Kinematics,Dynamics and Power Consumption Analyses for Turning Motion of a Six-Legged Robot

This paper deals with kinematics, dynamics and power consumption analyses of a six-legged robot generating turning motions to follow a circular path. Direct and inverse kinematics analysis has been carried out for each leg in order to develop an overall kinematics model of the six-legged robot. It aims to estimate energy-optimal feet forces and joint torques of the six-legged robot, which are necessary to have for its real-time control. To determine the optimum feet forces, two approaches are developed, such as minimization of norm of feet forces and minimization of norm of joint torques using a least square method, and their performances are compared. The developed kinematics and dynamics models are tested through computer simulations for generating turning motion of a statically stable six-legged robot over flat terrain with four different duty factors. The maximum values of feet forces and joint torques decrease with the increase of duty factor. A power consumption model has been derived for the statically stable wave gaits to minimize the power requirement for both optimal foot force distributions and optimal foot-hold selection. The variations of average power consumption with the height of the trunk body and radial offset have been analyzed in order to find out energy-optimal foothold. A parametric study on energy consumption has been carried out by varying angular velocity of the robot to minimize the total energy consumption during locomotion. It has been found that the energy consumption decreases with the increase of angular velocity for a particular traveled distance.     

Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot

Minimization of energy consumption plays a key role in the locomotion of a multi-legged robot used for various purposes. Turning gaits are the most general and important factors for omni-directional walking of a six-legged robot. This paper presents an analysis on energy consumption of a six-legged robot during its turning motion over a flat terrain. An energy consumption model is developed for statically stable wave gaits in order to minimize dissipating energy for optimal feet forces distributions. The effects of gait parameters, namely angular velocity, angular stroke and duty factors are studied on energy consumption, as the six-legged robot walks along a circular path of constant radius with wave gait. The variations of average power consumption and energy consumption per unit weight per unit traveled length with the angular velocity and angular stroke are compared for the turning gaits of a robot with four different duty factors. Computer simulations show that wave gait with a low duty factor is more energy-efficient compared to that with a high duty factor at the highest possible angular velocity. A stability analysis based on normalized energy stability margin is performed for turning motion of the robot with four duty factors for different angular strokes.     

Estimation of optimal feet forces and joint torques for on-line control of six-legged robot

The present study aims to estimate optimal feet forces and joint torques necessary for real-time control of a six-legged robot. Two approaches have been developed, such as minimization of norm of feet forces and minimization of norm of joint torques using the least squared method. Results of these two approaches have been compared with each other, and with those of available literature. As both of these approaches are found to be computationally fast, these are suitable for real-time control of the six-legged robot.     

Torque Distribution in a Six-Legged Robot

In this paper, distribution of required forces and moments to the supporting legs of a six-legged robot is handled as a torque-distribution problem. This approach is comparatively contrasted to the conventional approach of tip-point force distribution. The formulation of dynamics is performed by using the joint torques as the primary variables. The sum of the squares of the joint torques on the supporting legs is considered to be proportional to the dissipated power. The objective function is constructed as this sum, and the problem is formulated as to minimize this quadratic objective function with respect to linear equality and inequality constraints. It is demonstrated that the torque-distribution scheme results in a much more efficient distribution compared with the conventional scheme of force distribution. In contrast to the force distribution, the torque-distribution scheme makes good use of interaction forces and friction in order to minimize the required joint torques     

Design and Control of 6-DOF Mechanism for Twin-Frame Mobile Robot

A new lightweight six-legged robot that uses a simple mechanism and can move and work with high efficiency has been developed. This robot consists of two leg-bases with three legs each, and walks by moving each leg-base alternately. These leg-bases are connected to each other with a 6 degrees of freedom (DOF) mechanism. While designing this robot, the output force, velocity, and workspace of various connection mechanisms were compared, and the results showed that good performance could be achieved with a serial/parallel hybrid mechanism. The serial/parallel hybrid mechanism consists of three 6-DOF serially linked arms positioned with radial symmetry about the center of each leg-base; each leg-base is composed of two active and four passive joints. Walking experiments with this robot confirmed that this mechanism has satisfactory performance not only as a walking robot, but also as an active walking platform. Furthermore, in this robot, the entire leg-drive mechanism acts as a 6-axis force sensor, and individual sensors at the feet are not necessary. The forces and moments can be calculated from the changes in the joint angles. Experiments conducted verified that smooth contact with the ground by the swing-leg and successful switching from swing to support leg can be achieved using this force control and force measurement method.     

Soft computing-based expert systems to predict energy consumption and stability margin in turning gaits of six-legged robots

Turning gaits are the most general and very important ones for omni-directional walking of a six-legged robot. Soft computing-based expert systems have been developed in the present work to predict specific energy consumption and stability margin of turning gait of a six-legged robot. Besides back-propagation neural network, three approaches based on adaptive neuro-fuzzy inference system have been developed and their performances are compared with each other. Genetic algorithm-tuned multiple adaptive neuro-fuzzy inference systems are found to perform better than other approaches. This could be due to a more exhaustive search conducted by the genetic algorithm in place of back-propagation algorithm and the use of two separate adaptive neuro-fuzzy inference systems for two different outputs.     

Relation between global velocity and local torque optimization of redundant manipulators

In this article, the relation between the global optimization of joint velocity and local optimization of joint torque is investigated. The local minimization of the weighted joint torques can be matched to the global optimization of the corresponding weighted joint velocities when the weighted matrices satisfy certain sufficient conditions. A straightforward matching is obtained using the local optimization of the inertia inverse weighted dynamic torque and the global minimization of the kinetic energy. Another easy solution can be found, as will be shown later, if the inertia matrix is a constant and gravity is neglected. Based on that, it can be seen why a Cartesian robot, which has a constant inertia matrix, is always stable. © 1994 John Wiley & Sons, Inc.     

六足步行机的能量稳定性

本文详细讨论了六足步行机器人的能量稳定方法,给出并证明了六足步行机能量稳定裕量的一般计算公式,分析了横向及纵向行走的六足步行机采用三角步态时的能量稳定性,比较了能量稳定法和几何稳定法.     

Soft computing-based approaches to predict energy consumption and stability margin of six-legged robots moving on gradient terrains

Soft computing-based approaches have been developed to predict specific energy consumption and stability margin of a six-legged robot ascending and descending some gradient terrains. Three different neuro-fuzzy and one neural network-based approaches have been developed. The performances of these approaches are compared among themselves, through computer simulations. Genetic algorithm-tuned multiple adaptive neuro-fuzzy inference system is found to perform better than other three approaches for predicting both the outputs. This could be due to a more exhaustive search carried out by the genetic algorithm in comparison with back-propagation algorithm and the use of two separate adaptive neuro-fuzzy inference systems for two different outputs. A designer may use the developed soft computing-based approaches in order to predict specific energy consumption and stability margin of the robot for a set of input parameters, beforehand.     

Power Consumption Optimization for a Hexapod Walking Robot

Power consumption is one of the main operational restrictions on autonomous walking robots. In this paper, an energy efficiency analysis is performed for a hexapod walking robot to reduce these energy costs. To meet the power-saving demands of legged robots, the torque distribution algorithm required to minimize the system’s energy costs was established with an energy-consumption model formulated. In contrast to the force distribution method, where the objective function is related to the tip-point force components, the torque distribution scheme is based on minimization of the mechanical energy cost and heat loss power. The simulation results show that this scheme could reduce the system energy costs with use of the appropriate walking velocities and duty factors for the robot. The paper also discusses the effects of the gait patterns and the mechanical structure on the system energy costs. For this purpose, the prescribed periodic walking gait of the robot is described in terms of several parameters, including the duty factor, the stride length, the body height, and the foot trajectory lateral offset. The numerical results indicate some analogies between the characteristics of the simulated walking robot and those of animals in nature. The optimized parameters derived here are intended for robot platform development applications.     

Time optimization of the continuous-path motions of industrial robots

This paper presents an engineering approach to the time optimization of robotic motions with specified paths and trapezoidal velocity profiles. Optimizations of this type occur when dealing with continuous-path motions of commercial manipulators. Parameterized path equations and full non-linear robot dynamics are used in conjunction with the actuator limitations and the specified path and velocity profile in order to transform the problem into a non-linear programming form. The optimal velocity profile and the corresponding joint torques/forces are obtained via a simple search algorithm, without resorting to any constrained optimization technique, numerical integration, or search for the switching curve. Three examples of time-optimized robotic motions are presented.     

Torque Optimizing Control with Singularity-Robustness for Kinematically Redundant Robots

A new control method for kinematically redundant manipulators having the properties of torque-optimality and singularity-robustness is developed. A dynamic control equation, an equation of joint torques that should be satisfied to get the desired dynamic behavior of the end-effector, is formulated using the feedback linearization theory. The optimal control law is determined by locally optimizing an appropriate norm of joint torques using the weighted generalized inverses of the manipulator Jacobian-inertia product. In addition, the optimal control law is augmented with fictitious joint damping forces to stabilize the uncontrolled dynamics acting in the null-space of the Jacobian-inertia product. This paper also presents a new method for the robust handling of robot kinematic singularities in the context of joint torque optimization. Control of the end-effector motions in the neighborhood of a singular configuration is based on the use of the damped least-squares inverse of the Jacobian-inertia product. A damping factor as a function of the generalized dynamic manipulability measure is introduced to reduce the end-effector acceleration error caused by the damping. The proposed control method is applied to the numerical model of SNU-ERC 3-DOF planar direct-drive manipulator.     

A recurrent neural network for minimum infinity-norm kinematiccontrol of redundant manipulators with an improved problem formulationand reduced architecture complexity

This paper presents an improved neural computation where scheme for kinematic control of redundant manipulators based on infinity-norm joint velocity minimization. Compared with a previous neural network approach to minimum infinity-non kinematic control, the present approach is less complex in terms of cost of architecture. The recurrent neural network explicitly minimizes the maximum component of the joint velocity vector while tracking a desired end-effector trajectory. The end-effector velocity vector for a given task is fed into the neural network from its input and the minimum infinity-norm joint velocity vector is generated at its output instantaneously. Analytical results are given to substantiate the asymptotic stability of the recurrent neural network. The simulation results of a four-degree-of-freedom planar robot arm and a seven-degree-of-freedom industrial robot are presented to show the proposed neural network can effectively compute the minimum infinity-norm solution to redundant manipulators.     

Force-guided motions of a 6-d.o.f. industrial robot with a joint space approach

This article deals with the interaction between humans and industrial robots, more specifically with the new design and implementation of an algorithm for force-guided motions of a 6-d.o.f. robot. It may be used to comfortably teach positions without using any teaching pendant or for some assistance tasks. For this purpose, from readings of the force/torque sensor mounted in the robot wrist, the gravity forces and torques first have to be eliminated. To control the robot in joint space, it is then convenient to transform the external force and torque values from Cartesian space into joint space using the manipulator transposed Jacobian. This is why with the present approach the Jacobian matrix of the robot used was calculated. Now, from the computed joint torques, suitable position commands of the robot arm can be generated to obtain the desired behavior. A suggestion for this desired behavior is also included in this article. It is based on the impedance control approach in joint space. The proposed algorithm was implemented with the standard Stäubli RX90B industrial robot.     

Gait and foot trajectory planning for versatile motions of a six-legged robot

This article deals with the problem of planning and controlling a radially symmetric six-legged walker on an uneven terrain when a smooth time-varying body motion is required. The main difficulties lie on the planning of gaits and foot trajectories. As for the gaits, this article discusses the forward wave gait of a variable duty factor and a variable wave direction. With the commanded body motion, the maximum possible duty factor is computed using the speed limit of the leg swing motion. Guaranteeing this maximum duty factor contributes to obtain higher stability. We prove the “continuity” of this forward wave gait planning algorithm adds the versatility to gaits planned. The foot trajectory planning algorithm dynamically generates a smooth foot trajectory as a function of the instantaneous body motions by modifying standard leg motion templates. The robot can negotiate an uneven terrain by modifying a vertical leg motion by a signal of tactile sensors on the foot. The experiments prove that the robot can successfully track smooth curves with body rotations on an uneven terrain, and thus prove the robustness of the algorithms. © 1997 John Wiley & Sons, Inc.     

Redundant robot control using task based performance measures

The joint velocities required to move the end-effector of a redundant robot with a desired linear and angular velocity depend on its configuration. Similarly, the joint torques produced due to the force and moment at the end-effector also depend on its configuration. When the robot is near a singular configuration, the joint velocities required to attain the end-effector velocity in certain directions are extremely high. Similarly, in some configurations the joint torque produced at certain joints may be high for a relatively small magnitude of external force. An infinite number of trajectories in the joint space can be used to achieve a desired end-effector trajectory for redundant robots. However, a joint trajectory resulting in robot configurations requiring lower joint velocities or joint torques is desired. This may be achieved through a proper utilization of redundancy. Local performance measures for redundant robots are defined in this article as indicators of their ability to follow a desired end-effector trajectory and their ability to apply desired forces at the end-effector. Thus, these performance measures depend on the task to be performed. Control algorithms which can be efficiently applied to redundant robots to improve these performance measures are presented. These control algorithms are based on the gradient projection method. Gradients of the performance measures used in the control schemes result in simple symbolic expressions for “real world” robots'. Feasibility and effectiveness of these control schemes is demonstrated through the simulation of a seven-degree-of-freedom redundant robot derived from the PUMA geometry.     

冗余机械臂优化控制新方法

针对五自由度冗余机械臂,提出了一种新的基于伪逆的优化控制方法：利用一个可调权值因子,将最小速度范数方法（加速度层）和最小加速度范数方法进行加权组合,来实现对冗余机械臂的运动控制。该优化方法可以实现关节速度范数和关节加速度范数的同时最小化,而且使得机械臂的关节速度在运动末态时接近零。计算机仿真结果进一步验证了所给出的优化控制方法的可行性和优越性。     

基于六维力/力矩传感器和关节力矩的仿人机器人步态补偿算法

为实现仿人机器人的稳定行走,提出一种根据其足底六维力/力矩传感器信息、针对关节力矩的步态补偿算法．利用直流伺服电机的过载能力,来改善仿人机器人关节在大负载扰动下的动态性能．行走实验证明了该算法在离线实施过程中的有效性．     

机器人俯仰关节能耗特性分析

以降低架空线移动机器人能耗为目标,从结构设计角度出发提出一种基于平行四边形机构的机器人俯仰关节,由单电机配合柔索驱动。首先,在考虑摩擦因素的情况下进行了关节受力及能耗分析,分别给出本文关节与传统俯仰关节的能耗计算方法。再分别就多单元串联式机器人俯仰运动、以及架空线移动机器人越障运动的能耗特性,进行了本文关节和传统俯仰关...     

Improving feasibility of robotic milling through robot placement optimisation

Milling performed with robots is quite demanding, even for low-strength materials, due to the high accuracy requirements, the generally high and periodically varying milling forces and the low stiffness of robots compared to CNC machine tools. In view of the generally improved recently robot stiffness, it is desirable to perform the milling operation in regions of the robot’s workspace where manipulability, both kinematic and dynamic, is highest, thereby exhausting the robot’s potential to cope with the process. In addition, by selecting the most suitable initial pose of the robot with respect to the workpiece, a reduction in the range of necessary joint torques may be reached, to the extent of alleviating the heavy requirements on the robot. Two genetic algorithms (GAs) are employed to tackle these problems. The values of several robot variables, such as joint positions and torques, which are needed by the genetic algorithms, are calculated using inverse kinematics and inverse dynamics models. In addition, initial positions and poses leading to singularities along the milling path are penalized and, thus, avoided. The first GA deals solely with robot kinematics to maximize manipulability. The second GA takes into account milling forces, which are computed numerically according to the particular milling parameters, to minimise joint torque loads.