In this lesson, we will go over the basics of the vehicle actuation system such as throttling, braking, and steering. By the end of this video, you will be able to; define common models for the steering, throttle, and brake systems of the vehicle and connect these models to the vehicle dynamic equations derived in the previous videos. Let's get started. The main input to the lateral dynamics is steering angle and the main inputs to the longitudinal dynamics are throttle pedal position and brake pedal position. These inputs define some of the forces and moments that act on the vehicle and feed into the ordinary differential equations that govern the state of the vehicle. Note that the lateral dynamics and the longitudinal dynamics can affect each other. Although the models we have built so far are separated by assumption. The lateral forces and moments then drive the vehicle lateral kinematics, which produce a vehicle lateral velocity in your rate. Similarly, the longitudinal forces drive the longitudinal kinematics, which defines the resulting forward velocity and displacement. The main task of vehicle control is to provide suitable steering throttle and brake commands to keep the vehicle on the desired path and following a desired speed profile. We'll assume these desired elements are provided by the motion planning system and we'll see how to build such a planner in the fourth course of this specialization. Now, let's turn to modeling each of the three command inputs subsystems to further refine our full vehicle model. First, let's take a look at the steering model. The steering model is simply the driver's command or the autonomy systems command to turn the vehicle to the right or left. The steering angle is translated into a wheel angle through a special mechanism and gear ratios that provide the lateral forces to keep the vehicle on a curved path. In the simplest model for the steering system, the wheel angle can be defined as proportional to the steering angle. So, the steering angle Delta S, is linearly proportional to the wheel angle Delta, with a steering coefficient C. This is sufficient for our work in simulation and is often used as a starting point for non-aggressive driving. In reality, the steering system is more complex than the previous simple formulation and a fully dynamic model may be needed if steering commands are very near the bandwidth of the steering assembly. This figure shows the main subsystem in a steering assembly such as the steering wheel, steering column, steering gears and linkages that connect the steering column to the left and right wheels. This figure also shows the rack and pinion gears on the right which translate the rotational motion of the steering wheel to the linear motions needed to move the wheel linkages. We've included links to more detailed dynamic models of steering assemblies in the supplemental materials if you'd like to learn more. Next up is the power train model. As we saw earlier in this module, the vehicle power train determines the vehicles forward velocity and acceleration. In automatic transmission cars, a driver or the autonomy system has two inputs to accelerate or decelerate the vehicle, the gas, and brake. This diagram shows the mechanism to translate the driver or autonomy systems commands into wheel motions. Let's now look at the typical power flow through the power train. Let's review the power flow diagram from the longitudinal dynamics video. The power flow diagram starts from the power generation unit such as the internal combustion engine or electric motor. A throttle pedal position drives the torque produced by the power generation unit. This torque is passed to the transmission system. In an automatic transmission system, the fluid coupling system or torque converter is placed between the engine shafts and the gearbox unit. Then, based on the operating mode and desired speeds, the gearbox changes the gear as needed. Gears one and two are torque modes and the higher gears are called speed modes, referring to the different modes of operation in the torque converter. Then the power flows to the wheels through a differential and generates the wheel torques, which ultimately generate traction forces. The traction force must be higher than the resistance force, which includes the aerodynamic force and road friction to accelerate the vehicle forward in the longitudinal direction. The power which is the source of the vehicle motion can be generated through combustion in an internal combustion engine or from the battery for an electric motor. Simply put, the driver puts their foot on the gas pedal to define the level of torque demand needed to accelerate the vehicle. The actual response is a bit more complex and depends on the type of power generation unit involved. The characteristics of the internal combustion engine, diesel engines, and electric motors are all different. The torque-speed diagram is used as a diagram to represent these characteristics for power units. The left diagram shows a torque-speed curve for a gas engine. For a range of engine angular speeds are RPMs. The highest torque operating point for a gas engine tends to be in the middle RPMs typically 2,000 or 3,000 RPM for a passenger vehicle engine. At low and high speeds, the ability of the engine to produce torque falls off. The middle diagram is a torque characteristic for the diesel engines, which show more consistent torque generation over a wider range of speeds. This is why diesel engines are more suitable for heavy-duty vehicles and the gasoline engines are best suited for small and city cars. The right diagram shows the torque characteristic of an electric motor. The electric motor is more efficient at lower RPMs such as 1,500. However, it is not very efficient at higher RPM. Note that to compensate the lack of torque characteristics at the higher RPM in electric motors, the hybrid electric vehicles use the internal combustion engine to improve performance over electric motors at higher speeds. The torque characteristic plots of an internal combustion engine at different throttle angles is plotted in this figure. The torque to RPM relation can be represented as a second-order polynomial which is a simple but fairly good control, oriented model. In the following equations, the engine torque is represented as Te. The throttle pedal position is X-Theta and the engine angular speed is Omega e. The coefficients, A knot, A_1 and A_2 are identified and tuned for different engines. This model is called a semi-empirical model, and more detailed models can include the dynamics of fluids, heat transfer, combustion and many other phenomena which are not in the scope of this course. Given the engine speed and throttle position, it is possible to compute the engine torque produced based on this semi-empirical map, which then feeds into the longitudinal dynamics model for the vehicle. Let's now turn to model development for the brake system. The braking process starts from the driver commanded brake pedal position, which is translated into a brake pressure by the electronic control unit. The brake pressure results in a braking force on the brake disc or drum, which becomes a braking wheel torque at the wheel. The braking torque on the wheels creates a negative longitudinal force to decelerate the vehicle. Because of the control unit management of the braking torque, the response to the braking system is very predictable. For the purposes of this course, it is not necessary to model the brakes in much detail and once again, a simple linear mapping from pedal position to brake torque can be used. The braking system is of course, vital to control the motion of a vehicle. In fact, brakes play a range of important roles in vehicle control. Some of the primary functions of a braking system include: shortening stopping distance through hard braking, maintaining steerability during braking through anti-lock braking, maintaining stability during braking to avoid overturning. These functions help to expand the set of safe operating conditions that we can drive in and modern braking capabilities have led to significant advances in vehicle safety and performance. We've now completed our discussion of the actuator components of the vehicle. Let's summarize what we've done so far. In this video, we looked at the vehicle actuation system and the main commands used to move the vehicle in both the lateral and longitudinal directions. In the autonomous car, these actuation signals will be the main output of the vehicle control module. We also developed steering, engine and brake models that convert these commands into wheel angles and torques on the wheels. In the next video, we will go through the final piece of our dynamic vehicle modeling process. The tire that connects the vehicle to the road. See you there.
