Vehicle Dynamic Control Allocation for Path Following Moritz Gaiser

Transcription

1 Vehicle Dynamic Control Allocation for Path Following Moritz Gaiser INSTITUT FÜR THEORETISCHE ELEKTROTECHNIK UND SYSTEMOPTIMIERUNG (ITE) KIT Die Forschungsuniversität in der Helmholtz-Gemeinschaft

2 Motivation System Design for autonomous platforms Automotive Application: System for path following Path planning: Straight lines, curve... Guidance problem Controller Structure 2

3 Introduction Guidance Navigation w x Controller u c Sensor data Sensors Environment Vehicle w: Target values x: Estimated actual values u c : Actuator values 3

4 Outline Motivation and Introduction Guidance Controller Simulation Results Conclusion 4

5 Spline-Based Guidance North e p Projection p Lookahead Trajectory Input to guidance: Path (Spline data) Vehicle state x Nav y Nav Objective Path Following: Minimize cross-track error (lateral deviation) East 5

6 Spline-Based Guidance 1. Find closest point on trajectory (Newton-Raphson method) y n y d Θ = 1 y d Θ x d Θ x n x d Θ y d Θ y y d Θ + x d Θ x x d Θ = 0 2. Move forward on the spline by increasing the parametrizing variable Θ y d Θ + = a Θ b Θ c Θ + + d 3. Calculate desired course angle χ d Δ: Look ahead distance Θ: Parametrizing variable 6

7 Controller Structure Controller Guidance Command Filter w F Dynamic Control u c Virtual Controller Allocation Vehicle 7

8 Command Filter Receives commanded values from guidance Smooths and limits the values by taking vehicle dynamics into account Supplies the inputs to the virtual controller: Commanded position r c Commanded velocity v c Commanded acceleration a c y = 2Dω 0 ω o 2D e y y D: Damping coefficient ω 0 : Circular frequency Output signals are continuous and reasonable w.r.t. vehicle dynamics 8

9 Virtual Controller Virtual with the meaning of not actually controlling the vehicle Calculates the necessary force in body-frame Derivation of the control law: Translation dynamic: x n y n = 1 m F n v,x F n v,y + F n h,x + F n h,y n F W,x n F W,y v n eb = 1 C m b n Cb s F s v + F b n h F W n F v,x/y n F h,x/y n F W,x/y : Force front axle : Force back axle : Air resistance 9

10 Virtual Controller Define error dynamics e p = e v e v = p c v = p c 1 m C b n F b F W n Apply backstepping control with Lyapunow Control law: F Virtual = C n b [m r desired + K 1 + K 2 v + I 2x2 + K 1 K 2 r + F W ] K i : Controller parameter 10

11 Dynamic Control Allocation Control Allocation (CA): Distribute forces/moments among longitudinal and lateral forces of individual tires. Distribution in an optimal manner (Cost function) Two CA techniques Static Control Allocation Dynamic Control Allocation v F v,x δ Fv v,y Optimization problem with eq. constraint: min u J u, x, t τ d = h u h F h,x h F h,y 11

12 Dynamic Control Allocation Objective function: 4 J x, u, t = u T Wu w F ln c i (F i ) w δ ln c 5 (δ) + ln c 6 (δ) i=1 1. Part: Minimizing actuators u = F v v,x, F v v,y, F h h,x, F h h,y, δ 2. Part: Barrier functions penalizing the objective function when exceeding certain force and steering angle areas Extend OP with Lagrange multipliers to Lagrange function: L x, u, λt = J x, u, t + λ T τ d x, t h u 12

13 Dynamic Control Allocation Dynamic update law: u λ = ΓΗ L u L λ + Η 1 2 L τ d u 2 L τ d λ τ d Γ = γ ΗWΗ + εi 1 Η = 2 L u 2 2 L λ u 2 L u λ 0 13

14 Simulation Results Simulation using CarMaker Monte-Carlo simulations varying sensor noise to prove robustness of the system Target Trajectory 200m Straight Line 270 Curve with R=50m 125m Straight Line 90 Curve with R=25m 50m Straight Line 90 Curve with R=25m 125m Straight Line 14

15 Conclusion Design of a system for path following in automotive applications using Spline-based guidance with time-varying lookahead distance, Backstepping controller, And dynamic control allocation. Future goals Improve robustness of the guidance Introduce speed control to the guidance Reduce and simplify amount of tuneable parameters 15