## INTRODUCTION

Spirit and Opportunity (known as MER-A and MER-B) are two twin NASA rover sent to Mars and landed on January, 2004. The expected life was about 90 days, but the real one was much longer: Spirit has remained on the Red Planet more than 6 years (till March 22, 2010), Opportunity is still there.

Mars Science Laboratory (MSL), called Curiosity, is another NASA rover, sent on November 26, 2011, and landed on August 6, 2012. The expected duration of the mission is about 2 years, and the final aim is to investigate the Mars ability to sustain life.

All these rover are based on a particular suspension system called Rocker-Bogie, that permits the rover to go over almost any type of obstacles.

## PROJECT AIM

The aim of this work is to rebuild, through LMS Virtual LAB multibody software, a simple model of an hybrid rover, inspired to the rovers listed before and based on Rocker-Bogie suspension, and to analyze its behavior on road.

## GEOMETRIC MODELING

To realize a realistic model of the rover we use pictures and scheme available on the Web. So the measurements and the proportions give a likely representation of the rovers listed before.

Also the gravity conditions have been considered: the gravity force for the simulations is set to the value of 3,69 m/s^{2}

The MER provides a separate Rocker-Bogie system for the left and right wheels.

Both the Rocker and the Bogie arm consists in an after and a forward part, and these two parts of each arm are made together in order to keep fixed the link.

We use the model “simple tires” to create the six wheels: the wheels are linked to the suspension system through a particular strut. Each of the six wheels has a drive motor, but only the front and the rear wheels are free to steer, the central ones could only go straight.

The chassis has a simple structure and shape: it is fixed to the suspension system by revolute joints.

## SIMULATION

### - ANALYSIS WITH OBSTACLES

To simulate the behavior of the rover we build up a road path with many “obstacles”, in order to get closer to the Mars ground conditions.

We test several behaviors of the MER:

- In the first one we use constrains on each wheel by a position driver ruled by a polynomial function. In this function we set a velocity of 10 turn/min.
- In the second one we apply a 16 N/m torque value on each wheel.

Is interesting to analyze the difference between these two settings: both of them let the Rover to go through the obstacles, even if we changed the idea with which the wheels are set in motion.

The pictures below represent the forces on the tires (Picture 5) and on the chassis (Picture 6):

In this figure, we can see the behavior of the rover when it is on an obstacle and when it is on a flat road.

The blue line represents the normal force, the red one the longitudinal force and the green one the lateral force. As expected, the lateral force remain nearly zero for all the simulation, except for some low vibrations.

When the rover go through the flat part the forces remain constant.

This figure represents the force that acts on the chassis. The picture evidences some low vibration around a constant value.

### - ROTATIONAL MOVEMENT ANALYSIS

We make another analysis in which the rover could rotates on itself.

In this case, there is also a non-zero lateral force on the wheels, as we can see in the following picture (the lateral force is represented with the blue line).

### - FINAL ANALYSIS

In this case the solution includes an obstacles path road (Picture 8), a steering system and a Matlab based control.

Because of the complexity of the model, the graphs are not so smooth as the previous ones.

Below, we report the graphs related to the tire forces and the forces on the chassis.

The following link refers to a video that shows the three different types of analysis described before. Mars Rover

### - STABILITY ANALYSIS

To realize a stability analysis we enable the linearization and set the following parameters:

– Eigenvalues = “True”;

– Perturbation factor = 10^{-6};

– Print interval = 1 s .

This analysis is made with the rover going through a flat and straight road.

In this condition we should not have any instability. However, the picture below shows that the second and the third mode are instable (the real part of the eigenvalues is positive) due to numerical errors.

## MATLAB SIMULATION: THE CONTROL SYSTEM

The model can also be controlled from a Matlab Simulink scheme.

We use a simple control scheme, based on velocity feedback and the PID block.

We give a speed reference using a ramp and a saturation block with the upper limit set to 0.2. This low limit is justified by the data relating to the actual speed of the rover.

The “plantout” block is the result of the LMS simulation. The block output is the forward speed of the rover and corresponds to the Input Control Node “Forward Speed” defined in the model; the block input is the torque applied to the wheels and corresponds to the Output Control Node “Torque” defined in the model.

The feedback loop permits to compare the target speed with the actual speed of the rover.

The PID block is set with the following parameters:

• proportional (P): 500

• integral (I): 200

• derivative (D): 1

With a derivative block, we get the target acceleration and then we obtain the force by multiplying the acceleration with the mass of the rover. Finally a velocity ratio coefficient gives the torque applied to the wheels.

A scope permits to directly compare the target and the actual behavior of the rover model.

## CONCLUSIONS

The obtained model gives a realistic representation of the behavior of a Mars Rover in a variety of situations: on flat roads, on obstacles path road, with steer. The fundamental elements for a likely analysis are been considered, developed and studied. The control systems for the model are plenty for the aim of our study, for the verification of the rover and the suspension system behavior and for realize a realistic simulation.

Anyway, some improvements could be realized. For example, it could be developed a full detailed model, with more sophisticated motion laws or control system (even in LMS simulation or in Matlab scheme). Moreover, a vibration control system could be implemented.