1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
|
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 final double MAX_LEG_ANGLE_DEG = 40.0;
/**
* 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;
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?!";
/**
* At t=0, the body is at x=0; the right foot at x=-1/4 and the left
* foot at x=1/4. During the transition from t=0 to t=1/2, the right
* foot accelerates to x=3/4 while the left foot stays at x=-1/4
* (something has to support the robot while it is moving...).
*/
Point body = new Point(t / 2.0, 1.0);
Point foot_l = new Point(.25, 0.0);
Point foot_r = new Point(.25, 0.0);
double support_dist;
if (supported_by_left) {
foot_r.x = -.25 + t;
foot_r.y = FOOT_MAX_LIFT * sin(t * PI);
support_dist = foot_r.x - body.x;
} else {
foot_l.x = -.25 + t;
foot_l.y = FOOT_MAX_LIFT * sin(t * PI);
support_dist = foot_l.x - body.x;
}
// base the robot body bottom position on the foot that is supporting
// the robot.
body.y = sqrt(1.0 - support_dist * support_dist);
// 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);
// base rotation for legs
leg_angle_right = calcAngle(body, foot_r);
leg_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);
// correct the foot position due to the bent leg
leg_angle_left += cosineRule(legTopLength, dist_leg_l, legBottomLength);
leg_angle_right += cosineRule(legTopLength, dist_leg_r, legBottomLength);
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 0;
}
@Override
public double getArmAngleRight() {
return 0;
}
@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;
}
}
}
|
