Adaptive and Singularity-Free Inverse Dynamics Models for Control of Parallel Manipulators With Actuation Redundancy

2011 ◽  
Author(s):  
Andreas Mu¨ller ◽  
Timo Hufnagel
Keyword(s):  
Range Of Motion ◽  
Inverse Dynamics ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Torque Control ◽  
Alternative Formulation ◽  
Dynamics Model ◽  
Model Based ◽  
Control Forces

Redundant actuation of parallel kinematics machines (PKM) is a way to eliminate input-singularities and so to enlarge the usable workspace. From a kinematic point of view the number m of actuator coordinates exceeds the DOF δ of a redundantly actuated PKM (RA-PKM). The dynamics model, being the basis for model-based control, is usually expressed in terms of δ independent actuator coordinates. This implies that the model exhibits the same singularities as the non-redundant PKM, even though the RA-PKM is not singular. Consequently the admissible range of motion of the RA-PKM model is limited to that of the non-redundant PKM. In this paper an alternative formulation of the dynamics model in terms of the full set of m actuator coordinates is presented. It leads to a redundant system of m motion equations that is valid in the entire range of motion. This formulation gives rise to an inverse dynamics formulation tailored for real-time implementation. In contrast to the standard formulation in independent coordinates, the proposed inverse dynamics formulation does not involve control forces in the null space of the control matrix, i.e. it does not allow for the generation of internal prestresses, however. This is not problematic as the latter is usually not exploited. The proposed method is compared to the recently proposed adaptive coordinate switching method. Experimental results are reported if the inverse dynamics solution is introduced in model-based computed torque control scheme of a planar 2DOF RA-PKM.

Uncertainty Problems in Model-Based Control of Redundantly Actuated Parallel Manipulators

2008 ◽  
Author(s):  
Andreas Mu¨ller
Keyword(s):  
Inverse Dynamics ◽  
Closed Form Solution ◽  
Parallel Manipulators ◽  
Form Solution ◽  
Torque Control ◽  
Secondary Tasks ◽  
Control Schemes ◽  
Dynamics And Control ◽  
Redundantly Actuated ◽  
Control Forces

The inverse dynamics and control of redundantly actuated PKM in the presence of uncertainties is the focus of this paper. Actuation redundancy allows for a purposeful distribution of control forces, taking into account secondary tasks, such optimal force distribution, active stiffness, and backlash avoiding control. A closed form solution of the inverse dynamics problem for simply redundantly actuated PKM is given. The applicability of the augmented PD and computed torque control schemes is analyzed. It is shown that, in the presence of model uncertainties, adopting the standard control schemes leads to parasitic perturbation forces that can not be compensated by the controls. An amended version of these control scheme is proposed that does not suffer from such effects.

Decentralized LPV Gain-Scheduled PD Control of a Robotic Manipulator

2009 ◽  
Author(s):  
H. Abbas ◽  
S. M. Hashemi ◽  
H. Werner
Keyword(s):  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Controller Design ◽  
Robotic Manipulator ◽  
Low Complexity ◽  
Torque Control ◽  
Tracking Performance ◽  
Pd Controller ◽  
Model Based ◽  
Gain Scheduled

In this paper, low-complexity linear parameter-varying (LPV) modeling and control of a two-degrees-of-freedom robotic manipulator is considered. A quasi-LPV model is derived and simplified in order to facilitate LPV controller synthesis. An LPV gain-scheduled, decentralized PD controller in linear fractional transformation form is designed, using mixed sensitivity loop shaping to take — in addition to high tracking performance — noise and disturbance rejection into account, which are not considered in model-based inverse dynamics or computed torque control schemes. The controller design is based on the existence of a parameter-dependent Lyapunov function — employing the concept of quadratic separators — thus reducing the conservatism of design. The resulting bilinear matrix inequality (BMI) problem is solved using a hybrid gradient-LMI technique. Experimental results illustrate that the LPV controller clearly outperforms a decentralized LTI-PD controller and achieves almost the same accuracy as a model-based inverse dynamics and a full-order LPV controllers in terms of tracking performance while being of significantly lower complexity.

MOTION RECOVERY AFTER JOINT FAILURE IN PARALLEL MANIPULATORS

2011 ◽  
Vol 35 (4) ◽  
pp. 559-571 ◽  
Author(s):  
Leila Notash
Keyword(s):  
Failure Modes ◽  
Jacobian Matrix ◽  
Null Space ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Partial Recovery ◽  
Joint Failure ◽  
Motion Recovery ◽  
Motion Performance ◽  
Planar Parallel Manipulators

In this paper, the failure of parallel manipulators is investigated. Failure modes of parallel manipulators and their causes and effects from the kinematics point of view are discussed. Methodologies for investigating the effect of failures, due to joint failure or singularity, on the motion performance of manipulators are presented, and the criteria for full and partial recovery from these failures are established. The proposed methodologies are based on the projection of the lost motion onto the orthogonal complement of the null space of the Jacobian matrix after failure. The procedure is simulated for planar parallel manipulators to examine if after joint failure the required motion of manipulator could be fully recovered; as well as to calculate the corrections to the motion of remaining joints for recovering the lost motion.

Force-based Active Compliance Control of Hydraulic Quadruped Robot

2021 ◽  
Author(s):  
Zhu Rui ◽  
Yang Qingjun ◽  
Chen Chen ◽  
Jiang Chunli ◽  
Li Congfei ◽  
...  
Keyword(s):  
Stance Phase ◽  
Inverse Dynamics ◽  
Rigid Motion ◽  
Quadruped Robot ◽  
Rigid Body Dynamics ◽  
Torque Control ◽  
Dynamics Model ◽  
Constraint Force ◽  
Recursion Method ◽  
Trot Gait

The hydraulically driven quadruped robot has received extensive attention from many scholars due to its high power density and adaptability to unstructured terrain. However, the research on hydraulic quadruped robots based on torque control is not mature enough, especially in the aspect of multi-rigid body dynamics. In this paper, the most commonly used gait trot is selected as the research object. First, the multi-rigid motion equation of the quadruped robot is established by the spin recursion method based on Lie groups. Next, the Lagrange multiplier is used to represent the constraint force to establish the 12-degree-of-freedom inverse dynamics model of the quadruped robot’s stance phase. And the hybrid dynamics method is used to reduce the dimension of the inversion matrix, which simplifies the solution process of the dynamics model. Then, the trajectory of the foot is planned. Through the analysis of the simplified model, it is concluded that the gait cycle and the initial position of the stance phase are important factors affecting the stability of the trot gait. Finally, the controller framework of the quadruped robot is introduced, and the effectiveness of the algorithm designed in this paper is verified through the co-simulation of the trot gait. The co-simulation results show that the inverse dynamics algorithm can be used as the feedforward of the control system, which can greatly reduce the gains of the PD controller; the robot has good compliance and can achieve stable trotting.

Model-based joint and task space control strategies for a kinematically redundant parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-17
Author(s):  
João Vitor de Carvalho Fontes ◽  
Fernanda Thaís Colombo ◽  
Natássya Barlate Floro da Silva ◽  
Maíra Martins da Silva
Keyword(s):  
Parallel Manipulator ◽  
Control Strategies ◽  
Parallel Manipulators ◽  
Torque Control ◽  
Redundancy Resolution ◽  
Task Space ◽  
Kinematic Redundancy ◽  
Model Based ◽  
The Impact ◽  
Computed Torque

Abstract One alternative to overcome the presence of singularities within Parallel Manipulators’ workspace is kinematic redundancy. This design alternative can be realized by adding an extra active joint to a kinematic chain. Due to this addition, the IKM presents an infinite number of solutions requiring a redundancy resolution scheme. Moreover, Parallel Manipulators’ control may require complex strategies due to their coupled and complex dynamic and kinematic relations. In this work, a model-free, a joint space computed torque, and a hybrid joint-task-space computed torque control strategies are experimentally compared for a kinematically redundant parallel manipulator. The latter is a novel strategy that requires the measurement of the end-effector’s pose, which is performed by an eye-to-hand limited frame rate camera. The impact of up to three kinematic redundancy levels is also experimentally evaluated using prepositioning and ongoing positioning redundancy resolution schemes. The data are assessed by evaluating a prescribed trajectory executed using a planar kinematically redundant parallel manipulator. These results indicate that kinematic redundancy can not only be used as an alternative design for reducing the presence of singular regions, as claimed in the literature, but also be used along with model-based control strategies for improving dynamic performance and accuracy of parallel manipulators.

Wire Deactivation Methodology for Inverse Dynamics of Wire-Actuated Redundant Manipulators

2004 ◽  
Author(s):  
Amin Kamalzadeh ◽  
Leila Notash
Keyword(s):  
Dynamic Modeling ◽  
External Force ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Null Space ◽  
Parallel Manipulators ◽  
Inverse Dynamic ◽  
End Effector ◽  
Serial Manipulators ◽  
Passive Joint

Wire-actuated robot manipulators are generally lighter than other manipulators as actuated wires are used instead of joint actuators. The inverse dynamic modeling of these manipulators is complicated by the existence of multiple kinematic constraints as well as redundancy in actuation. In wire-actuated parallel manipulators with a constraining linkage and in tendon-driven serial manipulators, wires are used to control the joints. In these manipulators, each wire can provide a torque/force on a link about/along its revolute/prismatic passive joint in one direction, as wires only act in tension. Using one wire for each link sometimes does not fully constrain the motion of the link about/along its passive joint. Therefore, a second wire is attached to some links in a “counterbalance” configuration; i.e., the second wire can provide a “complementary” torque/force in the opposite direction of the torque/force produced by the first wire on the link about/along its passive joint. Depending on the end effector trajectory and external force at each instant, one of the mentioned two wires provides the desired direction of torque/force and the other, “counteracting wire,” imposes a “counteracting” torque/force on the link about/along its passive joint. Using more actuators than degrees of freedom (DOF) in the manipulator causes redundancy in actuation, which means that for a unique end effector trajectory and external force, inverse dynamic results (actuator torques/forces) have infinite solutions within a null space of actuator torques/forces. Obtaining a unique result within the null space requires several considerations, such as avoiding negative tensions in wires and decreasing the actuator torques/forces. The purpose of this article is to find a methodology to limit the infinite inverse dynamic solutions to one while the negative wire tensions are avoided and actuator torques/forces are relatively decreased. As explained in this article, by reducing the counteracting wire tensions, other actuator torques/forces are decreased, because a portion of other actuator torques/forces neutralizes the tensions of counteracting wires. A methodology is developed to detect the counteracting wires in real-time and to present the corresponding tensions to a low positive value; i.e., the counteracting wires are “deactivated.” The proposed methodology can be implemented in the inverse dynamic modeling of wire-actuated parallel manipulators with a constraining linkage and tendon-driven serial manipulators via using the Lagrangian method. This methodology can be used to provide optimum actuator torques/forces and avoid negative tensions in actuated wires. The methodology is implemented in the inverse dynamic modeling of a 4-DOF wire-actuated manipulator where there is one degree of actuation redundancy. In the simulation results, the inverse dynamic model based on the proposed methodology is observed to be quite robust in terms of avoiding negative wire tensions by deactivating the right actuated wire.

scholarly journals Inverse Dynamics Model-Based Shape Control of Soft Continuum Finger Robot Using Parametric Curve

2021 ◽  
pp. 1-1
Author(s):  
Steeve Mbakop ◽  
Gilles Tagne ◽  
Marc-Henri Frouin ◽  
Melingui Achille ◽  
Rochdi Merzouki
Keyword(s):  
Shape Control ◽  
Inverse Dynamics ◽  
Dynamics Model ◽  
Parametric Curve ◽  
Model Based

Effects of Dynamic Model Errors in Task-Priority Operational Space Control

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Paolo Di Lillo ◽  
Gianluca Antonelli ◽  
Ciro Natale
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Null Space ◽  
Control Algorithms ◽  
Model Errors ◽  
Operational Space ◽  
Dynamic Level ◽  
Concurrent Tasks ◽  
Modeling Errors

SUMMARY Control algorithms of many Degrees-of-Freedom (DOFs) systems based on Inverse Kinematics (IK) or Inverse Dynamics (ID) approaches are two well-known topics of research in robotics. The large number of DOFs allows the design of many concurrent tasks arranged in priorities, that can be solved either at kinematic or dynamic level. This paper investigates the effects of modeling errors in operational space control algorithms with respect to uncertainties affecting knowledge of the dynamic parameters. The effects on the null-space projections and the sources of steady-state errors are investigated. Numerical simulations with on-purpose injected errors are used to validate the thoughts.

scholarly journals Closed-form time derivatives of the equations of motion of rigid body systems

2021 ◽  
Author(s):  
Andreas Müller ◽  
Shivesh Kumar
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Formulation ◽  
Dynamics Of Rigid Body ◽  
Control Forces ◽  
And Control ◽  
Derivatives Of ◽  
Insight Into

AbstractDerivatives of equations of motion (EOM) describing the dynamics of rigid body systems are becoming increasingly relevant for the robotics community and find many applications in design and control of robotic systems. Controlling robots, and multibody systems comprising elastic components in particular, not only requires smooth trajectories but also the time derivatives of the control forces/torques, hence of the EOM. This paper presents the time derivatives of the EOM in closed form up to second-order as an alternative formulation to the existing recursive algorithms for this purpose, which provides a direct insight into the structure of the derivatives. The Lie group formulation for rigid body systems is used giving rise to very compact and easily parameterized equations.

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