We have made a systematic study of the gait of a straight leg planar passive walking model through simulations and experiments. Three normalised parameters, which represent the foot radius, the position of the mass centre and the moment of inertia, are used to characterise the walking model.

In the simulation, we have obtained the fixed points and the basins of attraction of the walking models with different parameter combinations by the aid of the cell mapping method. With the results of fixed points, we investigated the effects of parameter variations on the gait descriptors, including step length, period, average speed and energy inefficiency. A model that has a large basin of attraction has been obtained, and it can start walking far from its fixed point. However, the size of the basin of attraction is not a good measurement of robustness. Thus, we proposed floors with random slope angles or stairs with random heights to test robustness. Five hundred times of simulations with 100 non-dimensional time units were implemented for each parameter combination. The times that the walker failed to arrive at the end were recorded. The simulation results showed that the model with a larger foot radius and higher position of mass centre has a lower possibility of falling on uneven floors. A large moment of inertia is helpful for walking on a random slope angle floor, while low values of moment of inertia are good for navigating random stairs.

Prototype experiments have validated the simulation results, which showed that models with larger feet have a longer step length and high speed. However, period differences were difficult to obtain in the experiments since the differences were very small. We have tested the sensitivity with the initial conditions of the models with different foot radii on a flat floor, and have also tested the robustness of the models on a floor with random slope angles. The times that the model reached the end of the floor were recorded. The experimental results showed that a large foot radius is good for improving the basin of attraction and robustness on uneven floors. Finally, the exceptions of the experiment are explained.

The kinematics, statics, and workspace of a 2(3-SPR) serial-parallel manipulator (S-PM) are studied systematically in this paper. First, a 2(3-SPR) S-PM including an upper 3-SPR parallel manipulator (PM) and a lower 3-SPR PM is constructed, and the inverse/forward displacements, velocity, acceleration, and statics of the lower and upper 3-SPR PMs are studied, respectively. Second, the kinematics and statics of the lower and upper 3-SPR PMs are combined and the displacement, velocity, acceleration, and statics of a 2(3-SPR) S-PM are analyzed systematically. Third, a workspace of the 2(3-SPR) S-PM is constructed and analyzed. Finally, the analytic solved results are given and verified by the simulation mechanism.

Recursive matrix relations in kinematics and dynamics of a Delta parallel robot having three revolute actuators are established in this paper. The prototype of the manipulator is a three degrees-of-freedom space mechanism, which consists of a system of parallel closed kinematical chains connecting to the moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot's element. Further, the inverse dynamic problem is solved using an approach based on the fundamental principle of virtual work. Finally, a comparative study on time-history evolution of the torques of the three actuators is analysed.

Flexible manipulators have received wide attention because they surpass their rigid counterparts in many criteria. Unfortunately, traditional controller design methods for flexible arms implemented by human experts are usually tedious and intractable. In order to improve system behaviour, this paper proposes schemes based on genetic algorithms (GAs) which optimise the parameters of a fuzzy logic controller for a robotic manipulator with two-link flexibility and two-joint elasticity. Two alternative GA-optimised schemes are simulated and their control behaviour is compared with that of human-expert-designed controller.

This paper presents a continuous wall-following controller for wheeled mobile robots based on odometry and distance information. The reference for this controller is the desired distance from the robot to the wall and allows the robot to follow straight wall contour as well as smoothly varying wall contours by including the curvature of the wall into the controller. The asymptotic stability of the control system is proved using a Lyapunov analysis. The controller is designed so as to avoid saturation of the angular velocity command to the robot. A novel switching scheme is also proposed that allows the robot to follow discontinuous contours allowing the robotic system to deal with typical problems of continuous wall-following controllers such as open corners and possible collisions. This strategy overcomes these instances by switching between dedicated behavior-based controllers. The stability of the switching control system is discussed by considering Lyapunov concepts. The proposed control systems are verified experimentally in laboratory and office environments to show the feasibility and good performance of the control algorithms.

In this paper, a biped that combines the merits of both powered and passive bipeds is proposed. The semi-activeness of the biped is due to the fact that during most of a walking cycle, only half of the joints are actuated to follow specific trajectories, and the other half of joints remain unactuated but have passive springs connected between adjacent links. It is expected that by having unactuated joints, the biped can preserve the power-saving feature of the passive biped, and by having actuated joints under active control, the biped can also achieve the stability and performance of the powered biped. To devise a systematic design methodology for the biped, its dynamics as well as the walking constraints are carefully studied. Furthermore, an optimization procedure is also proposed to compute the optimal trajectories for the actuated joints and spring constants, which can lead to minimum energy consumption. The feasibility of the proposed biped, including the system design and the control strategy, is verified by hardware implementation. Experiments indicate that the biped walking in the semi-active manner consumes 80% less the electrical power than the fully powered biped that performs the same gait and is more energy-efficient than several state-of-the-art bipeds.

The inverse kinematics of a 12 degrees-of-freedom (DOFs) biped robot is formulated in terms of certain parameters. The biped walking gaits are developed using the parameters. The walking gaits are optimized using genetic algorithm (GA). The optimization is carried out considering relative importance of stability margin and walking speed. The stability margin depends on the position of zero-moment-point (ZMP) while walking speed varies with step-size. The ZMP is computed by an approximation-based method which does not require system dynamics. The optimal walking gaits are experimentally realized on a biped robot.

Snake robots have the potential to make substantial contributions in areas such as rescue missions, firefighting, and maintenance where it may either be too narrow or too dangerous for personnel to operate. During the last 10–15 years, the published literature on snake robots has increased significantly. The purpose of this paper is to give a survey of the various mathematical models and motion patterns presented for snake robots. Both purely kinematic models and models including dynamics are investigated. Moreover, the different approaches to biologically inspired locomotion and artificially generated motion patterns for snake robots are discussed.

In this paper, finding the maximum load carrying capacity of mobile manipulators for a given two-end-point task is formulated as an optimal control problem. The solution methods of this problem are broadly classified as indirect and direct. This work is based on the indirect solution which solves the optimization problem explicitly. In fixed-base manipulators, the maximum allowable load is limited mainly by their joint actuator capacity constraints. But when the manipulators are mounted on the mobile bases, the redundancy resolution and nonholonomic constraints are added to the problem. The concept of holonomic and nonholonomic constraints is described, and the extended Jacobian matrix and additional kinematic constraints are used to solve the extra DOFs of the system. Using the Pontryagin's minimum principle, optimality conditions for carrying the maximum payload in point-to-point motion are obtained which leads to the bang-bang control. There are some difficulties in satisfying the obtained optimality conditions, so an approach is presented to improve the formulation which leads to the two-point boundary value problem (TPBVP) solvable with available commands in different softwares. Then, an algorithm is developed to find the maximum payload and corresponding optimal path on the basis of the solution of TPBVP. One advantage of the proposed method is obtaining the maximum payload trajectory for every considered objective function. It means that other objectives can be achieved in addition to maximize the payload. For the sake of comparison with previous results in the literature, simulation tests are performed for a two-link wheeled mobile manipulator. The reasonable agreement is observed between the results, and the superiority of the method is illustrated. Then, simulations are performed for a PUMA arm mounted on a linear tracked base and the results are discussed. Finally, the effect of final time on the maximum payload is investigated, and it is shown that the approach presented is also able to solve the time-optimal control problem successfully.

This paper deals with the computation of the orientation error and the kinematic model of a 3-DOF translational parallel manipulator called the RAF robot. We derived a simple analytical model allowing the computation of the orientation, generated by the deformation of the PKLs, when an external load is applied to the platform. These models allowed us to map the orientation error on the workspace of the robot. We showed in particular that the minimum orientation error can be obtained when the platform is in a certain region of its workspace. Due to its analytical nature, the developed model can also be used for a sensitivity analysis in order to maximize the manipulator precision.

A cable manipulator controls its end-effector by a number of cables. If the cables can balance any external and inertia wrenches at a certain pose of the end-effector, the cable manipulator is said to have a force-closure at this pose. Since a cable can work only in tension, the force-closure at a specific pose may not exist. Thus, how to check the existence of force-closure at a given pose is an important issue for design and control of cable manipulators. This paper describes a systematic method of verifying the existence of force-closure at a specific pose of a general 6-DOF cable manipulator with seven or more cables. By examining the Jacobian matrix of the manipulator, the method can determine whether a force-closure exists at the pose corresponding to the Jacobian matrix. The necessity and sufficiency of the proposed method are mathematically proven. Moreover, a convex-analysis-based simplification of the method for manipulators with more than seven cables is also discussed.

In this paper, we present an on-line task modification method (OTMM) to realize singularity avoidance for nonredundant and redundant manipulators at the velocity level. The method introduces a correction vector, constructed from the task velocity and the singular vector corresponding to the minimum singular value, into the task velocity. The performance is simply affected by the choice of the lower limit of the minimum singular value and a scalar adjusting function, which is monotone with respect to the minimum singular value. The method makes unnecessary avoiding the singularity point by off-line path planning for nonredundant or redundant manipulators, and the effort to check whether the singularity is escapable for redundant manipulators. The simulation results show the effectiveness of the OTMM for on-line singularity avoidance in manipulator motion control.

This paper provides a comprehensive description of a new method of factorization for the Coriolis/centripetal matrix. In the past three decades, studies on dynamics have rapidly developed through the efforts of many researchers in the field of mechanics. While direct methods for deriving the Coriolis/centripetal matrix are well known and have been widely used in the last century, the entries of this matrix were always obtained by means of the Christoffel symbols of first kind. Startling techniques for deriving dynamic equations of robot manipulators first appeared about 30 years ago. Since then, much has been done to refine and develop the method, but it is still a highly active field of research, with many outstanding problems, both theoretical and in applications. This work presents, in a unitary frame and from a new perspective, the main concepts and results of one of the most fascinating aspects of mechanics, namely the factorization of structures, and offers the reader another point of view concerning a possible way to approach the Coriolis/centripetal matrix. It aims to study a theory of representation for such a matrix based on an elegant method of fundamental matrices. The paper is intended to be self-contained by presenting complete properties emerging from these novel structures. This work is useful not only to researchers in mechanics, but also to control engineers who are interested in learning some of the mechanical modeling. Toward this end, the paper provides numerical examples, as well as practical adaptive applications for modern designers to use at the system level.

This paper describes a numerical algorithm to solve the inverse kinematics of parallel robots based on numerical integration. Inverse kinematics algorithms based on numerical integration involve the drift phenomena of the solution; as a consequence, errors are generated when the end-effector location differs from that desired. The proposed algorithm associates a novel method to describe the differential kinematics with a simple numerical integration method. The methodology is presented in this paper and its exponential stability is proved. A numerical example and a real application are presented to outline its advantages.

FastSLAM is a framework for simultaneous localization and mapping using a Rao-Blackwellized particle filter (RBPF). But, FastSLAM is known to degenerate over time due to the loss of particle diversity, mainly caused by the particle depletion problem in resampling phase. In this work, improved particle filter using geometric relation between particles is proposed to restrain particle depletion and to reduce estimation errors and error variances. It uses a KD tree (k-dimensional tree) to derive geometric relation among particles and filters particles with importance weight conditions for resampling. Compared to the original particle filter used in FastSLAM, this technique showed less estimation error with lower error standard deviation in computer simulations.

Several problems of practical interest in robotics can be modelled as the convolution of functions on the Euclidean motion group. These include the evaluation of reachable positions and orientations at the distal end of a robot manipulator arm. A natural inverse problem arises when one wishes to design rather than to model manipulators. Namely, by considering a serial-chain robot arm as a concatenation of segments, we examine how statistics of known segments can be used to select, or design, the remainder of the structure so as to attain the desired statistical properties of the whole structure. This is then a deconvolution density estimation problem for the Euclidean motion group. We prove several results about the convergence of these deconvolution estimators to the true underlying density under certain smoothness assumptions. A practical implementation to the design of planar robot arms is demonstrated.

This paper presents a passive dynamic walking model with toed feet that can walk down a gentle slope under the action of gravity alone. The model is the simplest of its kind with a point mass at the hip and two rigid legs each hinged at the hip on the one end and equipped with toed foot on the other end. We investigate two cases of the model, one with massless legs and another with infinitesimal leg masses. Rotation of the stance foot about the toe joint is initiated by ankle-strike, which is caused by the inelastic collision of the stance leg with a stop mounted on the stance foot. Numerical simulations of walking show that larger step lengths, higher speeds, stability, and energy efficiency can be achieved than what is achievable by a point-feet walker of same hip mass and leg lengths. Period-two gait of a point-feet walker is compared with period-one gait of the toed-feet walker and the mechanism responsible for achieving longer step lengths is described. It is shown that the advantage of the proposed walker comes from its relation to arc-feet walker. The characteristics of deterministic gait with infinitesimal leg masses is compared with that of nondeterministic gait with zero leg masses. It is shown that deterministic gait does not give maximum speed and efficiency compared to nondeterministic gait with swing leg control. Finally, active dynamic walking of the proposed walker is discussed.

In this paper, control of nonlinear teleoperator systems where both the master and slave systems are kinematically redundant robot manipulators is addressed. The controller is developed under the assumption that the user and environmental input forces are unmeasurable. Lyapunov-based stability analysis is used to prove that the proposed controller yields asymptotic tracking results and ensures the coordination of the master and slave systems while satisfying a sub-task objective. Numerical simulation results are presented to illustrate the effectiveness of the proposed controller.

In our previous work, a novel force control actuator, called series damper actuator (SDA), has been proposed. This paper proposes a general design procedure for the SDA system. From design requirements, several key parameters of the SDA plant can be determined. Based on these parameters, the selection or design of the series damper and the motor can be carried out. A case study is included to illustrate the effectiveness of the procedure. As there could be more than one feasible solutions from the procedure, the mechatronic design quotient (MDQ) method can be adopted to select the best solution from a feasible solution space.

Based on the Lie-group-algebraic properties of the displacement set and intrinsic coordinate-free geometry, several novel 4-dof overconstrained hybrid parallel manipulators (HPMs) with uncoupled actuation of three spatial translations and one rotation (3T-1R) are proposed. In these HPMs, three limbs are those of Cartesian translational parallel mechanisms (CTPMs) and the fourth limb includes an Oldham-type constant velocity shaft coupling (CVSC). The Lie subgroup of Schoenflies (X) displacements of the displacement Lie group and its mechanical generators with nine categories of their general architectures are recalled. A comprehensive enumeration of all possible Oldham-type CVSC limbs is derived from X-motion generators. Their constant velocity (CV) transmissions are verified by group-algebraic approach. Then, combining one CTPM and one CVSC, we synthesize a lot of uncoupled 3T-1R overconstrained HPMs, which are classified into nine distinct classes of general architectures. In addition, all possible architectures with at least one hinged parallelogram or with one cylindrical pair are disclosed too. At last, related non-overconstrained HPMs are attained by the addition of one idle pair in each limb of the previous HPMs.