Enhanced flatbed tow truck model for stable and safe platooning in - PowerPoint PPT Presentation

Enhanced flatbed tow truck model for stable and safe platooning in presences of lags, communication and sensing delays 1 ALAN ALI GAËTAN GAR CIA P H ILIP P E M AR TIN ET

INDEX 2  I. Introduction  II. Modeling:  Vehicle,  Platoon  III. Control  IV. Stability  Without communication delay  With all delays  V. Safety  VI. Simulation  VII. Conclusion

I. INTRODUCTION 3  Why platooning:  Increases traffic density.  Increases safety:  Weak collision (Small relative velocity).  No human factor.  Small reaction time.  decreases fuel consumption.  decreases driver tiredness

I. INTRODUCTION 4  Global Control and Local Control :  Data (at least from leader, adjacent vehicles)  Sophisticated sensors (needed, Not needed).  Adaptation in the environment (Maybe, Not needed)  Communication system ( need very reliable , not needed )  Trajectory tracking and inter distance keeping (accurate , Not very accurate)  The ca r is tota lly a utonom ous (No, Yes).

I. INTRODUCTION 5  Variable inter-vehicle distances :  Distances are proportional to velocity in Constant Time Headway(CTH)  Low traffic density.  Stable without communication.  The cars can work autonomously.    X L hv i  Constants inter-vehicle distances:  High traffic density.  The communication between vehicles is mandatory.  X  L

I. INTRODUCTION 6  Delays and lags:  Lags and times delays make the net engine torque is not immediately equal to the desired torque computed by the controller.  Delays types and sources:  Actuator lags:  The lag in the engine response,  The lag of the throttle actuator,  The lag of the brake actuator…  Sensing delays:  The delay due to the sensors response time,  The delay due to the sensors filter…  Com m unication delays:  Communication transfer time,  Packet drops,  Connection loss…

I. INTRODUCTION 7  State of the art:  Stability with lags and sensing delays:  Study can be found for many control laws [ 2010:Ling-yun, 2001:Rajamani, Swaroop, Yanakiev ].  A detailed study when using classical time headway for homogeneous and heterogeneous platoons is found in [ Lingyun(2011) ].  Effects of communication delays:  The platoon is unstable for any propagation delays in the communicated leader information [ 2001: Hedrick ] !!!!!.  A solution in [ 2001: Xiangheng ] by synchronizing all the controllers of the vehicles,  But Clock jitter, which can be seen as a delay and may cause instability according to [2001: Hedrick] result, was briefly mentioned!!!!!.  [ Lingyun(2011) ] proved string stability for the leader-predecessor and predecessor- successor framework neglecting information delays between vehicles.  The effect of losing the communication is presented in [2010: Teo]. It has been proved that string stability can be retained, with limited spacing error, by estimating lead vehicle’s state during losses.  In this Work we prove the stability and the safety of the platoon in presence of all the delays in extension to [ 2001: Hedrick ],

II. MODELING ( Longitudinal Model ) 8 Aero dynamical  Newton’s law, force Gravitationnel Rolling force resistance  Applying the exact linearization system, x    W    x x W x 1 1 s s

II. Modeling (Platoon) 9  Platoon:  Vehicles following each other.  The leader:  Driven Manually or automatically/ it can be virtual or real.  The other vehicles:  Run at the same speed keeping desired inter-vehicle distances.  � : Desired inter distance. : Position of vehicle i. x  i : speed of vehicle i. v  i    : Spacing error between vehicle i and e x x L   1 i i i vehicle i-1.

III. CONTROL 10  Control Objectives.  Keep a desired distance between the vehicles,  Make the vehicles move at the same speed,  Ensure vehicles and platoon stability [1-5],  Control on highways [1,3] and in urban areas [2,4],  Ensure vehicles and platoon safety [ ICARCV14 ],  Increase traffic density,  Ensure the stability and safety even in case of :  Entire communication loss between vehicles [ ICARCV14 ],  Existence of actuating, sensing lags and com m unication delays.

III. CONTROL 11  Control law:        New  ( ) ( ) ( ( ) ( )) e t e t h v t V t e  i i 1 V term W i i h e : Is the error between the position of the virtual truck and the vehicle i. V i The position of the truck is calculated by integrating V.

II. CONTROL (With delays) 12  Modeling of the platoon with delays:  Lags τ � : so �� � � �� � τ � � � � � � �  Sensing delays ∆ � : � � � , �� � � , � � � � � � ∆ � , �� � � � ∆ � , � � � ∆ �  Communication delays τ � � : so � � , � � � � � �∆ � � τ �� � , � � � � �∆ � � τ �� � � �� �� � � �∆ � � � �∆ � � � �∆ � �

III. CONTROL(With delays) 13  The error function of the i-th vehicle becomes:     c e ( s ) G ( s ) e ( s ) G ( s ) e V ( s ) i  i e i 1 V Transfer functions G ( s ), G ( s ) e V Impulse functions g ( t ), g ( t ) e V

IV. STABILITY 14  Platoon stability:  All state variables are always limited for all the vehicles:       , , : i i i          e ( t ) & e ( t ) & e ( t )   i i i i i i     1 ,..., 0 i N and t

IV. STABILITY 15  Stability with communication delay: out     e ( s ) G ( s ) e ( s ) G ( s ) e c V ( s ) i  e i 1 V  Sufficient stability condition (error do not increase through platoon)   e ( t ) e 1 t ( )   i i  It is sufficient to prove: e ( s )   i G ( s ) 1  i e ( s )   i 1  We get stability conditions:               h 2 ( ) 2 h 1            1 1 1 & & & h 2 ( )            2 ( h ( ) ) 2 h

IV. STABILITY 16  Stability with communication delay:     c e ( s ) G ( s ) e ( s ) G ( s ) e V ( s ) i  i e i 1 V  We can’t use   e ( t ) e 1 t ( )   i i  We calculate � as a function of � and :     s i 2 1 ( G e ) c      i 1 s e e ( s ) G ( s ) e ( s ) G ( s ) e V ( s ) c    i e 1 V s 1 G e c e  Sufficient stability condition is to prove that the errors is always limited for all the vehicles and all the times:          : e ( t ) i 1 ,..., N and t 0  i i i

IV. STABILITY 17  Stability with communication delay:  If � � � , � � ��� are positive impulse functions then we get:       ( ) ( ) ( )     e s F v s F V s j i 2 0 1 ( G ( ) e ) 2 c 1 e 0 V e  The only problem can appears near low G    ( ) G ( 0 ) 1 frequencies when (X V -x 0 ) become very big e e        h ( V v ) ( X x ) i 1 V 0       j i 2  1 ( G ( ) e )   c 1 i     e e ( t ) G ( ) e ( t ) G ( ) V ( t )          i e 1 V  j 1 G ( ) e c  e Bounded if the        Converge to zero propagation delay j 0 1 G ( ) e 2 c e  ∆ � is bounded G    ( ) G ( 0 ) 1  G    e e   ( ) G ( 0 ) 1     1 G ( ) G ( 0 ) e e      V V c   1

V.SAFETY 18  We want to limit the maximum error to keep the inter-vehicle distances always bigger than zero :      ( ) ( ) ( ) ( ) ( ) 2 ,..., e t G e t G V t i N      i e i 1 V                   Taking max(   will limit the max error, we get: ) L L      G ( ) ( 1 G ( ) ) i 2 ,..., N  V e  V ( t )  L        i 2 ,..., N c c c  i i 1 max( V ( t )) Limit for communication propagation delay that prevents collisions

V.SAFETY 19  For the first error � :    e ( t ) K ( s ) e ( s ) K ( s ) a ( s ) 1 e V V V  Taking � we get:  e ( t ) K ( s ) a ( s ) 1 V 0  e ( t ) K ( s ) a ( s )   1 V 0 a    1  0 h L