Higher-order derivatives of kinematic mappings give insight into the motion characteristics of complex mechanisms. Screw theory and its associated Lie group theory have been used to find these derivatives of loop closure equations up to an arbitrary order. In this paper, this is extended to the higher-order derivatives of the solution to these loop closure equations to provide an approximation of the finite motion of serial and parallel mechanisms. This recursive algorithm, consisting solely of matrix operations, relies on a simplified representation of the higher-order derivatives of open chains. The method is applied to a serial, a multi-DOF parallel, and an overconstrained mechanism. In all cases, adequate approximation is obtained over a large portion of the workspace.

As for the obstacle avoidance and formation control for the multi-robot systems, this paper presents an obstacle-avoidance method based on the improved artificial potential field (IAPF) and PID adaptive tracking control algorithm. In order to analyze the dynamics and kinematics of the robot, the mathematical model of the robot is built. Then we construct the motion situational awareness map (MSAM), which can map the environment information around the robot on the MSAM. Based on the MSAM, the IAPF functions are established. We employ the rotating potential field to solve the local minima and oscillations. As for collisions between robots, we build the repulsive potential function and priority model among the robots. Afterwards, the PID adaptive tracking algorithm is utilized to multi-robot formation control. To demonstrate the validity of the proposed method, a series of simulation results confirm that the approaches proposed in this paper can successfully address the obstacle- and collision-avoidance problem while reaching formation.

This paper presents a hybrid strategy-based coordinate controller with a novel nonlinear disturbance observer for autonomous underwater vehicle manipulator systems (UVMSs). This method can reduce the influence from external unknown disturbances, inner coupling effects and model uncertainties by using a modified disturbance observer. Considering the natural redundancy property of the UVMS, the redundancy resolution algorithm is often utilized to give desired trajectories in the vehicle–joint space. However, because of the calibration errors, assembling errors and numerical errors, these desired trajectories may not lead the end-effector to the goal point accurately. To realize accurate motion control even when small errors exist in the planning phase, a hybrid strategy is introduced to transform the controller in the joint–vehicle space to the controller in the task space. Numerical simulations based on a UVMS have been carried out to testify the effectiveness of the proposed coordinate controller and the hybrid strategy. During the simulations, unknown disturbances are exerted upon the system. The trajectory tracking and error fixing performances are discussed in comparative analyses. The controller also maintains robust characteristics in comparison with the passivity-based controller and the proposed controller but without the disturbance observer. Experiments are also carried out to test its performance.

In this paper, a dynamic model of a seven-joints manipulator operated in a zero-g simulation system is established. The errors of the friction, the suspension force, and the flexible deformation of arms are considered. Furthermore, the unloading ratio, which can evaluate the performance of the simulation system, is presented. It can reflect the level of similarity between the system and the space environment directly and effectively. The results of experimental and theoretical analyses verify the correctness of the model. It helps us to get the joint torques when the actual space manipulator without the torque sensor operates in this system and guarantees the safety of the experiments.

This paper addresses the systematic approach to design formation control for kinematic model of unicycle-type nonholonomic mobile robots. These robots are difficult to stabilize and control due to their nonintegrable constraints. The difficulty of control increases when there is a requirement to control a cluster of nonholonomic mobile robots in specific formation. In this paper, the design of the control scheme is presented in a three-step process. First, a robust state-feedback point-to-point stabilization control is designed using sliding mode control. In the second step, the controller is modified so as to address the tracking problem for time-varying reference trajectories. The proposed control scheme is shown to provide the desired robustness properties in the presence of the parameter variation, in the region of interest. Finally, in third step, tracking problem of a single nonholonomic mobile robot extends to formation control for a group of mobile robots in the leader–follower scenario using integral terminal- based sliding mode control augmented with stabilizing control. Starting with the transformation of the mathematical model of robots, the proposed controller ensures that the robots maintain a constant distance between each other to avoid collision. The main problem with the proposed controller is that it requires all states specially velocities. Therefore, the state-feedback control scheme is then extended to output feedback by incorporating a highgain observer. With the help of Lyapunov analysis and appropriate simulations, it is shown that the proposed output-feedback control scheme achieves the required control objectives. Furthermore, the closed loop system trajectories reach to desired equilibrium point in finite time while maintaining the special pattern.

A Pneumatic Muscle Actuator (PMA) is a new pneumatic component sharing similar characteristics with biological muscles, and the flexible manipulator actuated by PMAs can better reflect the flexibility of the mechanism. First and foremost, based on the study of the characteristics of human shoulder joints, the configuration design of the flexible manipulator is analyzed, and its kinematics and dynamics models are established. Furthermore, with regard to the nonlinearity, time-invariance and uncertainty of the control system, three aspects of improvement are proposed, which are based on the Radial Basis Function (RBF) network torque control algorithm. The Genetic Algorithm is used to optimize the initial values of RBF network parameters; RBF network parameters are adjusted dynamically by using the additional momentum method; the Levenberg--Marquardt (LM) algorithm, instead of the gradient descent method, is adopted to adjust Proportion Integration Differentiation (PID) parameters online in real time. At last, to test the effects that the improved algorithm exerts on the flexible manipulator control system, some physical platform experiments are carried out. It turns out that the control accuracy and robustness of the improved algorithm are well improved, and the mechanism can be controlled better to track the circular arc trajectory. It lays fundamental importance to the practical application for the working environment.

A time-optimal problem for redundantly actuated robots moving on a specified path is a challenging problem. Although the problem is well explored and there are proposed solutions based on phase plane analysis, there are still several unresolved issues regarding calculation of solution curves. In this paper, we explore the characteristics of the maximum velocity curve and propose an efficient algorithm to establish the solution curve. Then we propose a straightforward method to calculate the maximum or minimum possible acceleration on the path based on the pattern of saturated actuators, which substantially reduces the computational cost. Two numerical examples are provided to illustrate the issues and the solutions.

The fundamental cause for the statically indeterminate problem in the force analysis of overconstrained parallel mechanisms (PMs) is found to be the presence of the linearly dependent overconstrained wrenches. Based on the fundamental cause, a unified expression of the solution for the magnitudes of the constraint wrenches of both the limb stiffness decoupled and limb stiffness coupled overconstrained PMs is derived. When the weight of each link is considered, depending on whether additional component forces are generated along the axes of the overconstrained wrenches, two different situations should be considered. One situation is that no additional component force is generated along the axes of the overconstrained wrenches under the weight of the links in the corresponding limb. In this case, the added constraint wrenches at the limb’s end can be calculated directly, and used as a part of the generalized external wrench. The other situation is that additional component forces are generated. In this case, the elastic deformations in the axes of the overconstrained wrenches generated by those component forces should be considered, and the deformation compatibility equations between the overconstrained wrenches are reformulated.

The article presents the experimental evaluation of an integrated approach for path following and obstacle avoidance, implemented on wheeled robots. Wheeled robots are widely used in many different contexts, and they are usually required to operate in partial or total autonomy: in a wide range of situations, having the capability to follow a predetermined path and avoiding unexpected obstacles is extremely relevant. The basic requirement for an appropriate collision avoidance strategy is to sense or detect obstacles and make proper decisions when the obstacles are nearby. According to this rationale, the approach is based on the definition of the path to be followed as a curve on the plane expressed in its implicit form f(x, y) = 0, which is fed to a feedback controller for path following. Obstacles are modeled through Gaussian functions that modify the original function, generating a resulting safe path which – once again – is a curve on the plane expressed as f′(x, y) = 0: the deformed path can be fed to the same feedback controller, thus guaranteeing convergence to the path while avoiding all obstacles. The features and performance of the proposed algorithm are confirmed by experiments in a crowded area with multiple unicycle-like robots and moving persons.

Serial spherical linkages have been used in the design of a number of robots for minimally invasive surgery, in order to mechanically constrain the surgical instrument with respect to the incision. However, the typical serial spherical mechanism suffers from conflicting design objectives, resulting in an unsuitable compromise between avoiding collision with the patient and producing good kinematic and workspace characteristics. In this paper, we propose a multi-robot system composed of two redundant serial spherical linkages to achieve this purpose. A multi-objective optimization for achieving the aforementioned design goals is presented first for a single redundant robot and then for a multi-robot system. The problem of mounting multiple robots on the operating table as well as the way cooperative actions can be performed is addressed. The sensitivity of each optimal solution (single-robot and multi-robot) to uncertainties in the design parameters is investigated.

This paper reports an extended state observer (ESO)-based robust dynamic surface control (DSC) method for triaxial MEMS gyroscope applications. An ESO with non-linear gain function is designed to estimate both velocity and disturbance vectors of the gyroscope dynamics via measured position signals. Using the sector-bounded property of the non-linear gain function, the design of an $\mathcal{L}_2$-robust ESO is phrased as a convex optimization problem in terms of linear matrix inequalities (LMIs). Next, by using the estimated velocity and disturbance, a certainty equivalence tracking controller is designed based on DSC. To achieve an improved robustness and to remove static steady-state tracking errors, new non-linear integral error surfaces are incorporated into the DSC. Based on the energy-to-peak ($\mathcal{L}_2$-$\mathcal{L}_\infty$) performance criterion, a finite number of LMIs are derived to obtain the DSC gains. In order to prevent amplification of the measurement noise in the DSC error dynamics, a multi-objective convex optimization problem, which guarantees a prescribed $\mathcal{L}_2$-$\mathcal{L}_\infty$ performance bound, is considered. Finally, the efficacy of the proposed control method is illustrated by detailed software simulations.

Recently, the idea of applying “jamming” of appropriate media has been exploited for a novel continuum robot design. It is completed by applying vacuum in a robot structure filled with granular media. The backbone deformation and motion are achieved by controlling the fluid pressure. A jammable robotic manipulator does not certainly follow constant curvature during bending, that is, gravitational loads cause section sag. The kinematics describes the deformation of continuum manipulators. This formulation is expected to facilitate additional synthesis and analysis on workspace. This paper presents a Jacobian-based approach to obtain the forward kinematics solution. The proposed kinematic formulation in this paper tries to combine the key advantages of the techniques in constant curvature and variable curvature models. Hence, the deformation of any arbitrary bending is modeled. The workspace synthesis is continued by kinematic analysis, and in this regard, the manipulability measure is computed. This is an important improvement when compared with existing work for this kind of manipulators. It shows how manipulability measure can determine the workspace quality, where usually reachability is used for robot’s capabilities representation. As a result, the forward kinematics and manipulability analysis based on a piecewise-constant-curvature approximation are discussed in the simulation. The simulation has been carried out according to the fabricated experimental robot.

The paper develops a simulation and animation environment for high-mobility rovers based on kinematic modeling. Various kinematic chains starting from the rover body to the wheels are analyzed and aggregated to obtain the model of the rover body motion in terms of the wheel motions. This model is then used to determine the actuations of the joints, wheels speed, and steering motors to achieve a desired motion of the rover over uneven terrain while avoiding loss of balance and tip-over. The simulation environment consists of a number of modules, including terrain and trajectory generation, and kinematic models for rover actuation and navigation. The animation of the rover motion over various terrains is developed, which allows observing the rover from various viewpoints and interacting with the system through a graphical user interface. The performance of the overall system is demonstrated by modeling a high-mobility space exploration rover, and the responses of the rover on uneven terrains are provided, which show the usefulness of the proposed modeling, simulation, and animation scheme.

An approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Recently, autonomous field robots have been investigated as a labor-reducing means to scout through commercial strawberry fields for disease detection or fruit harvesting. To achieve accurate over-bed and cross-bed motions, it is preferred to design the motion controller based on a precise dynamic model. Here, a dynamic model is developed for a custom-designed strawberry field robot considering terramechanic wheel–terrain interaction. Different from existing models, a torus geometry is considered for the wheels. In order to obtain a control affine model, the longitudinal force is curve-fitted using a polynomial function of the slip/skid ratio, while the lateral force is curve-fitted using an exponential function of both the slip/skid ratio and slip angle. An extended Kalman filter (EKF) is then developed to estimate the unknown parameters in the approximated model such that the state variables propagated by such a model can match experimental data. The approximated model and the EKF-based parameter estimation method are then validated in a commercial strawberry farm.

This paper studies the problem of optimizing the kinematic structure of an eight degree-of-freedom upper-limb rehabilitation exoskeleton. The objective of optimization is achieving minimum volume and maximum dexterity in the workspace of daily activities specified by a set of upper-arm configurations. To formulate the problem, a new index is proposed for effective characterization of kinematic dexterity for wearable robots. Additionally, a set of constraints are defined to ensure that the optimal design can cover the desired workspace of the exoskeleton, while singular configurations and physical interferences are avoided. The formulated multi-objective optimization problem is solved using an evolutionary algorithm (Non-dominated Sorting Genetic Algorithm II) and the weighted sum approach. Among the resulted optimal points, the point with least sensitivity with respect to the variations of design variables is chosen as the final design.

Trajectory tracking of a mobile manipulator in the Cartesian space based on decentralized control is considered in this paper. The dynamic model is first rearranged to take the form of two interconnected subsystems with constraint flow, namely, a nonholonomic mobile platform subsystem and a holonomic manipulator subsystem. Secondly, using the inverse kinematics, the workspace desired trajectory of the mobile manipulator is transformed to the manipulator joint space as well as the platform desired trajectory. The kinematic control is developed from the desired trajectory of the platform. Then, the desired velocity is derived using the kinematic controller of the mobile platform, after which the velocity is used to obtain the control law of the mobile platform subsystem. Thirdly, the control law of the manipulator subsystem is developed based on the desired and real values of the manipulator, as well as the desired velocity. According to the Lyapunov stability theory, the proposed decentralized control strategy guarantees the global stability of the closed-loop system, and the tracking errors are bounded. Experimental results obtained on a 3-DOF manipulator mounted on a mobile platform are given to demonstrate the feasibility and effectiveness of the proposed approach. This is confirmed by a comparison with the computed torque approach.

This paper aims at estimating the tremor torque using extended Kalman filter (EKF) applied to a two-link 3-DOF robot with nonlinear dynamics modelled using Lie-group and Lie-algebra theory. Later, it is generalised to d number of links with (d + 1) -DOF. The configuration of each link at any time is described by its rotation relative to the preceding link. Using this formulation, an elegant formula for the kinetic energy of the (d + 1) -DOF system is obtained as a quadratic form in the angular velocities with coefficients being highly nonlinear trigonometric functions of the angles. Properties of the Lie algebra generators and the Lie adjoint map are used to arrive at this expression. Further, the gravitational potential energy and the torque potential energy are expressed as nonlinear trigonometrical functions of the angles using properties of the SO(3) group. The input torque comprises a nonrandom intentional torque component and a highly nonlinear tremor torque component. The tremor torque is modelled as a stochastic differential equation (sde) satisfying Ornstein–Uhlenbeck (OU) process with diffusion and damping coefficients. Further, the tremor is treated as the disturbance. The Euler–Lagrange equations for the angles are derived. These form a system of sdes, and the EKF is used to get a more accurate disturbance estimate than that provided by the usual disturbance observer. The EKF is based on noisy angle measurements and yields as a bonus the angle and angular velocity estimates on a real-time basis. The parameters in the OU process model of the tremor torque, and parameters of the Fourier components of the intentional torque have also been estimated.

This paper presents a concept of sequentially actuated multi-degree-of-freedom (DOF) robot with only one motor. A switching mechanism allowing to actuate sequentially the different joints–or combinations of the joints–of the robot is also proposed. Potential actuation schemes (joint combinations) are presented and their properties are discussed. Cartesian pick-and-place trajectories are then considered using different actuation schemes. An optimisation algorithm is presented in order to provide the best possible sequence by minimising the amplitude of the joint rotations for a given actuation combination. A simple planar two-DOF and the SCARA architectures are used to illustrate the concept. Finally, a prototype is developed with the aim of demonstrating the sequentially actuated manipulator concept.

The present paper discusses on development and implementation of back-propagation neural network integrated modified DAYANI method for path control of a two-wheeled self-balancing robot in an obstacle cluttered environment. A five-layered back-propagation neural network has been instigated to find out the intensity of various weight factors considering seven navigational parameters as obtained from the modified DAYANI method. The intensity of weight factors is found out using the neural technique with input parameters such as number of visible intersecting obstacles along the goal direction, minimum visible front obstacle distances as obtained from the sensors, minimum left side obstacle distance within the visible left side range of the robot, average of left side obstacle distances, minimum right side obstacle distance within the visible right side range of the robot, average of right side obstacle distances and goal distance from the robot’s probable next position. Comparison between simulation and experimental exercises is carried out for verifying the robustness of the proposed controller. Also, the authenticity of the proposed controller is verified through a comparative analysis between the results obtained by other existing techniques with the current technique in an exactly similar test scenario and an enhancement of the results is witnessed.