Inverse Dynamics of a Flexible Robot Arm by Optimal Control

1993 ◽  
Vol 115 (2) ◽  
pp. 289-293 ◽  
Author(s):  
T. Kokkinis ◽  
M. Sahraian
Keyword(s):  
Optimal Control ◽  
Inverse Dynamics ◽  
Robot Arm ◽  
Flexible Robot ◽  
Joint Torques ◽  
Practical Applications ◽  
End Point ◽  
Point Tracking ◽  
Flexible Arms ◽  
High Frequency Content

The problem of end-point positioning of flexible arms is discussed. Because of the nonminimum phase nature of the problem, inversion fails to produce bounded joint torques. Bounded noncausal joint torques for achieving the task of end-point tracking for a multilink arm are found using optimal control theory. The torques obtained have no high-frequency content, and are suitable for practical applications. The method is illustrated by simulation of a single-link arm, for which stability and robustness considerations for design are given.

End-point tracking for a flexible robot arm

1994 ◽  
Vol 27 (14) ◽  
pp. 687-692
Author(s):  
L. Benvenuti ◽  
M.D. Di Benedetto
Keyword(s):  
Robot Arm ◽  
Flexible Robot ◽  
End Point ◽  
Point Tracking

Optimal control of a flexible robot arm

1988 ◽  
Vol 29 (3) ◽  
pp. 459-467 ◽  
Author(s):  
James D. Lee ◽  
Ben-Li Wang
Keyword(s):  
Optimal Control ◽  
Robot Arm ◽  
Flexible Robot

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.

About the Use of the Floating Frame in the Optimal Control of the Flexible Robot Arm

1992 ◽  
Vol 4 (4) ◽  
pp. 330-338 ◽  
Author(s):  
M. Bisiacco ◽  
◽  
R. Caracciolo ◽  
M. Giovagnoni ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Linear Model ◽  
Equations Of Motion ◽  
Flexible Manipulator ◽  
Robot Arm ◽  
Flexible Robot ◽  
Coupled Equations ◽  
Weakly Coupled ◽  
Tip Position ◽  
The Mathematical Model

The mathematical model of a single-link flexible manipulator is obtained by measuring transverse deflections in a rotating reference frame which is floating with respect to the link. The use of this particular frame, the rigidbody mode frame, enables one to obtain weakly coupled equations of motion. The size of the inertia coupling terms can be easily evaluated: these terms can be shown to be negligible thus leading to an essentially linear model. An example of optimal control of manipulator's tip position is numerically reproduced. The same controller is first applied to the mechanical model of the arm accounting for non-linear coupling and then to the linear model: the two responses are found to be very close to each other.

Inverse Dynamics of a Redundantly Actuated Four-Bar Mechanism Using an Optimal Control Formulation

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Olavo Luppi Silva ◽  
Luciano Luporini Menegaldo
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Inverse Dynamics ◽  
Industrial Robots ◽  
Chain Mechanism ◽  
Dynamical Equations ◽  
Open Chain ◽  
Standard Case ◽  
Joint Torques ◽  
Redundantly Actuated

This paper presents an approach to estimating joint torques in a four-bar closed-chain mechanism with prescribed kinematics and redundant actuation, i.e., with more actuators than degrees of freedom. This problem has several applications in industrial robots, machine tools, and biomechanics. The inverse dynamics problem is formulated as an optimal control problem (OCP). The dynamical equations are derived for an open-chain mechanism, what keeps the formulation simple and straightforward. Sets of constraints are explored to force the three-link open-chain to behave as a four-bar mechanism with a crank rotating at a constant velocity. The controls calculated from the OCP are assumed to be the input joint torques. The standard case with one torque actuator is solved and compared to cases with two and three actuators. The case of two actuators presented the smallest peak and mean torques, using one specific set of constraints. Such torques were smaller than the solution obtained using an alternative method existing in literature that solves the redundancy problem by means of the pseudo-inverse matrix. Comparison with inverse dynamics solutions using well-established methods for the one-actuator closed-loop four-bar were equal. Reconstructed kinematical trajectories from forward integration of the closed-loop mechanism with the OCP obtained torques were essentially similar. The results suggest that the adopted procedure is promising, giving solutions with lower torque requirements than the regularly actuated case and redundantly actuated computed with other approaches. The applicability of the method has been shown for the four-bar mechanism. Other classes of redundantly actuated, closed-loop mechanisms could be tested using a similar formulation. However, the numerical parameters of the OCP must be chosen carefully to achieve convergence.

Acceleration Profiles for Causal Solutions of the Inverse Dynamics Approach to the Control of Single Link Flexible Arms

1991 ◽  
Vol 113 (4) ◽  
pp. 752-754 ◽  
Author(s):  
H. C. Moulin ◽  
E. Bayo
Keyword(s):  
Inverse Dynamics ◽  
Peak Torque ◽  
Discrete Models ◽  
Actuation Time ◽  
End Point ◽  
Single Link ◽  
Flexible Arms

A scheme for the design of rest-to-rest acceleration profiles to be used in the inverse dynamics approach to the control of the end-point of single link flexible arms is described. The scheme uses linear discrete models, and a stable pole-cancellation method to obtain acceleration profiles that yield inverse dynamics torques with the same supports as that of the end-point acceleration profiles; it allows for a design which reaches a balance between overshoot, peak torque and actuation time.

A13 Basic Research of End Point Position Control for Two Links Flexible Robot Arm

2009 ◽  
Vol 2009.11 (0) ◽  
pp. 167-170
Author(s):  
Kiyoharu NAKAGAWA ◽  
Ryouta AIKAWA ◽  
Toru WATANABE ◽  
Kazuto SETO
Keyword(s):  
Position Control ◽  
Basic Research ◽  
Robot Arm ◽  
Flexible Robot ◽  
Point Position ◽  
End Point
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