Control of Redundant Mechanical Systems Under Equality and Inequality Constraints on Both Input and Constraint Forces

2011 ◽  
Vol 6 (3) ◽  
Author(s):  
Farhad Aghili
Keyword(s):  
Inverse Dynamics ◽  
Null Space ◽  
Inequality Constraints ◽  
Control Technique ◽  
Orthogonal Complement ◽  
Control Input ◽  
Constraint Forces ◽  
Constraint Force ◽  
Closed Loops ◽  
Equality And Inequality Constraints

The equality and inequality constraints on constraint force and/or the actuator force/torque arise in several robotic applications, for which different controllers have been specifically developed. This paper presents a unified approach to control a rather general class of robotic systems with closed loops under a set of linear equality and inequality constraints using the notion of projection operator. The controller does not require the kinematic constraints to be independent, i.e., systems with time-varying topology can be dealt with, while demanding minimum-norm actuation force or torque in the case that the system becomes redundant. The orthogonal decomposition of the control input force yields the null-space component and its orthogonal complement. The null-space component is obtained using the projected inverse dynamics control law, while the orthogonal complement component is found through solving a quadratic programming problem, in which the equality and inequality constraints are derived to be equivalent to the originally specified ones. Finally, a case study is presented to demonstrate how the control technique can be applied to multi-arms manipulation of an object.

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.

Second-order consensus for a class of uncertain multi-agent systems subject to input saturation

2018 ◽  
Vol 41 (7) ◽  
pp. 1957-1964 ◽  
Author(s):  
Ming-Can Fan ◽  
Miaomiao Wang
Keyword(s):  
A Priori ◽  
Input Saturation ◽  
Second Order ◽  
Control Technique ◽  
Control Input ◽  
Multi Agent Systems ◽  
State Information ◽  
Agent Systems ◽  
Barbalat’S Lemma ◽  
Multi Agent

This paper investigates the leaderless and leader-following consensus problem for a class of second-order multi-agent systems subject to input saturation, that is, the control input is required to be a priori bounded. Moreover, the control coefficients are assumed to be unavailable, which cannot be lower or upper bounded by any known constants. Distributed consensus protocols are proposed based only on agents’ own velocity state information and relative position state information among neighbouring agents and the leader. By virtue of the adaptive control technique, algebraic graph theory and Barbalat’s lemma, it is proved that the states of the multi-agent systems can achieve consensus under the assumption that the interconnection topology is undirected and connected. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results.

scholarly journals A singularity handling algorithm based on operational space control for six-degree-of-freedom anthropomorphic manipulators

2019 ◽  
Vol 16 (3) ◽  
pp. 172988141985891
Author(s):  
Zhi-Hao Kang ◽  
Ching-An Cheng ◽  
Han-Pang Huang
Keyword(s):  
Null Space ◽  
Singularity Analysis ◽  
Degree Of Freedom ◽  
Control Input ◽  
Real Time Control ◽  
Time Control ◽  
Operational Space ◽  
Industrial Manipulators ◽  
Space Motion ◽  
Six Degree Of Freedom

In this article, we analyze the singularities of six-degree-of-freedom anthropomorphic manipulators and design a singularity handling algorithm that can smoothly go through singular regions. We show that the boundary singularity and the internal singularity points of six-degree-of-freedom anthropomorphic manipulators can be identified through a singularity analysis, although they do not possess the nice kinematic decoupling property as six-degree-of-freedom industrial manipulators. Based on this discovery, our algorithm adopts a switching strategy to handle these two cases. For boundary singularities, the algorithm modifies the control input to fold the manipulator back from the singular straight posture. For internal singularities, the algorithm controls the manipulator with null space motion. We show that this strategy allows a manipulator to move within singular regions and back to non-singular regions, so the usable workspace is increased compared with conventional approaches. The proposed algorithm is validated in simulations and real-time control experiments.

Inverse Dynamic Analysis and Linearisation of a High Speed Parallel Mechanism

2005 ◽  
Author(s):  
M. Necip Sahinkaya ◽  
Yanzhi Li
Keyword(s):  
Dynamic Analysis ◽  
Parallel Mechanism ◽  
High Speed ◽  
Inverse Dynamics ◽  
Motion Path ◽  
Model Parameters ◽  
Control Input ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
Dynamics Models

Inverse dynamic analysis of a three degree of freedom parallel mechanism driven by three electrical motors is carried out to study the effect of motion speed on the system dynamics and control input requirements. Availability of inverse dynamics models offer many advantages, but controllers based on real-time inverse dynamic simulations are not practical for many applications due to computational limitations. An off-line linearisation of system and error dynamics based on the inverse dynamic analysis is developed. It is shown that accurate linear models can be obtained even at high motion speeds eliminating the need to use computationally intensive inverse dynamics models. A point-to-point motion path for the mechanism platform is formulated by using a third order exponential function. It is shown that the linearised model parameters vary significantly at high motion speeds, hence it is necessary to use adaptive controllers for high performance.

scholarly journals Relations between Abs-Normal NLPs and MPCCs. Part 2: Weak Constraint Qualifications

2021 ◽  
Vol Volume 2 (Original research articles>) ◽  
Author(s):  
Lisa C. Hegerhorst-Schultchen ◽  
Christian Kirches ◽  
Marc C. Steinbach
Keyword(s):  
Normal Form ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Inequality Constraints ◽  
First Order ◽  
Nonlinear Programs ◽  
Mathematical Programs ◽  
Ongoing Effort ◽  
Equality And Inequality Constraints ◽  
Smooth Optimization

This work continues an ongoing effort to compare non-smooth optimization problems in abs-normal form to Mathematical Programs with Complementarity Constraints (MPCCs). We study general Nonlinear Programs with equality and inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their relation to equivalent MPCC reformulations. We introduce the concepts of Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a specific slack reformulation suggested in [10], the relations are non-trivial. It turns out that constraint qualifications of Abadie type are preserved. We also prove the weaker result that equivalence of Guginard's (and Abadie's) constraint qualifications for all branch problems hold, while the question of GCQ preservation remains open. Finally, we introduce M-stationarity and B-stationarity concepts for abs-normal NLPs and prove first order optimality conditions corresponding to MPCC counterpart formulations.

Inverse Dynamics Algorithm for Space Robots

1996 ◽  
Vol 118 (3) ◽  
pp. 625-629 ◽  
Author(s):  
Subir Kumar Saha
Keyword(s):  
Efficient Algorithm ◽  
Dynamic Models ◽  
Inverse Dynamics ◽  
Recursive Algorithm ◽  
Space Robot ◽  
Orthogonal Complement ◽  
Free Base ◽  
Space Robots ◽  
Primary Body ◽  
Kinematic Models

An efficient algorithm for the inverse dynamics of free-flying space robots, consisting of a serial manipulator mounted on a free-base, e.g., a spacecraft, is presented. The kinematic and dynamic models are based on the concepts of the Primary Body (PB) and the Natural Orthogonal Complement, respectively, reported elsewhere. In this paper, besides the efficiency, the usefulness of the PB in deriving different kinematic models and selecting an efficient one is pointed out. Moreover, it is shown that a recursive algorithm for the inverse dynamics of the space robot at hand can be developed even without the consideration of the momenta conservation principle.

Gradient Optimization of Inverse Dynamics for Robotic Manipulator Motion Planning Using Combined Optimal Control

2017 ◽  
Author(s):  
Shangdong Gong ◽  
Redwan Alqasemi ◽  
Rajiv Dubey
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Inverse Dynamics ◽  
Null Space ◽  
Optimal Solution ◽  
Human Motion ◽  
Optimization Techniques ◽  
Redundant Manipulators ◽  
Robot Arm ◽  
Gradient Optimization

Motion planning of redundant manipulators is an active and widely studied area of research. The inverse kinematics problem can be solved using various optimization methods within the null space to avoid joint limits, obstacle constraints, as well as minimize the velocity or maximize the manipulability measure. However, the relation between the torques of the joints and their respective positions can complicate inverse dynamics of redundant systems. It also makes it challenging to optimize cost functions, such as total torque or kinematic energy. In addition, the functional gradient optimization techniques do not achieve an optimal solution for the goal configuration. We present a study on motion planning using optimal control as a pre-process to find optimal pose at the goal position based on the external forces and gravity compensation, and generate a trajectory with optimized torques using the gradient information of the torque function. As a result, we reach an optimal trajectory that can minimize the torque and takes dynamics into consideration. We demonstrate the motion planning for a planar 3-DOF redundant robotic arm and show the results of the optimized trajectory motion. In the simulation, the torque generated by an external force on the end-effector as well as by the motion of every link is made into an integral over the squared torque norm. This technique is expected to take the torque of every joint into consideration and generate better motion that maintains the torques or kinematic energy of the arm in the safe zone. In future work, the trajectories of the redundant manipulators will be optimized to generate more natural motion as in humanoid arm motion. Similar to the human motion strategy, the robot arm is expected to be able to lift weights held by hands, the configuration of the arm is changed along from the initial configuration to a goal configuration. Furthermore, along with weighted least norm (WLN) solutions, the optimization framework will be more adaptive to the dynamic environment. In this paper, we present the development of our methodology, a simulated test and discussion of the results.

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