped mass, shearing deformation, bending deformation, tensile deformation and lateral displacements, the Kineto-Elasto dynamics (KED) theory and Lagrange formula are used to derive the dynamic equations of planar flexible-links parallel robots. The dynamic behavior of the flexible-links planar parallel robot is well illustrated through numerical simulation of a planar 3-RRR parallel robot. Compared with the results of finite element software SAMCEF, the numerical simulation results show good coherence of the proposed method. The flexibility of links is demonstrated to have a significant impact on the position error and orientation error of the flexible-links planar parallel robot.     

平面两自由度驱动冗余并联机器人的运动及灵巧性分析

研究一种平面两自由度驱动冗余并联机器人的运动学求解，同时探讨了该并联机器人机构的工作空间，并绘制了工作空间的各种形状，在此基础上分析了该并联机器人机构的灵巧性，利用特例在其工作空间内绘制了灵巧性性能图谱，这些图谱是该并联机器人的机构设计的重要参考依据。     

Trajectory planning of mobile robots using indirect solution of optimal control method in generalized point-to-point task

This paper presents an optimal control strategy for optimal trajectory planning of mobile robots by considering nonlinear dynamic model and nonholonomic constraints of the system. The nonholonomic constraints of the system are introduced by a nonintegrable set of differential equations which represent kinematic restriction on the motion. The Lagrange’s principle is employed to derive the nonlinear equations of the system. Then, the optimal path planning of the mobile robot is formulated as an optimal control problem. To set up the problem, the nonlinear equations of the system are assumed as constraints, and a minimum energy objective function is defined. To solve the problem, an indirect solution of the optimal control method is employed, and conditions of the optimality derived as a set of coupled nonlinear differential equations. The optimality equations are solved numerically, and various simulations are performed for a nonholonomic mobile robot to illustrate effectiveness of the proposed method.     

Vibration suppression of speed-controlled robots with nonlinear control

In this paper, a simple nonlinear control strategy for the simultaneous position tracking and vibration damping of robots is presented. The control is developed for devices actuated by speed-controlled servo drives. The conditions for the asymptotic stability of the closed-loop system are derived by ensuring its passivity. The capability of achieving improved trajectory tracking and vibration suppression is shown through experimental tests conducted on a three-axis Cartesian robot. The control is aimed to be compatible with most industrial applications given the simplicity of implementation, the reduced computational requirements, and the use of joint position as the only measured signal.     

基于CPG的仿人机器人运动控制方法及研究进展

对基于CPG的仿人机器人运动控制方法的仿生学基础及控制原理、特性进行了阐述,并从控制模型、控制体系、参数调节、与其它控制器的联合几个方面对该方法的研究进展进行了分析和总结,对其发展趋势进行了展望.     

Determination of dynamic accuracy of manipulation systems of robots with elastic hinges

Two mathematical models for determining the dynamic accuracy of manipulation systems of robots with elastic hinges are considered. Mathematical models are the implementation of the method based on the Lagrange equation and using the transformation matrices of elastic coordinates. Mathematical models make it possible to determine the elastic deviations of manipulation systems of robots from programmed motion trajectories caused by elastic deformations in hinges, which are taken into account in directions of change of the corresponding generalized coordinates. One model is the exact implementation of the Lagrange method and makes it possible to determine the total elastic deviation of the manipulation system from the programmed motion trajectory. Another mathematical model is approximated and makes it possible to determine small elastic quasi-static deviations and elastic vibrations. The results of modeling the dynamics by two models are compared to the example of a three-link manipulation system. The considered models can be used when performing investigations of the mathematical accuracy of the manipulation systems of robots.     

大型复杂曲面喷漆机器人喷枪轨迹优化研究

根据实验数据推出平面上漆膜累积速率二次函数后,对大型复杂曲面进行分片,在每一片上进行喷漆机器人喷枪轨迹优化.按照两片交界处喷枪路径的位置关系,分三种情况讨论漆膜厚度的计算方法和喷枪轨迹优化问题,采用最速下降法和模式搜索法进行求解.最后通过计算机仿真验证了优化算法的可行性.     

全方位移动机器人编队控制研究

针对多机器人系统编队的控制问题,将编队行为分为了任务执行行为、队形保持行为、安全运行行为,并分别对各行为进行了研究,对各种传统编队方法进行了总结和比较,通过建立移动机器人的运动学模型,得到了车体运动的控制参数,提出了针对基于麦克纳姆轮的全方位移动机器人编队的基于行为的融合编队控制算法,利用Matlab软件对编队的各种行为进行了仿真。研究结果表明,该基于行为的融合编队控制算法能使全方位机器人完成编队行为,能够实现队形形成、队形保持、躲避静态障碍物、躲避机器人及驶向目标点等行为,编队基于该方法,实现迅速、可靠性高。     

冗余度机器人的非接触阻抗控制

机器人与运动物体接触的过程包括非接触、接触过渡和接触3个部分。对于机器人与高速运动目标接触等存在较大冲击的应用实例，进行有效的非接触阻抗控制是实现机器人稳定、安全作业的必然要求。这方面的研究是实现机器人捕捉运动物体的关键技术，在工业、军事和航天等领域均有重要意义。本文对冗余度机器人非接触阻抗控制的理论和应用研究的现状进行了详细的综述，并提出了需要进一步深入研究的一些问题。