# Voltage-Based Braking Controls for Electric Vehicles Considering Weather Condition and Road Slope
## 1 Introduction  
This article presents automatic braking controls for an electric vehicle with DC motors. It is assumed that the vehicle can detect the relative distance to an obstacle, such as other cars or pedestrians, in front of the vehicle. We consider the case where the vehicle has a long range radar with a maximum range of up to approx. 250 m [1]. While a vehicle moves, our goal is to generate automatic braking controls in real time, so that the vehicle stops safely and smoothly without slippage before it collides with the obstacle. It is desirable that the vehicle stops smoothly, considering a passengers' comfort. A passenger of the vehicle may not be comfortable if the vehicle stops abruptly. In the case where an obstacle is within the braking distance, the vehicle initiates automatic braking systems for avoiding collision with the obstacle. Automatic braking controls can be used for human-driven cars, as well as for autonomous vehicles. For example, suppose the driver of a car becomes sleepy and he loses his attention while he drives. Then, the driver may not press the brake pedal even if there exists an obstacle in front of the car. In this case, automatic braking controls must be initiated, so that the car can safely stop before hitting the obstacle. Obstacles, such as pedestrians, can be detected using on-board sensors, such as radar or Lidar [2, 3]. Reference [4] proposed the detection of stop signs and calculating the distance, which is essential in controlling the longitudinal velocity. This article thus assumes that sensors on the vehicle can detect obstacles in front of the vehicle. It is also assumed that the vehicle can measure the road condition based on camera sensors [5; 6; 7]. Assuming that the vehicle's inclination relative to the road is zero, the road slope can be measured by installing inertial measurement units (IMU) on the vehicle [8; 9]. In practice, road conditions can change depending on weather conditions, such as rain or snow. If the vehicle stops with the maximum deceleration on a rainy road, then it may slip on the road. Thus, while the vehicle stops, it must decrease its speed gradually such that it does not slip on the road. Furthermore, the vehicle's acceleration must be controlled carefully, in the case where the vehicle moves down on a steep slope. In other words, road slope can have an effect on the braking distance for the vehicle. Hence, the goal of this article is to derive the braking system, while considering both road slope and road conditions, i.e., this article presents the braking controls, so that the vehicle can stop safely and smoothly before it collides with an obstacle, such as other vehicles or pedestrians. Many papers introduces longitudinal control of a vehicle. Considering electric vehicles, Reference [10] tackled the problem of controlling the longitudinal motion of front wheels, while considering the specific case where a single DC motor is used for both front wheels. Reference [11] developed a longitudinal control based on a distributed controller known as cooperative adaptive cruise control (CACC). Reference [12] proposed a reference model-based control approach for automotive longitudinal control. The authors of [13] addressed an automated vehicle guidance strategy with a focus on the longitudinal control. In [13], a non-linear longitudinal control design was proposed considering the throttle, the brake, and the gear ratio. Non-linearity in the power train makes longitudinal control of autonomous vehicles difficult at low speeds. Reference [14] thus designed a longitudinal controller including the reverse plant model of the vehicle to overcome the non-linearity problem. However, longitudinal controls in this paragraph did not consider the fact that the vehicle must decrease its speed gradually depending on both road conditions and road slope, in order not to slip on a road. An ABS system is important for the safety of a vehicle as well as the objects.