Car testdrive (lane change manoeuvre) - Revision history

FelixMueller at 08:25, 27 July 2016

2016-07-27T08:25:36Z

← Older revision		Revision as of 08:25, 27 July 2016
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	\|nu = 3		\|nu = 3
	\|nw = 1		\|nw = 1
			\|nc = 1
	\|nri = 7		\|nri = 7
	}}		}}

FelixMueller: /* Source Code */

2016-06-28T07:48:34Z

Source Code

← Older revision		Revision as of 07:48, 28 June 2016
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	== Source Code ==		== Source Code ==

	~~=== C ===~~		Model descriptions are available in

	* [[:Category:Muscod \| Muscod code]] at [[Car testdrive (lane change manoeuvre) (Muscod)]]		* [[:Category:Muscod \| Muscod code]] at [[Car testdrive (lane change manoeuvre) (Muscod)]]

FelixMueller: /* Source Code */

2016-06-28T07:48:15Z

Source Code

@@ Line 132: / Line 132: @@
 === C ===
 * [[:Category:Muscod | Muscod code]] at [[Car testdrive (lane change manoeuvre) (Muscod)]]
 == Variants ==

FelixMueller: /* Source Code */

2016-06-28T07:46:35Z

Source Code

← Older revision		Revision as of 07:46, 28 June 2016
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	=== C ===		=== C ===
			* [[:Category:Muscod \| Muscod code]] at [[Car testdrive (lane change manoeuvre) (Muscod)]]

	The differential equations in C code:		The differential equations in C code:

FelixMueller: /* Resulting MIOCP */

2016-04-10T09:26:26Z

Resulting MIOCP

← Older revision		Revision as of 09:26, 10 April 2016
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	\begin{array}{llcl}		\begin{array}{llcl}
	\displaystyle \min_{x(\cdot), u(\cdot), \mu(\cdot)} & t_\text{f} \\[1.5ex]		\displaystyle \min_{x(\cdot), u(\cdot), \mu(\cdot)} & t_\text{f} \\[1.5ex]
	\mbox{s.t.} & \dot{x}~~(t)~~ & = & f(t, x~~(t)~~, u~~(t)~~, \mu~~(t)~~), \\		\mbox{s.t.} & \dot{x} & = & f(t, x, u, \mu), \\
	& x(t_0) &=& x_0, \\		& x(t_0) &=& x_0, \\
	& r(t,x~~(t)~~,u~~(t)~~) &\geq& 0, \\		& r(t,x,u) &\geq& 0, \\
	& \mu(t) &\in& \{1, 2, 3, 4, 5\}.		& \mu(t) &\in& \{1, 2, 3, 4, 5\}.
	\end{array}		\end{array}

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2015-12-30T20:32:10Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 20:32, 30 December 2015
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	}}		}}

	The testdrive control problem is a time optimal double lane change maneouvre with gear shift. It has been introduced as a benchmark problem for mixed-integer optimal control by <~~bibref>~~Gerdts2005</~~bibref~~>.		The testdrive control problem is a time optimal double lane change maneouvre with gear shift. It has been introduced as a benchmark problem for mixed-integer optimal control by <bib id="Gerdts2005" />.

	== Mathematical formulation ==		== Mathematical formulation ==
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	== Test course ==		== Test course ==

	The double-lane change manoeuvre presented in <~~bibref>~~Gerdts2005</~~bibref~~> is realized by constraining the car's position onto a prescribed track at any time <math>t\in[t_0,t_\text{f}]</math>. Starting in the left position with an initial prescribed velocity, the driver is asked to manage a change of lanes modeled by an offset of 3.5 meters in the track. Afterwards he is asked to return to the starting lane. This manoeuvre can be regarded as an overtaking move or as an evasive action taken to avoid hitting an obstacle suddenly appearing on the starting lane.		The double-lane change manoeuvre presented in <bib id="Gerdts2005" /> is realized by constraining the car's position onto a prescribed track at any time <math>t\in[t_0,t_\text{f}]</math>. Starting in the left position with an initial prescribed velocity, the driver is asked to manage a change of lanes modeled by an offset of 3.5 meters in the track. Afterwards he is asked to return to the starting lane. This manoeuvre can be regarded as an overtaking move or as an evasive action taken to avoid hitting an obstacle suddenly appearing on the starting lane.

	From a mathematical point of view, the test track is described by setting up piecewise cubic spline functions <math>P_\text{l}(x)</math> and <math>P_\text{r}(x)</math> modeling the top and bottom track boundary, given a horizontal position <math>x</math>.		From a mathematical point of view, the test track is described by setting up piecewise cubic spline functions <math>P_\text{l}(x)</math> and <math>P_\text{r}(x)</math> modeling the top and bottom track boundary, given a horizontal position <math>x</math>.
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	== Reference Solutions ==		== Reference Solutions ==

	Reference solutions for the case of a fixed time-grid are given in <~~bibref>~~Gerdts2005</~~bibref~~>. Solutions for a non-fixed time grid are given in <~~bibref>~~Gerdts2006</~~bibref~~>.		Reference solutions for the case of a fixed time-grid are given in <bib id="Gerdts2005" />. Solutions for a non-fixed time grid are given in <bib id="Gerdts2006" />.

	== Source Code ==		== Source Code ==

JonasSchulze: Text replacement - "" to ""

2015-12-30T20:28:25Z

Text replacement - "<bibreferences/>" to "<biblist />"

← Older revision		Revision as of 20:28, 30 December 2015
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	== References ==		== References ==
	<~~bibreferences~~/>		<biblist />

	<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->		<!--List of all categories this page is part of. List characterization of solution behavior, model properties, ore presence of implementation details (e.g., AMPL for AMPL model) here -->

AlexanderBuchner at 13:25, 26 November 2008

2008-11-26T13:25:13Z

← Older revision		Revision as of 13:25, 26 November 2008
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	\| align=center \| <math>I_\text{zz}</math> \|\| align=right \| 1.752e+3 \|\| kg m^2 \|\| Moment of inertia		\| align=center \| <math>I_\text{zz}</math> \|\| align=right \| 1.752e+3 \|\| kg m^2 \|\| Moment of inertia
	\|-		\|-
	\| align=center \| <math>c_\text{w}</math> \|\| align=right \| 0.3 \|\| \|\| Air drag coefficient		\| align=center \| <math>c_\text{w}</math> \|\| align=right \| 0.3 \|\| - \|\| Air drag coefficient
	\|-		\|-
	\| align=center \| <math>\varrho</math> \|\| align=right \| 1.249512 \|\| kg/m^3 \|\| Air density		\| align=center \| <math>\varrho</math> \|\| align=right \| 1.249512 \|\| kg/m^3 \|\| Air density

Ckirches: /* Parameters */

2008-11-25T12:37:36Z

Parameters

← Older revision		Revision as of 12:37, 25 November 2008
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	\| align=center \| <math>c_\text{w}</math> \|\| align=right \| 0.3 \|\| \|\| Air drag coefficient		\| align=center \| <math>c_\text{w}</math> \|\| align=right \| 0.3 \|\| \|\| Air drag coefficient
	\|-		\|-
	\| align=center \| <math>\~~rho~~</math> \|\| align=right \| 1.249512 \|\| kg/m^3 \|\| Air density		\| align=center \| <math>\varrho</math> \|\| align=right \| 1.249512 \|\| kg/m^3 \|\| Air density
	\|-		\|-
	\| align=center \| <math>A</math> \|\| align=right \| 1.4378946874 \|\| m^2 \|\| Effective flow surface		\| align=center \| <math>A</math> \|\| align=right \| 1.4378946874 \|\| m^2 \|\| Effective flow surface

Ckirches: /* Parameters */

2008-11-25T12:37:18Z

Parameters