Industrial robot - Revision history

TobiasWeber: /* Parameters */

2016-08-01T07:44:20Z

Parameters

← Older revision		Revision as of 07:44, 1 August 2016
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	* <math> \mathcal{X} = [-\bar{x}, \bar{x}], \text{ where } \bar{x} = (\bar{q},\bar{q},\bar{q},\bar{\dot{q}},\bar{\dot{q}},\bar{\dot{q}})^T \text{ with } \bar{q} = \infty \text{ rad}, \quad \bar{\dot{q}} = 0.5 \text{ rad/s} </math>		* <math> \mathcal{X} = [-\bar{x}, \bar{x}], \text{ where } \bar{x} = (\bar{q},\bar{q},\bar{q},\bar{\dot{q}},\bar{\dot{q}},\bar{\dot{q}})^T \text{ with } \bar{q} = \infty \text{ rad}, \quad \bar{\dot{q}} = 0.5 \text{ rad/s} </math>
	* <math> \mathcal{U} = [-\bar{u}, \bar{u}], \text{ where } \bar{u} = - (\bar{\tau},\bar{\tau},\bar{\tau})^T \text{ with } \bar{\tau} = 60 \text{ Nm} </math>		* <math> \mathcal{U} = [-\bar{u}, \bar{u}], \text{ where } \bar{u} = (\bar{\tau},\bar{\tau},\bar{\tau})^T \text{ with } \bar{\tau} = 60 \text{ Nm} </math>
	* <math> \mathcal{Z} = [\underline{z}, \bar{z}], \text{ where } \underline{z} = (0,0)^T, \bar{z} = (1750, \infty)^T </math>		* <math> \mathcal{Z} = [\underline{z}, \bar{z}], \text{ where } \underline{z} = (0,0)^T, \bar{z} = (1750, \infty)^T </math>
	* <math> \mathcal{V} = [-10^4, 8 \cdot 10^3] </math>		* <math> \mathcal{V} = [-10^4, 8 \cdot 10^3] </math>

2016-08-01T07:41:39Z

Parameters

← Older revision		Revision as of 07:41, 1 August 2016
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	The Implementation Parameters for the MPFC scheme are as follows.		The Implementation Parameters for the MPFC scheme are as follows.

	* <math> \mathcal{X} = [-\bar{x}, \bar{x}], \text{ where } \bar{x} = (\bar{q},\bar{q},\bar{q},\bar{\dot{q}},\bar{\dot{q}},\bar{\dot{q}})^T \text{ with } \bar{q} = \infty \text{ rad/s}, \quad \bar{\dot{q}} = 0.5 \text{ rad/s} </math>		* <math> \mathcal{X} = [-\bar{x}, \bar{x}], \text{ where } \bar{x} = (\bar{q},\bar{q},\bar{q},\bar{\dot{q}},\bar{\dot{q}},\bar{\dot{q}})^T \text{ with } \bar{q} = \infty \text{ rad}, \quad \bar{\dot{q}} = 0.5 \text{ rad/s} </math>
	* <math> \mathcal{U} = [-\bar{u}, \bar{u}], \text{ where } \bar{u} = - (\bar{\tau},\bar{\tau},\bar{\tau})^T \text{ with } \bar{\tau} = 60 \text{ Nm} </math>		* <math> \mathcal{U} = [-\bar{u}, \bar{u}], \text{ where } \bar{u} = - (\bar{\tau},\bar{\tau},\bar{\tau})^T \text{ with } \bar{\tau} = 60 \text{ Nm} </math>
	* <math> \mathcal{Z} = [\underline{z}, \bar{z}], \text{ where } \underline{z} = (0,0)^T, \bar{z} = (1750, \infty)^T </math>		* <math> \mathcal{Z} = [\underline{z}, \bar{z}], \text{ where } \underline{z} = (0,0)^T, \bar{z} = (1750, \infty)^T </math>

2016-07-29T13:34:07Z

Virtual system

← Older revision		Revision as of 13:34, 29 July 2016
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	== Virtual system ==		== Virtual system ==

	A virtual system is introduced to take care of the timing of the robot. This is an additional degree of freedom which is used here as an input into an integrator. This additional optimization variable <math> v </math> is integrated twice to produce <math> z_1 </math> which is used as the time parameter for the path (i.e. <math> p(z_1) </math>).		A virtual system is introduced to take care of the timing of the robot. This is an additional degree of freedom which is used here as an input into an integrator. This additional optimization variable, the virtual input, <math> v </math> is integrated twice to produce the virtual state <math> z_1 </math> which is used as the time parameter for the path (i.e. <math> p(z_1) </math>).

	<math> \left(		<math> \left(

2016-07-29T13:33:24Z

Virtual system

← Older revision		Revision as of 13:33, 29 July 2016
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	</math>		</math>

	The virtual state and input are constrained by the sets <math> \mathcal{Z} ~~\text{~~ and } \mathcal{V} </math> respectively.		The virtual state and input are constrained by the sets <math> \mathcal{Z} </math> and <math> \mathcal{V} </math> respectively.

	== Model ==		== Model ==

2016-07-29T13:33:05Z

Virtual system

← Older revision		Revision as of 13:33, 29 July 2016
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	</math>		</math>

	The virtual state and input are constrained by the sets <math> \mathcal{Z} \text and } \mathcal{V} </math> respectively.		The virtual state and input are constrained by the sets <math> \mathcal{Z} \text{ and } \mathcal{V} </math> respectively.

	== Model ==		== Model ==

2016-07-29T13:32:52Z

Virtual system

← Older revision		Revision as of 13:32, 29 July 2016
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	</math>		</math>

	The virtual state and input are constrained by the sets \mathcal{Z} and \mathcal{V} respectively.		The virtual state and input are constrained by the sets <math> \mathcal{Z} \text and } \mathcal{V} </math> respectively.

	== Model ==		== Model ==

2016-07-29T13:32:29Z

Virtual system

← Older revision		Revision as of 13:32, 29 July 2016
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	</math>		</math>

			The virtual state and input are constrained by the sets \mathcal{Z} and \mathcal{V} respectively.

	== Model ==		== Model ==

2016-07-29T13:30:27Z

Added parameter sets

← Older revision		Revision as of 13:30, 29 July 2016
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	\| <math> m </math>		\| <math> m </math>
	\|}		\|}

			The Implementation Parameters for the MPFC scheme are as follows.

			* <math> \mathcal{X} = [-\bar{x}, \bar{x}], \text{ where } \bar{x} = (\bar{q},\bar{q},\bar{q},\bar{\dot{q}},\bar{\dot{q}},\bar{\dot{q}})^T \text{ with } \bar{q} = \infty \text{ rad/s}, \quad \bar{\dot{q}} = 0.5 \text{ rad/s} </math>
			* <math> \mathcal{U} = [-\bar{u}, \bar{u}], \text{ where } \bar{u} = - (\bar{\tau},\bar{\tau},\bar{\tau})^T \text{ with } \bar{\tau} = 60 \text{ Nm} </math>
			* <math> \mathcal{Z} = [\underline{z}, \bar{z}], \text{ where } \underline{z} = (0,0)^T, \bar{z} = (1750, \infty)^T </math>
			* <math> \mathcal{V} = [-10^4, 8 \cdot 10^3] </math>

	== Reference Solutions ==		== Reference Solutions ==

2016-07-27T11:09:15Z

Parameters

2016-07-27T11:05:31Z

Model

← Older revision		Revision as of 11:05, 27 July 2016
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	</math>		</math>

	where <math> q = x_1 </math> and <math> \bar{d}_5 = d_5 + d_{tool} </math> with <math> d_i, i \in \{ 1,3,5 \} </math> being the lengths of the ~~link~~ of the robot and <math> d_{tool} </math> is the length of the pen and tool. These values can be found in the Parameters section as well.		where <math> q = x_1 </math> and <math> \bar{d}_5 = d_5 + d_{tool} </math> with <math> d_i, i \in \{ 1,3,5 \} </math> being the lengths of the links of the robot and <math> d_{tool} </math> is the length of the pen and tool. These values can be found in the Parameters section as well.


	== OCP ==		== OCP ==
	The optimization problem which is solved repetitively is given by		The optimization problem which is solved repetitively is given by