Operational Space Control for Planar PAN–1 Underactuated Manipulators Using Orthogonal Projection and Quadratic Programming

In this paper, we propose an operational space control formulation for a planar N-link underactuated manipulator (PA N–1 ) 1 with a passive first joint subject to actuator constraints (N ⩾ 3), covering both stabilization and tracking tasks. Such underactuated manipulators have an inherent first-order nonholonomic constraint, allowing us to project their dynamics to a space consistent with the nonholonomic constraint. Based on the constrained dynamics, we can design operational space controllers with respect to tasks assuming that all joints of the manipulator are active. Due to underactuation, we design a Quadratic Programming (QP) based controller to minimize the error between the desired torque commands and available motor torques in the null space of the constraint, as well as involve the constraint of motor outputs. The proposed control framework was demonstrated by stabilization and tracking tasks in simulations with both planar PA 2 and PA 3 manipulators. Furthermore, we verified the controller experimentally using a planar PA 2 robot

Control of an Underactuated Three-Link Passive-Active- Active Manipulator Based on Three Stages and Stability Analysis

This paper presents a novel three-stage control strategy for the motion control of an underactuated three-link passive-active-active (PAA) manipulator. First, a nonlinear control law is designed to make the angle and angular velocity of the third link convergent to zero. Then, a swing-up control law is designed to increase the system energy and control the posture of the second link. Finally, an integrated method with linear control and nonlinear control is introduced to stabilize the manipulator at the straight-up position. The stability of the control system is guaranteed by Lyapunov theory and LaSalle's invariance principle. Compared to other approaches, the proposed strategy innovatively introduces a preparatory stage to drive the third link to stretch-out toward the second link in a natural way, which makes the swing-up control easy and quick. Besides, the intergraded method ensures the manipulator moving into the balancing stage smoothly and easily. The effectiveness and efficiency of the control strategy are demonstrated by numerical simulations

Reinforcement Learning Adaptive PID Controller for an Under-actuated Robot Arm

Abstract: An adaptive PID controller is used to control of a two degrees of freedom under actuated manipulator. An actor-critic based reinforcement learning is employed for tuning of parameters of the adaptive PID controller. Reinforcement learning is an unsupervised scheme wherein no reference exists to which convergence of algorithm is anticipated. Thus, it is appropriate for real time applications. Controller structure and learning equations as well as update rules are provided. Simulations are performed in SIMULINK and performance of the controller is compared with NARMA-L2 controller. The results verified good performance of the controller in tracking and disturbance rejection tests

Nonprehensile Dynamic Manipulation: A Survey

Nonprehensile dynamic manipulation can be reason- ably considered as the most complex manipulation task. It might be argued that such a task is still rather far from being fully solved and applied in robotics. This survey tries to collect the results reached so far by the research community about planning and control in the nonprehensile dynamic manipulation domain. A discussion about current open issues is addressed as well

Feedback Linearization Techniques for Collaborative Nonholonomic Robots

Collaborative robots performing tasks together have significant advantages over a single robot. Applications can be found in the fields of underwater robotics, air traffic control, intelligent highways, mines and ores detection and tele-surgery. Collaborative wheeled mobile robots can be modeled by a nonlinear system having nonholonomic constraints. Due to these constraints, the collaborative robots arc not stabilizable at a point by continuous time-invariant feedback control laws. Therefore, linear control is ineffective, even locally, and innovative design techniques are needed. One possible design technique is feedback control and the principal interest of this thesis is to evaluate the best feedback control technique. Feedback linearization is one of the possible feedback control techniques. Feedback linearization is a method of transforming a nonlinear system into a linear system using feedback transformation. It differs from conventional Taylor series linearization since it is achieved using exact coordinates transformation rather than by linear approximations of the system. Linearization of the collaborative robots system using Taylor series results in a linear system which is uncontrollable and is thus unsuitable. On the other hand, the feedback linearized control strategies result in a stable system. Feedback linearized control strategies can he designed based on state or input, while both state and input linearization can be achieved using static or dynamic feedback. In this thesis, a kinematic model of the collaborative nonholonomic robots is derived, based on the leader-follower formation. The objective of the kinematic model is to facilitate the design of feedback control strategies that can stabilize the system and Minimize the error between the desired and actual trajectory. The leader-follower formation is used in this research since the collaborative robots are assumed to have communication capabilities only. The kinematic model for the leader-follower formation is simulated using MATLAB/Simulink. A comparative assessment of various feedback control strategies is evaluated. The leader robot model is tested using five feedback control strategies for different trajectories. These feedback control strategies are derived using cascaded system theory, stable tracking method based on linearization of corresponding error model, approximation linearization, nonlinear control design and full state linearization via dynamic feedback. For posture stabilization of the leader robot, time-varying and full state dynamic feedback linearized control strategies are used. For the follower robots using separation bearing and separation-separation formation, the feedback linearized control strategies are derived using input-output via static feedback. Based on the simulation results for the leader robot, it is found that the full state dynamic feedback linearized control strategy improves system performance and minimizes the mean of error more rapidly than the other four feedback control strategies. In addition to stabilizing the system, the full state dynamic feedback linearized control strategy achieves posture stabilization. For the follower robots, the input-output via static feedback linearization control strategies minimize the error between the desired and actual formation. Furthermore, the input-output linearized control strategies allow dynamical change of the formation at run-time and minimize the disturbance of formation change. Thus, for a given feasible trajectory, the full state feedback linearized strategy for the leader robot and input-output feedback linearized strategies for the follower robots are found to be more efficient in stabilizing the system