Car testdrive (elliptic track) - Revision history

FelixMueller at 08:25, 27 July 2016

2016-07-27T08:25:25Z

2016-04-10T09:26:01Z

Resulting MIOCP

2016-04-10T09:25:41Z

Resulting MIOCP

← Older revision		Revision as of 09:25, 10 April 2016
Line 24:		Line 24:
	\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), \\
	& c_\text{x}(t_0) &=& c_\text{x}(t_f), \\		& c_\text{x}(t_0) &=& c_\text{x}(t_f), \\
	& c_\text{y}(t_0) &=& c_\text{y}(t_f), \\		& c_\text{y}(t_0) &=& c_\text{y}(t_f), \\

2015-12-30T20:32:09Z

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

← Older revision		Revision as of 20:32, 30 December 2015
Line 7:		Line 7:
	}}		}}

	The elliptic track testdrive problem is a time optimal periodic control problem with gear shift, first introduced in <~~bibref>~~Sager2009a</~~bibref~~>.		The elliptic track testdrive problem is a time optimal periodic control problem with gear shift, first introduced in <bib id="Sager2009a" />.

	== Mathematical formulation ==		== Mathematical formulation ==

2015-12-30T20:28:25Z

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

← Older revision		Revision as of 20:28, 30 December 2015
Line 40:		Line 40:
	See testdrive [[Car testdrive \| overview page]].		See testdrive [[Car testdrive \| overview page]].
	== 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 -->

2008-11-25T13:08:16Z

2008-11-25T13:07:41Z

← Older revision		Revision as of 13:07, 25 November 2008
Line 11:		Line 11:
	== Mathematical formulation ==		== Mathematical formulation ==

	The mathematical equations form a small-scale [[:Category:ODE model\|ODE model]].		The mathematical equations form a small-scale [[:Category:ODE model\|ODE model]] as presented for the [[Car testdrive (lane change manoeuvre) \| lane change manoeuvre]].

	The vehicle dynamics are based on a single-track model, derived under the simplifying assumption that rolling and pitching of the car body can be neglected. Consequentially, only a single front and rear wheel is modeled, located in the virtual center of the original two wheels. Motion of the car body is considered on the horizontal plane only.		The vehicle dynamics are based on a single-track model, derived under the simplifying assumption that rolling and pitching of the car body can be neglected. Consequentially, only a single front and rear wheel is modeled, located in the virtual center of the original two wheels. Motion of the car body is considered on the horizontal plane only.

2008-11-25T13:04:14Z

Resulting MIOCP

← Older revision		Revision as of 13:04, 25 November 2008
Line 25:		Line 25:
	\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}(t) & = & f(t, x(t), u(t), \mu(t)), \\
	& x(t_0) &=& ~~x_0~~, \\		& c_\text{x}(t_0) &=& c_\text{x}(t_f), \\
			& c_\text{y}(t_0) &=& c_\text{y}(t_f), \\
			& v(t_0) &=& v(t_f), \\
			& \beta(t_0) &=& \beta(t_f) - 2\pi, \\
			& \psi(t_0) &=& \psi(t_f), \\
			& \delta(t_0) &=& \delta(t_f), \\
	& r(t,x(t),u(t)) &\geq& 0, \\		& r(t,x(t),u(t)) &\geq& 0, \\
	& \mu(t) &\in& \{1, 2, 3, 4, 5\}.		& \mu(t) &\in& \{1, 2, 3, 4, 5\}.

2008-11-25T13:00:27Z

@@ Line 17: / Line 17: @@
 Four controls represent the driver's choice on steering and velocity. We denote with <math>w_\delta</math> the steering wheel's angular velocity. The force <math>F_\text{B}</math> controls the total braking force, while the accelerator pedal position <math>\phi</math> is translated into an accelerating force. Finally, the selected gear <math>\mu</math> influences the effective engine torque's transmission.
 == References ==
 <bibreferences/>

2008-11-25T12:53:01Z

← Older revision		Revision as of 12:53, 25 November 2008
Line 19:		Line 19:
	== References ==		== References ==
	<bibreferences/>		<bibreferences/>

			<!--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 -->
			[[Category:MIOCP]]
			[[Category:ODE model]]
			[[Category:Minimum time]]
			[[Category:Bang bang]]
			[[Category:Transport]]
			[[Category:Periodic]]