Controlled Robotic Systems
A controller is an essential part of a robotic system in achieving desired motion. A Proportional Integral Derivative (PID) controller is the simplest form of controller used for this purpose. A PID controller is widely used in industries for the control
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Controlled Robotic Systems
A controller is an essential part of a robotic system in achieving desired motion. A Proportional Integral Derivative (PID) controller is the simplest form of controller used for this purpose. A PID controller is widely used in industries for the control of processes or machines. In a robotic system, e.g., an industrial robot, a PID controller independently controls motion of each joint ignoring the effects of the system’s dynamics. However, for accomplishing complex motion or task, a PID controller does not always result into best performance, as shown by Lewis et al. (2004), Kelly et al. (2005), and Craig (2006). The legged robots discussed in Chaps. 6 and 7 are meant to perform a variety of complex tasks. As a result, the use of a PID controller without taking into account dynamics of the legged robots would result into poor control performance. On the other hand, the use of model-based controllers (Lewis et al. 2004; Kelly et al. 2005) has become popular in order to improve the performance of the conventional PID controllers. The model-based controllers work based on the information of the dynamic model of a system. If the dynamic model of a robot is not very accurate, the model-based control approach will still be able to eliminate major nonlinearities due to the robot’s inertia. In this chapter, simulation of model-based control of several robotic systems will be carried out.
9.1 Model-Based Control Since model-based controllers work well on precise information of the dynamic model of a robot, the recursive algorithms for inverse and forward dynamics proposed in Chaps. 6 and 7 are valuable in the control of robots due to their efficiency, computational uniformity, and less numerical errors produced during the dynamic computations. While the inverse dynamics algorithm helps in calculating the controlling torques of the actuators located at different joints, the forward dynamics algorithm predicts the behavior of the robot. The latter also allows real time simulation, which helps in predicting the future state of a system for S.V. Shah et al., Dynamics of Tree-Type Robotic Systems, Intelligent Systems, Control and Automation: Science and Engineering 62, DOI 10.1007/978-94-007-5006-7 9, © Springer ScienceCBusiness Media Dordrecht 2013
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9 Controlled Robotic Systems
corrective control measures. Model-based controller, e.g., computed-torque control and feedforward control, are developed next for the fixed and floating-base robotic systems.
9.1.1 Computed-Torque Control The dynamic equations of motion obtained in Eq. (5.12) are rewritten as IqR C h D ; where h D CqP £F
(9.1)
Equation (9.1) is nonlinear as the elements of the Generalized Inertia Matrix (I) are nonlinear functions of the state variable q, and the elements of Matrix of P Hence, Convective Inertia (C) are nonlinear functions of the state variables q and q. the use of a classical PID controller will lead to a set of nonlinear differential equations for the closed-loop system that will still have the nonlinea
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