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Creating a Car with Wheel Joints

A Simple Car with Wheel Joints

A Simple Car with Wheel Joints

This example shows how to:

The basic workflow of creating a simple car with keyboard control is as follows:

  1. Create car geometry: frame and wheels.
  2. Assign rigid bodies and collision shapes to the frame and just a rigid body to all the wheels.
  3. Set up masses for the wheels and the frame.
    Notice
    Do not use real masses (e.g. 2000 kg for the frame and 10 kg for the wheels), as joints may become unstable! It might be better to use 64 kg for the body and 25 kg for each wheel to provide realistic behavior.
  4. Connect the wheels to the frame using wheel joints. Set up joint parameters.
  5. Enable car movement using joint motors and assign movement control to corresponding keyboard keys.

Creating Geometry and Adding Some Physics#

The first thing we are going to address in this tutorial is the geometry of our car. We are going to create a rectangular car body and four wheels. We are also going to add some physical parameters to the geometry. So, we need two functions:

  • The first one to create a box with specified parameters representing the car body:
Source code (C++)
/// function, creating a car body having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBody(char *name, const vec3& size, float mass, const vec4& color, const Mat4& transform)
{
	// creating a car body and setting up its parameters (name, material and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createBox(size);
	
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameterFloat4("albedo_color", color, 0);
	OMD->setName(name);
	
	// enabling collision detection for the body
	OMD->setCollision(1, 0);

	// adding physics, i.e. a rigid body and a box shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD);
	
	body->addShape(ShapeBox::create(size), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}
  • The second one to create a cylinder with specified parameters representing a wheel:
Source code (C++)
/// function, creating a wheel having a specified size and transformation
/// with a physical body and attaching it to the frame
ObjectMeshDynamicPtr createWheel(NodePtr frame, char *name, float radius, float height, const Mat4& transform)
{
	// creating a wheel, adding it to the frame as a child,
	// and setting up its parameters (name, material and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createCylinder(radius, height, 1, 32);
	frame->addChild(OMD);

	OMD->setTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameterFloat4("albedo_color", vec4_black, 0);
	OMD->setName(name);
	
	// enabling collision detection for the wheel
	OMD->setCollision(1, 0);

	// adding a rigid body 
	BodyRigidPtr body = BodyRigid::create(OMD);

	return OMD;
}

Now, using these functions we can create our car. We are going to use DynamicMesh objects for the frame and four wheels. For a proper mass balance let us set frame mass equal to 64 kg and the mass of each wheel - to 25 kg.

Source code (C++)
// defining DynamicMesh objects for the frame and four wheels
ObjectMeshDynamicPtr car_frame;
ObjectMeshDynamicPtr wheels[4];

// creating car frame
car_frame = createBody("car_frame", vec3(frame_width, frame_length, frame_height), 64.0f, vec4::RED, transform);
	
// creating car wheels
// front left wheel
wheels[0] = createWheel(car_frame, "car_wheel_f_l", wheel_radius, wheel_width, Mat4(translate(-(frame_width + wheel_width) / 2 - delta, frame_length / 2 - wheel_radius,  -frame_height / 2)* rotateY(90.0f)));

// front right wheel
wheels[1] = createWheel(car_frame, "car_wheel_f_r", wheel_radius, wheel_width, Mat4(translate((frame_width + wheel_width) / 2 + delta, frame_length / 2 - wheel_radius, -frame_height / 2)* rotateY(90.0f)));

// rear left wheel
wheels[2] = createWheel(car_frame, "car_wheel_r_l", wheel_radius, wheel_width, Mat4(translate(-(frame_width + wheel_width)/2 - delta,-0.25f * frame_length, -frame_height/2) * rotateY(90.0f)));

// rear right wheel
wheels[3] = createWheel(car_frame, "car_wheel_r_r", wheel_radius, wheel_width, Mat4(translate((frame_width + wheel_width) / 2 + delta, -0.25f * frame_length, -frame_height / 2) * rotateY(90.0f)));

Adding and Setting Up Joints#

Now that we have the frame and four wheels we can attach each wheel to the frame with a wheel joint.

To create a wheel joint we call the JointWheel() constructor and then set necessary parameters:

  1. Rigid body of the car frame
  2. Rigid body of the wheel
  3. Anchor point coordinates (this point is determined by the position(translation) of the wheel relative to the frame)
  4. Coordinates of suspension axis (a vertical axis along which a wheel moves vertically and rotates when steering)
  5. Coordinates of wheel spindle axis (a horizontal around which a wheel rotates when moving forward or backward)
Source code (C++)
for (int i = 0; i < 4; i++)
{
	wheel_joints[i] = JointWheel::create(car_frame->getBodyRigid(), wheels[i]->getBodyRigid());

	// calculating axes and anchor coordinates
	Mat4 wheel_t = wheels[i]->getTransform();
	Vec3 anchor0 = wheel_t.getTranslate();
	Vec3 anchor1 = Vec3_zero;
	vec3 axis00 = vec3_up;
	vec3 axis10 = vec3_right;
	vec3 axis11 = static_cast<vec3>(rotation(wheel_t) * axis10);

	// setting up joint's anchor and axes
	wheel_joints[i]->setAnchor0(anchor0);
	wheel_joints[i]->setAnchor1(anchor1);

	wheel_joints[i]->setAxis00(axis00);
	wheel_joints[i]->setAxis10(axis10);
	wheel_joints[i]->setAxis11(axis11);

	// setting wheel parameters
	wheel_joints[i]->setWheelRadius(wradius);
	wheel_joints[i]->setWheelMass(wmass);

	// setting restitution parameters
	wheel_joints[i]->setLinearRestitution(0.1f);
	wheel_joints[i]->setAngularRestitution(0.1f);

	// setting linear damping and spring rigidity
	wheel_joints[i]->setLinearDamping(400.0f);
	wheel_joints[i]->setLinearSpring(100.0f);

	// setting lower and upper suspension ride limits [-0.15; 0.15]
	wheel_joints[i]->setLinearLimitFrom(-0.15f);
	wheel_joints[i]->setLinearLimitTo(0.15f);
	wheel_joints[i]->setLinearDistance(0.0f);

	// setting number of iterations
	wheel_joints[i]->setNumIterations(8);
}

Using Joint Motors#

So, we have a car, let us make it move now.

To move the car forward or backward we are going to use joint motors of the rear wheels (2 and 3):

  • setting a positive velocity value will move our car forward.
  • setting a negative velocity value will move our car backward.
See the following code:
Source code (C++)
wheel_joints[2]->setAngularVelocity(velocity);
wheel_joints[3]->setAngularVelocity(velocity);
		
wheel_joints[2]->setAngularTorque(torque);
wheel_joints[3]->setAngularTorque(torque);

To steer the car left or right we are going to change Axis10 coordinates of the front wheels (0 and 1) using setAxis10() method:

Source code (C++)
wheel_joints[0]->setAxis10(rotateZ(angle_0).getColumn3(0));
wheel_joints[1]->setAxis10(rotateZ(angle_1).getColumn3(0));

To stop the car we are going to set a high angular damping value for all wheels via setAngularDamping() method:

Source code (C++)
for (int i = 0; i < 4; i++)
	wheel_joints[i]->setAngularDamping(20000.0f);

Adding Keyboard Controls#

To add keyboard control we are going to make a handler for the keys that we need. The handler must be put to the world script update() function to be called for each frame. We are going to update car physics (joint motors) in the updatePhysics() method.

Source code (C++)
int update()
{	
		// forward and backward movement by setting joint motor's velocity and torque
		if(controls->getState(Controls::STATE_FORWARD) || controls->getState(Controls::STATE_TURN_UP)) {
			// TODO: increase velocity by delta
			// set desired torque
		} else if(controls->getState(Controls::STATE_BACKWARD) || controls->getState(Controls::STATE_TURN_DOWN)) {
			// TODO: decrease velocity by delta
			// set desired torque
		} else {
			// TODO: decrease velocity gradually
		}
		
		// clamp velocity value
		velocity = clamp(velocity,-90.0f,90.0f);

		// steering left and right by changing Axis01 for front wheel joints
		if(controls->getState(Controls::STATE_MOVE_LEFT) || controls->getState(Controls::STATE_TURN_LEFT)) {
			// TODO: increase steering angle by some delta
		} else if(controls->getState(Controls::STATE_MOVE_RIGHT) || controls->getState(Controls::STATE_TURN_RIGHT)) {
			// TODO: decrease steering angle
		} else {
			// TODO: return steering angle to zero value gradually
		}

		// clamp steering angle value
		angle = clamp(angle,-30.0f,30.0f);
		
		// TODO: calculate steering angles for front joints (angle_0 and angle_1) 

		// set new Axis10 coordinates for front joints
		wheel_joints[0]->setAxis10(rotateZ(angle_0).getColumn3(0));
		wheel_joints[1]->setAxis10(rotateZ(angle_1).getColumn3(0));
		
		if(controls->getState(Controls::STATE_USE)) {
			// TODO: set a very high angular damping value for all joints
			// set velocity to zero
		} else {
			// TODO: set angular damping value to zero for all joints
		}
	}	
	
	return 1;
}

int updatePhysics()
{
	// set angular velocity for rear joints
	wheel_joints[2]->setAngularVelocity(velocity);
	wheel_joints[3]->setAngularVelocity(velocity);

	// set torque for rear joints		
	wheel_joints[2]->setAngularTorque(torque);
	wheel_joints[3]->setAngularTorque(torque);
		
	return 1;
}

Putting it All Together#

In this section let us sum up all described above and create a new class for our car. The final code for our tutorial will be as follows:

Add a new empty car.h header file to the project, and insert the following code:

Source code (C++)
// car.h

#include "UnigineGame.h"
#include "UnigineEngine.h"
#include "UnigineObjects.h"
#include "UniginePrimitives.h"

/// Car class definition
class Car
{
public:
	// car parameters
	float frame_width;
	float frame_height;
	float frame_length;
	float wheel_radius;
	float wheel_width;

	// initialization of movement parameters
	float angle = 0.0f;
	float velocity = 0.0f;
	float torque = 0.0f;

	Car()	{	}
	~Car()	{	}

	int update();
	int init(float blength, float bwidth, float bheight, float wradius, float wwidth, float wmass, const Unigine::Math::Mat4& transform);
	int updatePhysics();

private:

	// car elements
	Unigine::ObjectMeshDynamicPtr car_frame;
	Unigine::ObjectMeshDynamicPtr wheels[4];
	Unigine::JointWheelPtr wheel_joints[4];
	Unigine::ControlsPtr controls;
};

Add a new empty car.cpp file to the project, and insert the following code:

Source code (C++)
// car.cpp

#include "car.h"
using namespace Unigine;
using namespace Math;

/// function setting up bodies for a wheel joint
void setBodies(JointWheelPtr joint, const BodyRigidPtr &car_body, const BodyRigidPtr &wheel_body)
{
	joint->setBody0(car_body);
	joint->setBody1(wheel_body);

	Mat4 wheel_t = wheel_body->getObject()->getTransform();

	Vec3 anchor0 = wheel_t.getTranslate();
	Vec3 anchor1 = Vec3_zero;

	vec3 axis00 = vec3_up;
	vec3 axis10 = vec3_right;
	vec3 axis11 = static_cast<vec3>(rotation(wheel_t) * axis10);
	
	// setting up joint's anchor and axes
	joint->setAnchor0(anchor0);
	joint->setAnchor1(anchor1);

	joint->setAxis00(axis00);
	joint->setAxis10(axis10);
	joint->setAxis11(axis11);
}

/// function, creating a car body having a specified size, color and transformation with a body and a shape
ObjectMeshDynamicPtr createBody(char *name, const vec3& size, float mass, const vec4& color, const Mat4& transform)
{
	// creating a car body and setting up its parameters (name, material and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createBox(size);
	
	OMD->setWorldTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameterFloat4("albedo_color", color, 0);
	OMD->setName(name);
	
	// enabling collision detection for the frame
	OMD->setCollision(1, 0);

	// adding physics, i.e. a rigid body and a box shape with specified mass
	BodyRigidPtr body = BodyRigid::create(OMD);
	
	body->addShape(ShapeBox::create(size), translate(vec3(0.0f)));
	OMD->getBody()->getShape(0)->setMass(mass);

	return OMD;
}

/// function, creating a wheel having a specified size and transformation
/// with a physical body and attaching it to the frame
ObjectMeshDynamicPtr createWheel(NodePtr frame, char *name, float radius, float height, const Mat4& transform)
{
	// creating a wheel, adding it to the frame as a child,
	// and setting up its parameters (name, material and transformation)
	ObjectMeshDynamicPtr OMD = Primitives::createCylinder(radius, height, 1, 32);
	frame->addChild(OMD);

	OMD->setTransform(transform);
	OMD->setMaterial("mesh_base", "*");
	OMD->setMaterialParameterFloat4("albedo_color", vec4_black, 0);
	OMD->setName(name);
	
	// enabling collision detection for the wheel
	OMD->setCollision(1, 0);

	// adding a rigid body 
	BodyRigidPtr body = BodyRigid::create(OMD);

	return OMD;
}

/// Initializing a car with specified frame and wheel parameters
int Car::init(float blength, float bwidth, float bheight, float wradius, float wwidth, float wmass, const Mat4& transform)
{

	frame_width = bwidth;
	frame_height = bheight;
	frame_length = blength;
	wheel_radius = wradius;
	wheel_width = wwidth;

	float delta = 0.2f;

	car_frame = createBody("car_frame", vec3(frame_width, frame_length, frame_height), 64.0f, vec4::RED, transform);
	
	// initialization of wheels 
	wheels[0] = createWheel(car_frame, "car_wheel_f_l", wheel_radius, wheel_width, Mat4(translate(-(frame_width + wheel_width) / 2 - delta, frame_length / 2 - wheel_radius,  -frame_height / 2)* rotateY(90.0f)));
	wheels[1] = createWheel(car_frame, "car_wheel_f_r", wheel_radius, wheel_width, Mat4(translate((frame_width + wheel_width) / 2 + delta, frame_length / 2 - wheel_radius, -frame_height / 2)* rotateY(90.0f)));

	wheels[2] = createWheel(car_frame, "car_wheel_r_l", wheel_radius, wheel_width, Mat4(translate(-(frame_width + wheel_width)/2 - delta,-0.25f * frame_length, -frame_height/2) * rotateY(90.0f)));
	wheels[3] = createWheel(car_frame, "car_wheel_r_r", wheel_radius, wheel_width, Mat4(translate((frame_width + wheel_width) / 2 + delta, -0.25f * frame_length, -frame_height / 2) * rotateY(90.0f)));

	// initialization of wheel joints
	for (int i = 0; i < 4; i++)
	{
		wheel_joints[i] = JointWheel::create();
		
		// setting bodies and wheel parameters
		setBodies(wheel_joints[i], car_frame->getBodyRigid(), wheels[i]->getBodyRigid());
		wheel_joints[i]->setWheelRadius(wradius);
		wheel_joints[i]->setWheelMass(wmass);

		// setting restitution parameters
		wheel_joints[i]->setLinearRestitution(0.1f);
		wheel_joints[i]->setAngularRestitution(0.1f);

		// setting linear damping and spring rigidity
		wheel_joints[i]->setLinearDamping(400.0f);
		wheel_joints[i]->setLinearSpring(100.0f);

		// setting lower and upper suspension ride limits [-0.15; 0.15]
		wheel_joints[i]->setLinearLimitFrom(-0.15f);
		wheel_joints[i]->setLinearLimitTo(0.15f);
		wheel_joints[i]->setLinearDistance(0.0f);
		// setting number of iterations
		wheel_joints[i]->setNumIterations(8);
	}

	// setting up player and controls
	PlayerPersecutorPtr player = PlayerPersecutor::create();

	player->setFixed(1);
	player->setTarget(car_frame);
	player->setMinDistance(6.0f);
	player->setMaxDistance(11.0f);
	player->setPosition(Vec3(0.0f, -10.0f, 6.0f));
	player->setControlled(0);
	Game::setPlayer(player);
	Game::setEnabled(1);

	controls = player->getControls();

	return 1;
}

/// method updating current car state with a keyboard control handler
int Car::update()
{
	float ifps = Game::getIFps();
	
	// forward and backward movement by setting joint motor's velocity and torque
	if (controls->getState(Controls::STATE_FORWARD) || controls->getState(Controls::STATE_TURN_UP)) 
	{
		velocity = max(velocity, 0.0f);
		velocity += ifps * 50.0f;
		torque = 5.0f;
	}
	else if (controls->getState(Controls::STATE_BACKWARD) || controls->getState(Controls::STATE_TURN_DOWN)) 
	{
		velocity = min(velocity, 0.0f);
		velocity -= ifps * 50.0f;
		torque = 5.0f;
	}
	else 
	{
		velocity *= Math::exp(-ifps);
	}
	velocity = clamp(velocity, -90.0f, 90.0f);

	// steering left and right by changing Axis01 for front wheel joints
	if (controls->getState(Controls::STATE_MOVE_LEFT) || controls->getState(Controls::STATE_TURN_LEFT)) 
		angle += ifps * 100.0f;
	else if (controls->getState(Controls::STATE_MOVE_RIGHT) || controls->getState(Controls::STATE_TURN_RIGHT)) 
		angle -= ifps * 100.0f;
	else 
	{
		if (Math::abs(angle) < 0.25f) angle = 0.0f;
		else angle -= sign(angle) * ifps * 45.0f;
	}
	angle = clamp(angle, -30.0f, 30.0f);

	// calculating steering angles for front joints (angle_0 and angle_1)
	float base = 3.3f;
	float width = 3.0f;
	float angle_0 = angle;
	float angle_1 = angle;
	if (Math::abs(angle) > Consts::EPS)
	{
		float radius = base / Math::tan(angle * Consts::DEG2RAD);
		angle_0 = Math::atan(base / (radius + width / 2.0f)) * Consts::RAD2DEG;
		angle_1 = Math::atan(base / (radius - width / 2.0f)) * Consts::RAD2DEG;
	}

	wheel_joints[0]->setAxis10(rotateZ(angle_0).getColumn3(0));
	wheel_joints[1]->setAxis10(rotateZ(angle_1).getColumn3(0));

	// enabling or disabling a brake
	if (controls->getState(Controls::STATE_USE)) 
	{
		velocity = 0.0f;
		for (int i = 0; i < 4; i++)
			wheel_joints[i]->setAngularDamping(20000.0f);
	}
	else 
	{
		for (int i = 0; i < 4; i++)
			wheel_joints[i]->setAngularDamping(0.0f);
	}
	
	return 1;
}

/// method updating car physics
int Car::updatePhysics()
{
	// set angular velocity for rear joints
	wheel_joints[2]->setAngularVelocity(velocity);
	wheel_joints[3]->setAngularVelocity(velocity);
	
	// set torque for rear joints		
	wheel_joints[2]->setAngularTorque(torque);
	wheel_joints[3]->setAngularTorque(torque);
	
	return 1;
}

In the AppWorldLogic.h file, define our car.

Source code (C++)
// AppWorldLogic.h

/* ... */

#include "car.h"

/* ... */

class AppWorldLogic : public Unigine::WorldLogic {
	
public:
	/* .. */

private:
	Car car;
};

Insert the following code into the AppWorldLogic.cpp file.

Notice
Unchanged methods of the AppWorldLogic class are not listed here, so leave them as they are.
Source code (C++)
// AppWorldLogic.cpp

using namespace Unigine;
using namespace Math;
/* .. */

int AppWorldLogic::init() {
	
	// setting up physics parameters
	Physics::setGravity(vec3(0.0f, 0.0f, -9.8f * 2.0f));
	Physics::setFrozenLinearVelocity(0.1f);
	Physics::setFrozenAngularVelocity(0.1f);
	
	//enabling collision for the ground
	NodePtr ground = World::getNodeByName("ground");
	if (ground)
	{
		checked_ptr_cast<Object>(ground)->setCollision(1, 0);
		checked_ptr_cast<Object>(ground)->setPhysicsIntersection(1, 0);
	}
	
	// initializing our car
	car.init(4.0f, 2.0f, 0.5f, 0.5f, 0.5f, 25.0f, translate(Vec3(0.0f, 0.0f, 2.1f)));

	return 1;
}

int AppWorldLogic::update() {

	//updating our car
	car.update();
	
	return 1;
}

int AppWorldLogic::updatePhysics() {

	// updating car physics
	car.updatePhysics();
	
	return 1;
}

/* .. */
Last update: 2020-06-16