Optimal load distribution for two industrial robots handling a single object

The load distribution problem for two coordinating industrial robots handling a single object is studied in this paper. When two industrial robots grasp a single object, the total number of applied torques is usually greater than six. Thus the joint torques of two robots for a required motion of the object is not unique. The redundant degrees of freedom may be used to optimize certain kind of performance. We first select the least energy consumption as the optimization criterion. Optimal algorithms without and with a bound on the joint torques are investigated. The results show that the algorithms are computationally complicated which are not suitable for real-time applications. Alternatively, optimal algorithms are then proposed for load distribution with minimum exerted forces on the object. The algorithms are obtained with much less computational time, which makes it attractive for real-time applications. The algorithms are applied to two PUMA 560 type robots as an illustration.

Precise position force control is the core and difficulty of robot technology, especially for robots with redundant degrees of freedom. For example, track-based controls often fail to grind the robot due to the intolerable impact force applied to the end-effector. The main difficulties lie in the coupling of motion and contact forces, redundancy analysis and physical constraints. In this chapter, we propose a new motion force control strategy under the framework of recursive neural network. The tracking error and contact force are described respectively in the orthogonal space. By choosing the minimum joint torque as the secondary task, the control problem is transformed into the QP problem under multi-constraint conditions. In order to obtain real-time optimization of the joint torque relative to the non-convex joint angle, the original QP is reconstructed at the velocity level, and the original objective function is replaced by the time derivative. Then a convergent dynamic neural network is established to solve the improved QP problem online. The robot position control based on recursive neural network is extended to the robot position control based on position force, which opens a new way for the robot to turn from simple control angle to crossover design with convergence and optimality. Numerical results show that the proposed method can realize precise position force control, deal with inequality constraints such as joint angular velocity and torque limitation, and reduce joint torque consumption by 16% on average.

Demands have been increasing for skillful robots in many fields including atomic power generation, ocean bottom development, space craft, hospital aids, and so on. Such robots will essentially require high degrees of freedom. This paper discusses the advantages of a robot equipped with redundant degrees of freedom and outlines a method of positive use of such redundancy.

Redundancy of degrees of freedom (DOFs) during natural human movements is a central problem of motor control research. This study tests a novel interpretation that during arm movements, the DOF redundancy is used to support a preferred, simplified joint control pattern that consists of rotating either the shoulder or elbow actively and the other (trailing) joint predominantly passively by interaction and gravitational torques. We previously revealed the preference for this control pattern during nonredundant horizontal arm movements. Here, we studied whether this preference persists during movements with redundant DOFs and the redundancy is used to enlarge the range of directions in which this control pattern can be utilized. A free-stroke drawing task was performed that involved production of series of horizontal center-out strokes in randomly selected directions. Two conditions were used, with the arm's joints unconstrained (U) and constrained (C) to the horizontal plane. In both conditions, directional preferences were revealed and the simplified control pattern was used in the preferred and not in nonpreferred directions. The directional preferences were weaker and the range of preferred directions was wider in the U condition, with higher percentage of strokes performed with the simplified control pattern. This advantage was related to the usage of additional DOFs. We discuss that the simplified pattern may represent a feedforward control strategy that reduces the challenge of joint coordination caused by signal-dependent noise during movement execution. The results suggest a possibility that the simplified pattern is used during the majority of natural, seemingly complex arm movements.

End-effector self-reconfiguring live working robot autonomously replaces the end actuator of the robot arm for different tasks, and at the same time completes high-altitude work tasks according to the designed motion plan. In order to ensure uninterrupted operation on power transmission lines, the research methods to enhance the efficiency of robot arm work while reducing energy consumption is of significant importance. Based on this, the paper proposes a time-energy optimal trajectory optimization method for a six-joint robotic arm of a reconfigurable robot for power line maintenance based on Fourier series, taking into account the influence of both robot kinematics and dynamics on the motion trajectory, the positions, velocities, accelerations and joint torques are all considered as constraints. Time and energy are chosen as objective functions. By utilizing the Lagrangian equation method establish an energy-based robot dynamic model in generalized coordinates. The motion curves of each joint are obtained by the cubic spline interpolation method in the joint space, and the boundary conditions of the motion curves are optimized by Fourier series, so as to establish the optimal trajectory mathematical model. The time-energy optimal trajectory planning problem is transformed into a convex optimization problem, the DTW (Dynamic Time Warping) algorithm is used to regularize the difference between the time function and the energy function in the displacement sequence under the known trajectory, and the number of terms in the Fourier series of the minimum hour of the objective function is obtained by the GA-DQN (Genetic Algorithm-Deep Q-Network) algorithm. Finally, with the actuator replacement at the end of the robotic arm as the operation objective, the time-energy optimal trajectory is obtained from the desired positional attitude at the initial and termination of the end of the robotic arm. Simulation analysis is carried out under MATLAB and compared with the motion trajectory obtained by the fifth degree polynomial interpolation method, and the results show that by optimizing the motion trajectory with Fourier series, the motion time is shortened by about 35.67% and the energy consumption is reduced by about 39.63%. And online experiments were conducted in the field to measure the output errors of joints 2 and 5, as well as the actual energy and time consumption of outputting the optimal trajectories, which verified that the trajectories obtained under this optimization algorithm have better performance and can meet the requirements of online robot end self-reconfiguration operation.

The solution of task of maintaining the dynamic accuracy of control of working tools of multilink manipulators (MM) when they move along arbitrary spatial trajectories is presented in this paper. In this case, constructive restrictions in all degrees of freedom (DoF) of manipulators and special cases of location of their links are taken into account. These special (singular) positions are characterized by ambiguity in solving inverse kinematics problem of these MM. Maintaining of control accuracy is proposed to be ensured by excluding the enter of all DoFs of manipulators to the restrictions, as well as excluding the enter of their working tools to the boundaries of the working area. This is accomplished by using a redundant DoF when approaching these undesirable positions. In the first part of the article, the features of the new solution of the inverse kinematics problem are considered and singular positions for 6-DoF manipulators with PUMA kinematic schemes are described. The presented solution of the inverse kinematics problem takes into account various combinations of genera- lized coordinates of the MM, which ensure the movement of their working tools to the specified positions with the required spatial orientation. This solution has low computational complexity compared to other known methods. This allows the use of low-power microprocessor computers to control the MM. The results of the performed mathematical simulation confirmed the high efficiency of using the proposed approach to the contour control of the MM.

This paper reports the results of the kinematic redundancy resolution for the Baxter research robot arms. A robot manipulator arm is said to be kinematically redundant if it has more degrees of freedom than strictly needed for executing a given task. The redundant degrees of freedom can be used to achieve additional goals while the given task is executed. In this study, we will use cartesian velocity control to show that a Baxter robot arm can be programmed to improve its manipulability measure, avoid singularities or obstacles while its end effector follows the required six degrees of freedom motion trajectory.

This paper presents a new dynamic programming (DP) approach to the optimal path following problem. The method rests on an interpolation in the phase plane so that the resulting joint accelerations and joint torques are continuous. This allows for taking into account limits on the joint jerks and torque rates in addition to joint velocities, accelerations, torques, and the mechanical power. Most methods proposed in the literature yield values of optimal trajectories at discrete sampling times so that this must be interpolated subsequently to the trajectory optimization. This causes violations of the joint jerk and torque rate limits. The proposed method does not suffer from this problem, which is a main feature of this approach. Unlike most of the previously proposed methods, joint jerk and torque rate limits are addressed with a reasonable increase in the computation time of DP algorithms. Special attention is given to experimental validation of the optimization results. The presented experimental results confirm the importance of taking the motor torque characteristics as well as the Coulomb and viscous friction into account. Neglecting these effects (as most previous publications did) leads to trajectories that cannot be performed by real manipulators. Apart from DP, other approaches with smaller computation times exist. However, most of these methods are either limited to the time optimal case (which might not always be the desired criterion) and are not able to handle all earlier mentioned constraints or cannot take into account viscous friction effects. Apart from that a sequential convex programming (SCP) approach exists, which accounts for the same constraints as the presented approach. Therefore, the proposed DP approach is compared to this SCP method and an example is presented where the time optimal trajectory is performed by a real manipulator.

A discrete trajectory planner is described which has been shown to be capable of planning optimal trajectories for a six-degree-of-freedom robot with minimum time/energy objective functions and realistic constraints on the joint velocities, joint torques, joint jerks, and hand velocity. It is also flexible enough to handle other objective functions and constraints, provided they can be satisfactorily discretized. An alternative formulation of the discrete trajectory planner is also provided for the efficient generation of optimal trajectories when equal time intervals are required. Once an optimal trajectory is planned offline with the discrete trajectory planner, the open-loop solution can be fed to the online feedback controller for trajectory tracking. Computation time taken by the discrete trajectory planner is acceptable for offline planning purposes. Numerical examples are presented for the Stanford manipulator using all six degrees of freedom.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robots often switch from highly dynamic motion to delivering high torques at low speeds. The actuation requirements for these two regimes are very different. As a consequence, the average efficiency of the actuators is typically much lower than the efficiency at the optimal working point. A potential solution is to use multiple motors for a single motor joint. This results in a redundant degree of freedom, which can be exploited to make the system more efficient overall. In this work, we explore the potential of kinematically redundant actuators in dynamic applications. The potential of a kinematically redundant actuator with two motors is evaluated against a single-motor equivalent in terms of operating range, maximum acceleration, and energy consumption. We discuss how the comparison is influenced by the design of the actuator and the way how the power is distributed over the input motors. Our results support the idea that kinematically redundant actuators can resolve the conflicting torque–speed requirements typical of robots.

A central question of motor control is how the motor system deals with redundant degrees of freedom. Redundancy can be reduced by coupling multiple degrees of freedom into a single motor primitive. Previous studies measuring motor primitives in aimed limb movements were restricted to two-dimensional target planes. We asked whether a limited number of motor primitives would also be sufficient to capture the posture variance of aimed limb movements in a three-dimensional target volume. To this end, participants had to point towards virtual targets uniformly spaced in a three-dimensional workspace. Results showed that three motor primitives captured 89.7±2.8% of the data variance of unrestrained pointing movements. Each motor primitive corresponded to a valid movement of the arm. The findings imply that complex postures in a three-dimensional target volume can be reduced to three motor primitives. The reduction results in a unique mapping of target position and posture and, thus, solves the redundancy problem. The reduction further indicates that, in a pointing task, the motor system does not control hand rotation independent of hand translation.

Occupational therapy aims to restore independent living skills and to improve social participation for clients; therefore, optimising motor ability can be a major goal during intervention in clinical practice. Choosing the adequate approach for each client is critical to achieve treatment goals. As frame of reference is based on contemporary theories related to human behaviours, it is crucial to synthesise current theories of motor control for clinical application. In this review, four motor control theories were examined by the Bernstein's classical question: redundant degrees of freedom. By addressing the central issue in motor control theories, the strengths and weaknesses for each theory were discussed in detail. Classical literatures were selected for each theory and related references were reviewed as evidence to support the potential biological plausibility. The research of motor control theories have been developed for over centuries, researchers still strive to discover how human beings execute movements. To date, motor control theories were mainly proposed by three disciplines: biology, psychology and engineering. Each discipline has unique perspective to develop solutions for understanding the processes behind the execution of movement. For occupational therapists in clinics, it is imperative to integrate current knowledge and motor control theories into practice and to explore new approaches to treat clients with motor disability.

Control-moment gyroscopes (CMGs) are power-e‐cient attitude-control actuators that produce high torques on spacecraft. In this study, a method is investigated for maneuvering robotic arm segments in a spacecraft-mounted, CMG-actuated agile imaging payload with minimal power usage. A real-time optimization method is presented that includes null motion in a closed-loop end-efiector tracking problem. The proposed approach involves flrst establishing kinematic relationships between the end-efiector attitude coordinates and joint coordinates. These transformations are used to track a two-coordinate end-efiector attitude command by simultaneously controlling three joint degrees of freedom. With the redundant degree of freedom, there are multiple joint-angle solutions corresponding to a given boresight attitude command. While tracking this command, null motion is added to the commanded joint angles. The augmented joint-angle command causes a change in the body and gimbal motion that ultimately reduces power consumption. The null-angle component is determined by computing the null projection of the cost gradient with respect to the joint angles. A quadratic cost function is deflned, which is the sum of the squares of power for each CMG gimbal. Simulation results demonstrate that the power consumption of the system, when measured by the integral of non-recoverable power, is reduced by up to 42% when a certain amount of null motion is included in the feedback loop.

Inverse kinematic solutions for a dual redundant camera robot in position are examined in order to alleviate operation difficulty and reduce time. The inverse kinematic algorithm is based on a basic genetic algorithm, and the genetic algorithm which is used to solve the problem of a redundant robot is mainly optimized in the joint space. On this basis, the genetic algorithm improvement strategies are studied. In this paper, a genetic algorithm with constrained 2 redundant degrees of freedom (DOF) is proposed through setting 2 parameter variables, with more flexible structure of optimization objective function and more efficient algorithm than basic genetic algorithm. Finally, the result of inverse kinematic algorithm is achieved in terms of the physical prototype.

Industrial robots are required to interact with the surrounding environment to perform a given task (e.g., an assembly task). However, standard industrial robots are commonly position-controlled. Therefore, there is the need to implement an outer compliance controller to guarantee a safe interaction. Such compliance controllers require force/torque measurements to close the loop, and most of the industrial manipulators available on the market do not have embedded force/torque sensor(s), requiring additional efforts (i.e., additional costs and implementation resources) for such integration in the robotic setup. To provide a standard industrial sensorless position-controlled robot with the capabilities to execute an interaction task, the proposed paper defines an external joint torques observer for the implementation of an outer sensorless compliance controller. More in detail, exploiting the resulting position-controlled robot dynamics, an Extended Kalman Filter (EKF) is proposed to estimate the external joint torques. Exploiting such an estimation, an outer impedance controller can be designed, providing a position/velocity reference to the inner position controller. The described approach has been validated with experiments on a Franka EMIKA panda robot. A human operator interacts with the controlled robot, applying external wrenches (i.e., both Cartesian forces and torques). The resulting external joint torques are estimated making use of the proposed EKF, comparing the achieved results with the signals provided by the joint torque sensors of the Franka EMIKA panda robot (measurements used as a baseline for validation purposes). Experimental results show the capabilities of the proposed control framework in estimating the applied external joint torques while implementing a position control-based compliance controller.