Testing equality of two instances of a class when they are typed as their base class and subclass?

Lets say I have a high level interface IRobot

public interface IRobot
{
    Boolean DoAction(object action);
}

And two classes that implement this interface

public class WalkingRobot : IRobot
{
    public enum WalkAction { SLOW, FAST };
    public new Boolean DoAction(object inAction)
    {
        WalkAction action = (WalkAction)inAction;
        // Does the action based on argument
        return true;
    }
}

public class TalkingRobot : IRobot
{
    public enum TalkAction { ENGLISH, GERMAN };
    public new Boolean DoAction(object inAction)
    {
        TalkAction action = (TalkAction)inAction;
        // Does the action based on argument
        return true;
    }
}

If I then have a List<IRobot> that contain an instance of both of these classes

WalkingRobot walker = new WalkingRobot();
TalkingRobot talker = new TalkingRobot();
List<IRobot> robots = new List<>();
robots.Add(walker);
robots.Add(talker);

Will I be able to iterate over the List<> and compare each IRobot with my instances I have created?

WalkAction wAction = WalkAction.FAST;
TalkAction tAction = TalkAction.ENGLISH;
foreach(IRobot robot in robots)
{
    if(robot == walker)
        robot.DoAction((object)wAction);
    if(robot == talker)
        robot.DoAction((object)tAction);
}