Mobility of the Rover

Given we have flat and incline terrain, we need to understand the energy requirements for the rover to move from one point to another.

Force:

We can begin by calculating the force required to traverse the flat terrain and then extend the analysis to incline terrain.

As discussed in Mechanics of Motion

The min force required to move the rover on flat terrain is given by:

\[F_{\text{applied}} > F_{\text{friction}}\]

The minimum force required to move the rover on incline terrain is given by (climb up):

\[F_{\text{applied}} > F_{\text{friction}} + F_{\text{gravity\_component}}\]

The minimum force required to move the rover on incline terrain is given by (climb down):

\[F_{\text{applied}} > F_{\text{friction}} - F_{\text{gravity\_component}}\]

Work Done:

  1. Work done on flat terrain:

    The work done to move the rover on flat terrain is given by:

    \[W_{\text{flat}} = F_{\text{applied}} \cdot d\]
    • where: \(F\_{\text{applied}}\) is the force required to overcome friction and \(( d )\) is the distance traveled.

  2. Work done on flat terrain: a: Climb up

    The work done to move the rover up an incline is given by:

    \[W_{\text{up}} = (F_{\text{friction}} + F_{\text{gravity\_component}}) \cdot d\]

    where:

    • \(F\_{\text{friction}}\) is the force required to overcome friction.
    • \(F\_{\text{gravityComponent}}\) is the component of gravitational force acting along the incline, and d is the distance traveled along the incline.

    b: Climb down

    The work done to move the rover down an incline is given by:

    \[W_{\text{down}} = (F_{\text{friction}} - F_{\text{gravity\_component}}) \cdot d\]

    where:

    • \(F\_{\text{friction}}\) is the force required to overcome friction.
    • \(F\_{\text{gravityComponent}}\) is the component of gravitational force acting along the incline.
    • \(d\) is the distance traveled along the incline.

The total work done to move the rover from one point to another is given by:

\[W_{\text{total}} = W_{\text{flat}} + W_{\text{up}} + W_{\text{down}}\]

Power:

Power requirements: Power is the rate at which work is done. The power required to move the rover is given by:

\[P = \frac{W_{\text{total}}}{t}\]

where:

  • \(W\_{\text{total}}\) is the total work done to move the rover from one point to another.
  • \(t\) is the time taken to move the rover from one point to another.

Energy requirement:

Energy is the capacity to do work. The energy required to move the rover is given by:

\[E = W_{\text{total}}\]

Efficiency: In a real-world setting, the system’s components might show inefficiencies, which can be accounted for by introducing an efficiency factor. The efficiency factor is given by:

\[E_{\text{source}} = \frac{E_{\text{total}}}{\eta}\]

where:

  • \(\eta\) is the efficiency factor of the system.