Multi-agent system Inspired Distributed Control of a Manipulator

Abstract

Robotic manipulators are used in a wide variety of applications. In all the applications, the end-effector or the tool of the manipulator needs to be moved along a desired trajectory in its workspace. In this thesis we present model-based control schemes for robotic manipulators using a distributed architecture. Inspired by multi-agent/robotic systems, first we perceive a manipulator, which is MIMO multi-body system, as a multi-agent system with the joints (or the joint-link pairs) as sub-systems or agents, which interact with each other in a distributed manner. Here, the interaction between the joint-link agents is in the form of interactive forces and moments that lead to dynamic coupling. As the adjacency graph formed by the joint-link agents as nodes and links between two joints as edges is connected, the direct interactions between the immediate neighbors result in interaction (in the form of dynamic coupling) between any two joint-link agents. We carry out an analysis of the computational cost associated with the model-based control law for planar serial-link manipulators with degrees-of-freedom varying from 2 to 6 using Maple. Using this analysis, we establish the fact that the total computational cost associated with the model-based control law increases with the degrees-of-freedom. Toward mitigating the computational overhead associated with the conventional model-based control scheme, we propose a distributed architecture for the motion control of manipulator exploiting its multi-agent nature. Here, each joint-link agent is controlled by a dedicated controller, and the joint-level controllers communicate and cooperate among themselves. Though one of the primary motivation for the proposed distributed control scheme is to reduce the computational overhead, in this thesis we rely on the natural distributed nature of the manipulator dynamics rather than the program optimization or operation optimization techniques that are used at the algorithmic level. We propose a simple distributed control scheme based on the conventional model-based control law and show that it can be implemented using thedistributed control architecture. Here, apart from the reduced computational lead time due to distributed computation of the control law at the joint-levels, unlike the decentralized or independent joint control schemes, the proposed control scheme fully utilizes the knowledge of the system dynamics, leading to a feedback linearized closed-loop error dynamics. Though the proposed distributed control scheme is suitable for a general serial-link manipulator, in this thesis, we focus on planar manipulators with revolute joints. We prove, that the proposed distributed control scheme makes the links of the manipulator, and hence the end-effector, follow the desired trajectory, asymptotically. We define a quantity called distribution effectiveness to quantify how the distributed control schemes share the computational load among the individual joint-level controllers. We also provide a discussion on implication of the discrete-time implementation of the proposed distributed control scheme in contrast to the conventional model-based control scheme. We design a distributed model-based controller for a planar 3R manipulator, to illustrate the proposed distributed control scheme and the distributed control architecture for a manipulator. For the case of planar manipulators with degrees-of-freedom 2 − 6, we provide a method to reduce the computational cost associated with dynamic equations used in the control law by identifying repetitive terms, which may be generalized for any other manipulator in principle. In an attempt to further improve the distribution effectiveness and reduce the computational lead time, we propose a cooperative control scheme for a manipulator using the distributed control architecture. While in the basic distributed control scheme proposed, joint-level controllers interact amongst themselves in terms of exchanging desired and measured states (and their derivatives), in the case of the cooperative control scheme the joint-level controller cooperate by exchanging certain computed terms between them. Even in this case, we provide a discussion on implication of the discrete-time implementation. We prove, that the proposed cooperative control law makes the links of the manipulator, and hence the end-effector, follow the desiredtrajectory, asymptotically. We design a cooperative distributed model-based controller for a planar 3R manipulator, to illustrate the proposed cooperative manipulator control scheme implemented in the distributed control architecture. We also provide a discussion on computational effectiveness of the proposed cooperative distributed control scheme along with a method to further reduce the computational lead time by identifying repetitive terms in the control law. We present a detailed analysis of computational cost associated with the dynamic equation of planar manipulators with degrees-of-freedom from 2 to 6, where we analyze the cost involved in the proposed distributed control schemes in contrast to that in the conventional centralized model-based control scheme, using Maple. We provide results which indicate that the distribution effectiveness of the proposed simple distributed control schemes improves with degrees-offreedom of the manipulator. We also provide a detailed discussion on reducing the computational cost by identifying repetitive terms in the dynamic equations at each joint-level, for planar manipulators with degrees-of-freedom from 3 to 6. We then present simulation results demonstrating the proposed control schemes. We present results which show how the trajectory tracking performance of the model-based control law degrades with increase in the sampling time. Then we present results which demonstrate that with the proposed distributed control schemes every joint tracks the desired trajectory satisfactorily, in comparison with the independent-joint PID control scheme. We present details of implementation of the proposed distributed manipulator control scheme using Simulink-ROS hybrid platform based on Matlab’s Robotics toolbox, which provides a more realistic simulation result and it is also amenable for hardware implementation. Finally, we present a discussion to compare decentralized control schemes presented in the literature with the distributed control schemes presented in this thesis.