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...nsic properties of the arm and replace them with the target impedance. The impedance relation can have any functional form. It has been shown that general impedances are useful for obstacle avoidance =-=[6, 10, 17]-=-. However, it will be made clear in this section that sensor based, feedback controlled interaction with the environment requires the impedance to be linear and of second order at most. This is for tw...

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... the robot's position and the force it exerts. A complete introduction to impedance control is beyond the scope of this discussion and the reader is referred to the previous work of other researchers =-=[6, 8]-=-. The basic tenet of impedance control is that the arm should be controlled so that it behaves as a mechanical impedance to positional constraints imposed by the environment. This means that the force...

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...ulator becomes necessary in at least one of the degrees of freedom of the manipulator; the other degrees of freedom remain position controlled. Mason formalized this idea and called it Hybrid Control =-=[14]-=-. Simply put, the manipulator should be force controlled in directions in which the position is constrained by environmental interaction, and position controlled in all orthogonal directions. The Hybr...

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...tractive to switch controllers as well as gains, and get the best performance possible from the system. Stable response through the impact transient has been demonstrated by switching control schemes =-=[19, 11, 12]-=-. Therefore, the results of this work indicate two major points. First, second order impedance control must be recognized as essentially equivalent to proportional gain explicit force control with fee...

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... fp ! 1 or 0sK 0 fp ! 1. Figure 11 shows the proportional gain force control root locus for gains as low as negative one. The use of negative gains like this has appeared in the literature previously =-=[5, 7]-=-. However, this result is usually presented within the framework of impedance control. As will be seen in the following sections, the impedance controllers for which this result was obtained actually ...

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...bian, J . The subscripts c and m indicate commanded and measured quantities. Without force feedback this control scheme is equivalent to position control schemes such as Resolved Acceleration Control =-=[13]-=- and Operational Space Control [9]. These are only first order impedance control schemes since they just modify the stiffness and damping of the arm. Including force feedback information in the contro...

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...mmanded. This is typically the method employed, as will be shown. 3.2 Model Based Control Model based control involves the use of a dynamic model of the manipulator to determine the actuation torques =-=[2]. Mo-=-del based impedance control may be summarized by the following equations [6, 16]: �� A = Du + h + g + J T fm (10) u = J \Gamma1 isx u \Gamma J ` m j (11)sx u = M \Gamma1 [(C \Deltasx +K \Deltax) \...

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... the robot's position and the force it exerts. A complete introduction to impedance control is beyond the scope of this discussion and the reader is referred to the previous work of other researchers =-=[6, 8]-=-. The basic tenet of impedance control is that the arm should be controlled so that it behaves as a mechanical impedance to positional constraints imposed by the environment. This means that the force...

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...e drop-off which gives a minimum phase margin of �� 15 ffi at K fp �� 1. The addition of a lowpass filter in the feedback loop can improve the response by introducing a dominant pole on the re=-=al axis [1, 16]-=-. However, this pole placement and the behavior of the system closely match that provided by integral control. A discussion including integral force control is outside the scope of this paper [16]. Th...

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...dicate commanded and measured quantities. Without force feedback this control scheme is equivalent to position control schemes such as Resolved Acceleration Control [13] and Operational Space Control =-=[9]-=-. These are only first order impedance control schemes since they just modify the stiffness and damping of the arm. Including force feedback information in the controller yields second order impedance...

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...in each case, the response and stability of the system are essentially the same. All experiments were conducted using the CMU DD Arm II and implemented under the Chimera II real time operating system =-=[15]-=-. The experiments presented here were conducted by pushing on a common environment: a cardboard box with an aluminum plate resting on top. The parameters of a second order model of this environmental ...

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...tractive to switch controllers as well as gains, and get the best performance possible from the system. Stable response through the impact transient has been demonstrated by switching control schemes =-=[19, 11, 12]-=-. Therefore, the results of this work indicate two major points. First, second order impedance control must be recognized as essentially equivalent to proportional gain explicit force control with fee...

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...In this case, the value of active inertia is the acceleration feedback gain. Its value can be used to adjust M . Few researchers have proposed such acceleration feedback schemes for impedance control =-=[4]-=-. This is because an acceleration measurement typically requires a second derivative, which will be extremely noisy. Alternatively, the force may be measured and the acceleration commanded. This is ty...

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...cludes the active damping control loop. It has previously been shown that G can be considered a fourth order transfer function [3], and we have experimentally extracted parameter values for the model =-=[16, 18]-=-. The closed loop transfer function with the feedforward term is: F c Fm = (1 +K fp )G 1 +K fp G : (2) This is a Type 0 System and will have a nonzero steady-state error for a step input. The root loc...

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...cludes the active damping control loop. It has previously been shown that G can be considered a fourth order transfer function [3], and we have experimentally extracted parameter values for the model =-=[16, 18]-=-. The closed loop transfer function with the feedforward term is: F c Fm = (1 +K fp )G 1 +K fp G : (2) This is a Type 0 System and will have a nonzero steady-state error for a step input. The root loc...

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... fp ! 1 or 0sK 0 fp ! 1. Figure 11 shows the proportional gain force control root locus for gains as low as negative one. The use of negative gains like this has appeared in the literature previously =-=[5, 7]-=-. However, this result is usually presented within the framework of impedance control. As will be seen in the following sections, the impedance controllers for which this result was obtained actually ...

Citation Context

...tractive to switch controllers as well as gains, and get the best performance possible from the system. Stable response through the impact transient has been demonstrated by switching control schemes =-=[19, 11, 12]-=-. Therefore, the results of this work indicate two major points. First, second order impedance control must be recognized as essentially equivalent to proportional gain explicit force control with fee...