The tension distribution problem of cable-driven parallel robots is inevitable in real-time control. Currently, iterative algorithms or geometric algorithms are commonly used to solve this problem. Iterative algorithms are difficult to improve in real-time performance, and the tension obtained by geometric algorithms may not be continuous. In this paper, a novel tension distribution method for four-cable, 3-DOF cable-driven parallel robots is proposed based on the wave equation. The tension calculated by this method is continuous and differentiable, without the need for iterative computation or geometric centroid calculations, thus exhibiting good real-time performance. Furthermore, the feasibility and rationality of this algorithm are theoretically proven. Finally, the real-time performance and continuity of cable tension are analyzed through a specific numerical example.

The authors seek to design a lower limb exoskeleton to augment human finned swimming; however, data associated with human finned swimming previously did not exist, particularly data that characterizes the active joint torque requirements for human-scale finned swimming motion and the corresponding thrust generation. Since these data are not directly measurable nor easily computed in human subject experiments, the authors instead employed a human-scale robotic platform to characterize the relationship between joint torque, speed, power, and thrust production during flutter kick swimming, specifically at the hip joints. Among the useful insights from this study: (1) the underwater environment can be accurately modeled as a simple viscous load as seen by the hip joints, where viscous coefficient depends on the type of fin; (2) accordingly, for a given fin, movement at any amplitude and frequency is invariant when motion is normalized by amplitude; velocity and torque by the product of amplitude and frequency; and power and thrust by the square of the product of amplitude and frequency; (3) the power-specific thrust is invariant, regardless of fin type, amplitude of motion, and frequency of motion; and 4) the phasing between right and left legs does not have a significant effect on thrust generation (i.e., kicking in-phase and kicking in opposition behave similarly). The authors hope this data will be useful to other researchers interested in developing lower limb exoskeletons to augment underwater human finned swimming.

This article is devoted to the control of bio-inspired robots that are underactuated. These robots are composed of tensegrity joints remotely actuated with cables, which mimic the musculoskeletal system of the bird neck. A computed torque control (CTC) is applied to these robots as well as an original control called pseudo computed torque control (PCTC). This new control uses the dynamics and the pseudo-inverse of the Jacobian matrix. The stability of the two proposed controls is then analyzed through linearization of the dynamic model and expression of the closed-loop transfer function in the Laplace domain. We show that, depending on the desired trajectory, the CTC can be unstable when the controlled variables are the end effector position and orientation. For a robot with many joints and a limited number of cables, the CTC is always unstable. Instead, the PCTC shows a large domain of stability. The analysis is complemented by experimental tests demonstrating that the CTC and PCTC exhibit similar performance when the CTC is stable. Furthermore, the PCTC maintains stability on trajectories where the CTC becomes unstable, showing robustness to perturbations as well.

In this study, we present a hybrid kinematic modeling approach for serial robotic manipulators, which offers improved accuracy compared to conventional methods. Our method integrates the geometric properties of the robot with ground truth data, resulting in enhanced modeling precision. The proposed forward kinematic model combines classical kinematic modeling techniques with neural networks trained on accurate ground truth data. This fusion enables us to minimize modeling errors effectively. In order to address the inverse kinematic problem, we utilize the forward hybrid model as feedback within a non-linear optimization process. Unlike previous works, our formulation incorporates the rotational component of the end effector, which is beneficial for applications involving orientation, such as inspection tasks. Furthermore, our inverse kinematic strategy can handle multiple possible solutions. Through our research, we demonstrate the effectiveness of the hybrid models as a high-accuracy kinematic modeling strategy, surpassing the performance of traditional physical models in terms of positioning accuracy.

This paper presents a decentralized, cooperative, real-time avoidance control strategy for robotic manipulators. The proposed avoidance control law builds on the concepts of artificial potential field functions and provides tighter bounds on the minimum safe distance when compared to traditional potential-based controllers. Moreover, the proposed avoidance control law is given in analytical, continuous closed form, avoiding the use of optimization techniques and discrete algorithms, and is rigorously proven to guarantee collision avoidance at all times. Examples of planar and 3D manipulators with cylindrical links under the proposed avoidance control are given and compared with the traditional approach of modeling links and obstacles with multiple spheres. The results show that the proposed avoidance control law can achieve, in general, faster convergence, smaller tracking errors, and lower control torques than the traditional approach. Furthermore, we provide extensions of the avoidance control to robotic manipulators with bounded control torques.

The ability of quadruped robots to overcome obstacles is a critical factor that limits their practical application. Here, a design concept and a control algorithm are presented that aim at enhancing the explosive force of quadruped robots during jumping by utilizing elastic energy storage components. The hind legs of the quadruped robot are designed as energy storage units. Tension springs are utilized as components for storing energy and are installed in a parallel structure on the hind leg. Energy is stored during the compression process of the robot’s torso and released during the jumping phase. The optimal foot force is calculated using a single rigid body model. The mapping relationship between the force applied to the foot and the resulting joint torque is established by developing a dynamic model of the hind legs. Simulation experiments were conducted using the Webots physics engine to compare the impact of varying spring stiffness on joint torque during the jumping process. This study determined the optimal spring stiffness under specific conditions. The hind legs’ torque saving ratio reaches 19%, and the energy-saving ratio reaches 13%, which validates the effectiveness and feasibility of integrating elastic energy storage components.

This paper presents an algorithm for solving the inverse dynamics of a parallel manipulator (PM) with offset universal joints (RR–joints) via the Newton–Euler method. The PM with RR–joints increase the joint stiffness and enlarge the workspace but introduces additional joint parameters and constraint torques, rendering the dynamics more complex. Unlike existing studies on PMs with RR–joints, which emphasize the kinematics and joint performance, this paper studies the dynamical model. First, an iterative algorithm is established through a rigid body velocity transformation, which calculates the input parameters of the link velocity and acceleration. A linear system of equations in matrix form is then established for the entire PM through the Newton–Euler method. By using the generalized minimal residual method (GMRES) to solve the equation system, all the forces and torques on the joints can be obtained, from which the required actuation force can be derived. This method is validated through numerical simulations using the automatic dynamic analysis of multibody systems software. The proposed method is suitable for establishing the dynamic model of complex PMs with redundant or hybrid structures.

Heavy-duty hexapod robots are well-suited for physical transportation, disaster relief, and resource exploration. The immense locomotion capabilities conferred by the six appendages of these systems enable traversal over unstructured and challenging terrain. However, tipping can be a serious concern when moving with a tripod gait in these challenging environments, which may cause irreversible consequences such as compromised movement control and potential damage. In this paper, we focus on heavy-duty hexapod robot sideline tipping judgment and recovery during tripod gait motion, and a novel sideline tipping judgment and recovery method is proposed by adjusting an optimal swinging leg to the stance state. Considering the locomotion environments, motion mode, and tipping analysis, the robot’s stability margin is quantified, and the tipping event is evaluated by the Force Angle Stability Measure (FASM). The recovery method is initiated upon detecting that the robot is tipping, which involves the selection of an adjustment leg and the determination of an optimal foothold. Since the FASM is based on the foot force and robot center of gravity (CoG), the stability margin quantification expression is reformulated to the constraint form of quadratic programming (QP). Furthermore, a foot force distribution method, integrating stability margin considerations into the QP model, has been devised to ensure post-adjustment stability of the landing leg. Experiments on tipping judgment and recovery demonstrate the effectiveness of the proposed approaches on tipping judgment and recovery.

Although several studies have revealed that fractional order controllers usually outperform conventional integer-order control solutions, fractional order controllers are not yet widely applied in industrial applications due to their complex mathematical background. In this paper, further improvements of a simple weighted sum feedback design are introduced that imitates the behavior of a fractional order controller but is free from its various formal restrictions. The proposed control solution has the main characteristics of a fractional order controller, such as finite memory length, excellent transient response with no overshoot and robust behavior, but it is placed into a much simpler mathematical framework. In the current paper, a simple derivative term was incorporated in the design which made the controller’s output more stable by completely eliminating output chattering. The proposed control method was developed for a general second-order system. It was tested in a fixed point iteration-based adaptive control scenario, through simulations using a robotic example and on experimental basis as well, utilizing a simple one-degree-of-freedom electromechanical system. The presented experiments are the first systematic investigations of the fixed point iteration-based adaptive control method.

As a heavy load is applied to the parallel manipulators, it causes inaccuracies while positioning the end-effector or unbalanced dynamic forces in the legs. Various load-balancing techniques overcome this. However, the disadvantage of most load-balancing mechanisms is that they add inertia to the assembly and decrease the speed of motion. This article studies a new load-balancing method (a passive damper mechanism). The passive balancing mechanism is proposed to negate the inertia effects while countering the static inaccuracies in the parallel mechanism. This is verified by the structural analysis of the mechanism. The impact of the damper element on the dynamics of the mechanism is unknown. Hence, a complete mathematical model for the balancing mechanism has been developed to study its impact on the dynamics of the entire structure. Laplace transformations characterize the system response. The inclusion of a passive damper in a 3-prismatic-prismatic-revolute-spherical system was examined and found to be stable and critically damped. Such a passive damper was envisaged to facilitate additional force transmission for the actuators, and the DC gain from the system response validates the torque support for the actuators.

A robotic system constructed as a wheeled inverted pendulum (WIP) serves as an impressive demonstrator, since this kind of system is inherently nonlinear, unstable, and nonminimum phase. These properties may pose several difficulties, when it comes to control and trajectory planning. This paper shows a method for deriving a highly dynamic trajectory compliant with the system dynamics by means of solving an optimal control problem (OCP) using multiple shooting. The assumed task includes that the WIP should pass a height-restricting barrier. This can be achieved by leaning back or forth, in order to reduce the overall height of the WIP. The constraints inherent to the definition of this trajectory are nonconvex due to the shape of the robot. The constraint functions have a local minimum in an infeasible region. This can cause problems when the initial guess is within this infeasible region. To overcome this, a multistage approach is proposed for this special OCP to evade the infeasible local minimum. After solving four stages of subsequent optimization problems, the optimal trajectory is obtained and can be used as feedforward for the real system.

Machines and mechanisms realize processes, from the shaping process of a milling machine and the motion process of an automotive system to the trajectory realization of a robot. The dynamics of a machine generated by a properly chosen set of constraints in combination with an appropriate drive system is designed to meet the prescribed requirements of the process, which is done by projecting the machine equations of motion on the process dynamics. We get a set of nonlinear relations, which represent the machine motion in terms of the required process motion. A well-known example is the projection of arbitrary many robot degrees of freedom (DOFs) on a given path resulting in a set of nonlinear equations with one DOF only, the path coordinate s. Application of this idea can be used to construct a mobility space $(\ddot{s}, \dot{s}, s)$ for any combination of coordinates and constraints. The paper presents a corresponding approach for n-link robots by applying multibody system theory. Method might be interesting for layout of machines and mechanisms. Practical aspects are discussed, and an example is given.

In this study, a control algorithm is proposed and evaluated for a special type of kinematically redundant manipulator. This manipulator is comprised of two mechanisms, macro and micro mechanisms, with distinct acceleration and work space characteristics. A control algorithm is devised to minimize the task completion duration and the overall actuator effort with respect to the conventional manipulator. A general framework multi-priority controller for macro-micro manipulators is introduced by utilizing virtual dynamics, which is introduced in null-space projection to achieve secondary tasks. The proposed controller is evaluated on a simulation model based on a previously constructed macro-micro manipulator for planar laser cutting. Task completion duration and the total actuator effort are investigated and the results are compared.

This paper investigates artificial neural network (ANN)-based simulators as an alternative to physics-based approaches for evolving controllers in simulation for a complex snake-like robot. Prior research has been limited to robots or controllers that are relatively simple. Benchmarks are performed in order to identify effective simulator topologies. Additionally, various controller evolution strategies are proposed, investigated and compared. Using ANN-based simulators for controller fitness estimation during controller evolution is demonstrated to be a viable approach for the high-dimensional problem specified in this work.

Reducing the energy consumed by a car-like mobile robot makes it possible to move at a lower cost, yet it takes more working time. This paper proposes an optimization algorithm for trajectories with optimal times and analyzes the consequences of restricting the energy consumed on the trajectory obtained for a car-like robot. When modeling the dynamic behavior of the vehicle, it is necessary to consider its inertial parameters, the behavior of the motor, and the basic properties of the tire in its interaction with the ground. To obtain collision-free, minimum-time trajectories quadratic sequential optimization techniques are used, where the objective function is the time taken by the robot to move between two given configurations. This is subject to constraints relating to the vehicle and tires as well as the energy consumed, which is the basis for this paper. We work with a real random distribution of consumed energy values following a normal Gaussian distribution in order to analyze its influence on the trajectories obtained by the vehicle. The energy consumed, the time taken, the maximum velocity reached, and the distance traveled are analyzed in order to characterize the properties of the trajectories obtained. The proposed algorithm has been applied to 101 examples, showing that the computational times needed to obtain the solutions are always lower than those required to realize the trajectories. The results obtained allow us to reach conclusions about the energy efficiency of the trajectories.

Robotic swimmers are currently a subject of extensive research and development for several underwater applications. Clever design and planning must rely on simple theoretical models that account for the swimmer’s hydrodynamics in order to optimize its structure and control inputs. In this work, we study a planar snake-like multi-link swimmer by using the “perfect fluid” model that accounts for inertial hydrodynamic forces while neglecting viscous drag effects. The swimmer’s dynamic equations of motion are formulated and reduced into a first-order system due to symmetries and conservation of generalized momentum variables. Focusing on oscillatory inputs of joint angles, we study optimal gaits for 3-link and 5-link swimmers via numerical integration. For the 3-link swimmer, we also provide a small-amplitude asymptotic solution which enables obtaining closed-form approximations for optimal gaits. The theoretical results are then corroborated by experiments and motion measurement of untethered robotic prototypes with three and five links floating in a water pool, showing a reasonable agreement between the experiments and the theoretical model.

Designers of robotic groups are faced with the formidable task of creating effective coordination architectures that can deal with collisions due to changing environment conditions and hardware failures. Communication between robots is a mechanism that can at times be helpful in such systems, but can also create a time, energy, or computation overhead that reduces performance. In dealing with this issue, different communication schemes have been proposed ranging from those without any explicit communication, localized algorithms, and centralized or global communicative methods. Finding the optimal communication act is typically an intractable problem in real-world problems. As a result, we argue that at times group designers should use computationally bounded team communication approaches. We propose two such approaches: an algorithm selection approach to communication whereby robots choose between a known group of communication schemes and a parameterized communication framework whereby robots can reason about how large a communication radius is needed for a given problem. Both solutions use a novel coordination cost measure, combined coordination costs, to find the appropriate level of communication within such groups. Robots can then use this measure to create adaptive communication approaches that select between communication approaches as needed during task execution. We validated this approach through conducting extensive experiments in a canonical robotic foraging domain and found that robotic groups using these adaptive methods were able to significantly increase their productivity compared to teams that used only one type of communication scheme.

This paper presents the design, analysis, and experimental validation of a miniature modular inchworm robot (MMIR). Inchworm robots are capable of maneuvering in confined spaces due to their small size, a desirable characteristic for surveillance, exploration and search and rescue operations. This paper presents two generations of the MMIR (Version 1—V1 and Version 2—V2) that utilize anisotropic friction skin and an undulatory rectilinear gait to produce locomotion. This paper highlights design improvements and a multi-body dynamics approach to model and simulate the system. The MMIR V2 incorporates a slider-crank four-bar mechanism and a relative body revolute joint to produce high-frequency relative translation and rotation to increase forward velocity and enable turning capabilities. Friction analysis and locomotion experiments were conducted to assess the systems performance on various surfaces, validate the dynamic model and simulation results, and measure the maximum forward velocity. The MMIR V1 and V2 were able to achieve maximum forward velocities of 12.7 mm/s and 137.9 mm/s, respectively. These results are compared to reported results of similar robots published in the literature.

Singularity analysis of parallel manipulators is an active research field in robotics. The present article derives for the first time in the literature a condition under which a five-bar parallel robot encounters high-order parallel singularities. In this regard, by focusing on the planar 5R mechanism, a theorem is given in terms of the slope of its coupler curve at the parallel singular configurations. At high-order parallel singularities, the associated determinant vanishes simultaneously with at least its first-order time derivative. The determination of such singularities is quite important since in their presence, some special conditions should be satisfied for bounded inverse dynamic solutions.