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import static java.lang.Math.*;
/**
* A WalkAnimation that tries to be a bit more natural than the
* DumbWalkAnimation. It does so by making the foot follow a sine curve, from
* which the knee angles are also derived.
*
* @author Peter Wu
*/
public class SmarterWalkAnimation implements WalkAnimation {
/**
* Length of the upper leg from the groin to the knee.
*/
private final float legTopLength;
/**
* Length of the lower leg from knee to the floor.
*/
private final float legBottomLength;
/**
* Total length of the leg.
*/
private final double legLength;
private final double cycleLength;
private static final double MAX_LEG_ANGLE_DEG = 40.0;
private static final double MAX_ARM_ANGLE_DEG = 30.0;
/**
* Maximum percentage of the legs length to lift the feet.
*/
private static final double FOOT_MAX_LIFT = .20;
/**
* Angles in radians.
*/
private double leg_angle_left;
private double leg_angle_right;
private double knee_angle_left;
private double knee_angle_right;
private double bodyOffset;
private double arm_angle_left;
private double arm_angle_right;
SmarterWalkAnimation(float legTopLength, float legBottomLength) {
this.legTopLength = legTopLength;
this.legBottomLength = legBottomLength;
this.legLength = legTopLength + legBottomLength;
double maxLegAngle = MAX_LEG_ANGLE_DEG * PI / 180;
// single step = sin(maxLegAngle) * legsLength
cycleLength = 2 * sin(maxLegAngle) * (legTopLength + legBottomLength);
System.err.println("Cycle length (2 steps): " + cycleLength + " meter");
}
@Override
public void updatePosition(double pos) {
// adjust speed
pos /= cycleLength;
// whether the robot touches the ground with its left foot
boolean supported_by_left = pos % 2.0 <= 1.0;
double t = pos % 1.0;
assert t >= 0.0 : "Time went negative?!";
// The animation is modeled with a transition from t=0 to t=2.
// (Actually, the period t=0 to t=1 and t=1 to t=2 have the same
// transitions, but with the Right foot and Left foot swapped.)
// Picture of half a cycle (t=0.5 to t=1.0 is similar, swapping L and R):
// t= 0 0.5
// = =
// R L L R
// R L L R
// = = =
// A B C
//
// In this picture, the left foot stays at position B ("t=0.25") while
// the right foot moves from point A ("t=-1/4") to point C ("t=0.75").
// As you may have noticed, the body moves twice as slow as the foot.
// (hence body.x=t/2 below). The coordinates of body, foot_l and foot_r
// are in unit length (0.0 to 1.0). The body y position has yet to be
// determined, but assume that it is located near y=1.
Point body = new Point(t / 2.0, 1.0);
Point foot_l, foot_r;
Point supporting_foot = new Point(.25, 0.0);
Point moving_foot = new Point(-.25 + t,
FOOT_MAX_LIFT * sin(t * PI));
// Use Pythagoras to calculate the body bottom position from the
// leg length (1.0) and body to foot distance
body.y = sqrt(1.0 - pow(body.x - supporting_foot.x, 2));
if (supported_by_left) {
// supported by left, so the right foot is moving.
foot_l = supporting_foot;
foot_r = moving_foot;
} else {
foot_r = supporting_foot;
foot_l = moving_foot;
}
// distance between a bent leg and the body
double dist_leg_r, dist_leg_l;
dist_leg_l = legLength * distance(body, foot_l);
dist_leg_r = legLength * distance(body, foot_r);
double foot_angle_right, foot_angle_left;
// base rotation for legs
foot_angle_right = calcAngle(body, foot_r);
foot_angle_left = calcAngle(body, foot_l);
// bend the knees
knee_angle_right = cosineRule(legTopLength, legBottomLength, dist_leg_r);
knee_angle_left = cosineRule(legTopLength, legBottomLength, dist_leg_l);
// calculate leg rotations (and consider the bent knee to fit the foot
// above the floor)
leg_angle_left = foot_angle_left;
leg_angle_right = foot_angle_right;
leg_angle_left += cosineRule(legTopLength, dist_leg_l, legBottomLength);
leg_angle_right += cosineRule(legTopLength, dist_leg_r, legBottomLength);
// to balance the robot, rotate the arms in the opposite direction.
arm_angle_left = -foot_angle_left;
arm_angle_right = -foot_angle_right;
bodyOffset = legLength * body.y;
}
@Override
public double getLegAngleLeft() {
return leg_angle_left * 180 / PI;
}
@Override
public double getLegAngleRight() {
return leg_angle_right * 180 / PI;
}
@Override
public double getKneeAngleLeft() {
return knee_angle_left * 180 / PI;
}
@Override
public double getKneeAngleRight() {
return knee_angle_right * 180 / PI;
}
@Override
public double getArmAngleLeft() {
return arm_angle_left * 180 / PI;
}
@Override
public double getArmAngleRight() {
return arm_angle_right * 180 / PI;
}
@Override
public double getBottomOffset() {
return bodyOffset;
}
/*-
* Given a trangle:
* y| a a
* | / | | \
* | /___| |___\
* | b (c) (c) b
* -+------------------- x
* calculate angle a for length bc and ac. In the left case, the
* returned angle (in radians) is negative.
*/
private static double calcAngle(Point a, Point b) {
double ac = a.y - b.y;
double cb = b.x - a.x;
return atan(cb / ac);
}
/**
* Calculates the distance between two points.
*/
private static double distance(Point a, Point b) {
double side1 = a.x - b.x;
double side2 = a.y - b.y;
return sqrt(side1 * side1 + side2 * side2);
}
/**
* Given a triangle with sides a, b and c, calculate the angle opposite to
* side c.
*
* @return Angle opposed to side c in radians.
*/
private static double cosineRule(double a, double b, double c) {
// cosine rule: angle c = arccos( (aa + bb - cc) / 2ab )
return acos(((a * a) + (b * b) - (c * c)) / (2 * a * b));
}
private class Point {
private double x;
private double y;
Point(double x, double y) {
this.x = x;
this.y = y;
}
}
}
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