Joint Velocity Vector Research Articles

Failure recovery of manipulators under joint velocity limits using constrained optimization and partitioned Jacobian matrix

In this paper, the motion recovery methodologies are proposed to recover as many components of the manipulator twist as possible while minimizing the 2-norm of the joint velocity vector. If any component of the joint velocity vector after the recovery violates the corresponding limits, the joints with velocities exceeding the limits are treated as failed and their velocities are set to their limits. When the Jacobian matrix of the failed manipulator is full row-rank and the joint velocities remain within their limits, the full recovery is achieved using the inverse or generalized inverse of the reduced Jacobian matrix. If the Jacobian matrix of the failed manipulator is full row-rank, but the minimum 2-norm of the joint velocities violate their limits so as the full recovery is not achieved, an optimization method followed by partitioning the reduced Jacobian matrix is proposed. Also, when the Jacobian matrix is full column-rank and the joint velocities remain within their limits, the partial recovery is obtained using partitioning the reduced Jacobian matrix. As examples, planar serial and parallel manipulators are investigated to show the effectiveness of the methodologies.

Instantaneous Kinematics Analysis via Screw-Theory of a Novel 3-CRC Parallel Mechanism

This paper presents the mobility and kinematics analysis of a novel parallel mechanism that is composed by one base, one platform and three identical limbs with CRC joints. The paper obtains closed-form solutions to the direct and inverse kinematics problems, and determines the mobility of the mechanism and instantaneous kinematics by applying screw theory. The obtained results show that this parallel robot is part of the family 2R1T, since the platform shows 3 DOF, i.e.: one translation perpendicular to the base and two rotations about skew axes. In order to calculate the direct instantaneous kinematics, this paper introduces the vector mh, which is part of the joint velocity vector that multiplies the overall inverse Jacobian matrix. This paper compares the results between simulations and numerical examples using Mathematica and SolidWorks in order to prove the accuracy of the analytical results.

Motor equivalence and self-motion induced by different movement speeds

This study investigated pointing movements in 3D asking two questions: (1) Is goal-directed reaching accompanied by self-motion, a component of the joint velocity vector that leaves the hand's movement unaffected? (2) Are differences in the terminal joint configurations among different speeds of reaching motor equivalent (i.e., terminal joint configurations differ more in directions of joint space that do not produce different pointer-tip positions than in directions that do) or non-motor equivalent (i.e., terminal joint configurations differ equally or more in directions of joint space that lead to different pointer-tip positions than in directions that do not affect the pointer-tip position). Subjects reached from an identical starting joint configuration and pointer-tip location to targets at slow, moderate, and fast speeds. Ten degrees of freedom of joint motion of the arm were recorded. The relationship between changes in the joint configuration and the three-dimensional pointer-tip position was expressed by a standard kinematic model, and the range- and null subspaces were computed from the associated Jacobian matrix. (1) The joint velocity vector and (2) the difference vector between terminal joint configurations from pairs of speed conditions were projected into the two subspaces. The relative length of the two components was used to quantify the amount of self-motion and the presence of motor equivalence, respectively. Results revealed that reaches were accompanied by a significant amount of self-motion at all reaching speeds. Self-motion scaled with movement speed. In addition, the difference in the terminal joint configuration between pairs of different reaching speeds revealed motor equivalence. The results are consistent with a control system that takes advantage of motor redundancy, allowing for flexibility in the face of perturbations, here induced by different movement speeds.

Perturbation Sensing for Humanoid Robots using a Multiclass Support Vector Machine

Research on human posture control reveals that proprioception is a crucial sense for the control of stance. In particular, proprioceptive cues in the ankle, hips, and trunk trigger automatic postural responses to perturbations. Generally, the robotics literature discusses the use of the Zero Moment Point to stabilise stance. Humans can not calculate this point from proprioceptive cues, instead joint velocity information is used. This paper proposes the use of proprioception on a humanoid robot, where joint velocities are used directly to detect and determine the direction of a perturbation during quiet stance. A weighted Manhattan norm of the joint velocity vector is used for perturbation detection and a Support Vector Machine is used to classify a perturbation as belonging to a set of directions and locations. On application to a 23 degree of freedom humanoid the average detection time is 120ms. The direction is classified with 100% accuracy and the location is classified with 99.9% accuracy. The majority of proprioceptive information was provided by the upper body, in particular, the shoulders.

Redundancy, self-motion, and motor control.

Outside the laboratory, human movement typically involves redundant effector systems. How the nervous system selects among the task-equivalent solutions may provide insights into how movement is controlled. We propose a process model of movement generation that accounts for the kinematics of goal-directed pointing movements performed with a redundant arm. The key element is a neuronal dynamics that generates a virtual joint trajectory. This dynamics receives input from a neuronal timer that paces end-effector motion along its path. Within this dynamics, virtual joint velocity vectors that move the end effector are dynamically decoupled from velocity vectors that do not. Moreover, the sensed real joint configuration is coupled back into this neuronal dynamics, updating the virtual trajectory so that it yields to task-equivalent deviations from the dynamic movement plan. Experimental data from participants who perform in the same task setting as the model are compared in detail to the model predictions. We discover that joint velocities contain a substantial amount of self-motion that does not move the end effector. This is caused by the low impedance of muscle joint systems and by coupling among muscle joint systems due to multiarticulatory muscles. Back-coupling amplifies the induced control errors. We establish a link between the amount of self-motion and how curved the end-effector path is. We show that models in which an inverse dynamics cancels interaction torques predict too little self-motion and too straight end-effector paths.

Motor equivalent control of the center of mass in response to support surface perturbations

To claim that the center of mass (CM) of the body is a controlled variable of the postural system is difficult to verify experimentally. In this report, a new variant of the method of the uncontrolled manifold (UCM) hypothesis was used to evaluate CM control in response to an abrupt surface perturbation during stance. Subjects stood upright on a support surface that was displaced in the posterior direction. Support surface translations between 0.03 and 0.12 m, each lasting for 275 ms, were presented randomly. The UCM corresponding to all possible combinations of joints that are equivalent with respect to producing the average pre-perturbation anterior-posterior position of the center of mass (CM(AP)) were linearly estimated for each trial. At each point in time thereafter, the difference between the current joint configuration and the average pre-perturbation joint configuration was computed. This joint difference vector was then projected onto the pre-perturbation UCM as a measure of motor equivalence, and onto its complementary subspace, which represents joint combinations that lead to a different CM(AP) position. A similar analysis was performed related to control of the trunk's spatial orientation. The extent to which the joint velocity vector acted to stabilize the CM(AP) position was also examined. Excursions of the hip and ankle joints both increased linearly with perturbation magnitude. The configuration of joints at each instance during the perturbation differed from the mean configuration prior to the perturbation, as evidenced by the joint difference vector. Most of this joint difference vector was consistent, however, with the average pre-perturbation CM(AP) position rather than leading to a different CM(AP )position. This was not the case, however, when performing this analysis with respect to the UCM corresponding to the control of the pre-perturbation trunk orientation. The projection of the instantaneous joint velocity vector also was found to lie primarily in the UCM corresponding to the pre-perturbation CM(AP) position, indicating that joint motion was damped in directions leading to a change away from the pre-perturbation CM(AP) position. These results provide quantitative support for the argument that the CM position is a planned variable of the postural system and that its control is achieved through selective, motor equivalent changes in the joint configuration in response to support surface perturbations. The results suggest that the nervous system accomplishes postural control by a control strategy that considers all DOFs. This strategy presumably resists combinations of DOFs that affect the stability of important task-relevant variables (CM(AP) position) while, to a large extent, freeing from control combinations of those DOFs that have no effect on the task-relevant variables (Schöner in Ecol Psychol 8:291-314, 1995).

A recurrent neural network for minimum infinity-norm kinematic control of redundant manipulators with an improved problem formulation and 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.

Recurrent neural networks for minimum infinity-norm kinematic control of redundant manipulators

This paper presents two neural network approaches to minimum infinity-norm solution of the velocity inverse kinematics problem for redundant robots. Three recurrent neural networks are applied for determining a joint velocity vector with its maximum absolute value component being minimal among all possible joint velocity vectors corresponding to the desired end-effector velocity. In each proposed neural network approach, two cooperating recurrent neural networks are used. The first approach employs two Tank-Hopfield networks for linear programming. The second approach employs two two-layer recurrent neural networks for quadratic programming and linear programming, respectively. Both the minimal 2-norm and infinity-norm of joint velocity vector can be obtained from the output of the recurrent neural networks. Simulation results demonstrate that the proposed approaches are effective with the second approach being better in terms of accuracy and optimality.

A Lagrangian network for kinematic control of redundant robot manipulators

A recurrent neural network, called the Lagrangian network, is presented for the kinematic control of redundant robot manipulators. The optimal redundancy resolution is determined by the Lagrangian network through real-time solution to the inverse kinematics problem formulated as a quadratic optimization problem. While the signal for a desired velocity of the end-effector is fed into the inputs of the Lagrangian network, it generates the joint velocity vector of the manipulator in its outputs along with the associated Lagrange multipliers. The proposed Lagrangian network is shown to be capable of asymptotic tracking for the motion control of kinematically redundant manipulators.

Minimum effort inverse kinematics for redundant manipulators

This paper investigates the use of an infinity norm in formulating the optimization measures for computing the inverse kinematics of redundant arms. The infinity norm of a vector is its maximum absolute value component and hence its minimization implies the determination of a minimum effort solution as opposed to the minimum-energy criterion associated with the Euclidean norm. In applications where individual magnitudes of the vector components are of concern, this norm represents the physical requirements more closely than does the Euclidean norm. We first study the minimization of the infinity-norm of the joint velocity vector itself, and discuss its physical interpretation. Next, a new method of optimizing a subtask criterion, defined using the infinity-norm, to perform additional tasks such as obstacle avoidance or joint limit avoidance is introduced. Simulations illustrating these methods and comparing the results with the Euclidean norm solutions are presented.

Overview of damped least-squares methods for inverse kinematics of robot manipulators

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility. The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described. Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.

A weighted least-norm solution based scheme for avoiding joint limits for redundant joint manipulators

It is proposed to use weighted least-norm solution to avoid joint limits for redundant joint manipulators. A comparison is made with the gradient projection method for avoiding joint limits. While the gradient projection method provides the optimal direction for the joint velocity vector within the null space, its magnitude is not unique and is adjusted by a scalar coefficient chosen by trial and error. It is shown in this paper that one fixed value of the scalar coefficient is not suitable even in a small workspace. The proposed manipulation scheme automatically chooses an appropriate magnitude of the self-motion throughout the workspace. This scheme, unlike the gradient projection method, guarantees joint limit avoidance, and also minimizes unnecessary self-motion. It was implemented and tested for real-time control of a seven-degree-of-freedom (7-DOF) Robotics Research Corporation (RRC) manipulator. >

N-Player Stochastic Differential Games

The paper presents conditions which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. When the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.