velocityprofiletest.cpp
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1 #include "velocityprofiletest.hpp"
2 #include <frames_io.hpp>
3 CPPUNIT_TEST_SUITE_REGISTRATION( VelocityProfileTest );
4 
5 using namespace KDL;
6 
7 void VelocityProfileTest::setUp()
8 {
9 }
10 
11 void VelocityProfileTest::tearDown()
12 {
13 }
14 
15 void VelocityProfileTest::TestTrap_MaxVelocity1()
16 {
17  // 2 second ramp up (cover 2 distance),
18  // 2 second flat velocity (cover 4 distance)
19  // 2 second ramp down (cover 2 distance),
20  VelocityProfile_Trap v(2, 1);
21  double time;
22  v.SetProfile(2, 10);
23  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Duration(),epsilon);
24 
25  // start
26  time = 0;
27  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
28  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
29  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Acc(time),epsilon);
30 
31  // end of ramp up
32  time = 2;
33  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Pos(time),epsilon);
34  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
35  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
36 
37  // middle of flat velocity
38  time = 3;
39  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Pos(time),epsilon);
40  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
41  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
42 
43  // end of flat velocity
44  time = 4;
45  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
46  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
47  CPPUNIT_ASSERT_DOUBLES_EQUAL(-1.0, v.Acc(time),epsilon);
48 
49  // middle of ramp down
50  time = 5;
51  CPPUNIT_ASSERT_DOUBLES_EQUAL(9.5, v.Pos(time),epsilon);
52  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Vel(time),epsilon);
53  CPPUNIT_ASSERT_DOUBLES_EQUAL(-1.0, v.Acc(time),epsilon);
54 
55  // end
56  time = 6;
57  CPPUNIT_ASSERT_DOUBLES_EQUAL(10.0, v.Pos(time),epsilon);
58  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
59  CPPUNIT_ASSERT_DOUBLES_EQUAL(-1.0, v.Acc(time),epsilon);
60 
61  // fenceposts - before and after
62  time = -1;
63  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
64  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
65  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
66  time = 11;
67  CPPUNIT_ASSERT_DOUBLES_EQUAL(10.0, v.Pos(time),epsilon);
68  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
69  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
70 }
71 
72 void VelocityProfileTest::TestTrap_MaxVelocity2()
73 {
74  // 2 second ramp up (cover -2 distance),
75  // 2 second flat velocity (cover -4 distance)
76  // 2 second ramp down (cover -2 distance),
77  VelocityProfile_Trap v(2, 1);
78  v.SetProfile(2, -6);
79  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Duration(),epsilon);
80 }
81 
82 void VelocityProfileTest::TestTrap_MaxVelocity3()
83 {
84  // 2 second ramp up (cover 4 distance),
85  // 0 second flat velocity (cover 0 distance)
86  // 2 second ramp down (cover 4 distance),
87  VelocityProfile_Trap v(4, 2);
88  v.SetProfile(2, 10);
89  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Duration(),epsilon);
90 
91  // new profile
92  v.SetProfile(2, -6);
93  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Duration(),epsilon);
94 
95  // another new profile : ramp + 2 sec + ramp
96  v.SetProfile(13, 13 + 4 + 8 + 4);
97  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Duration(),epsilon);
98 }
99 
100 void VelocityProfileTest::TestTrap_SetDuration1()
101 {
102  // same as first max velocity test, but twice as
103  // long (max velocity gives 6 seconds)
104  VelocityProfile_Trap v(2, 1);
105  double time;
106  v.SetProfileDuration(2, 10, 12.0);
107  CPPUNIT_ASSERT_DOUBLES_EQUAL(12.0, v.Duration(),epsilon);
108 
109  // start
110  time = 0;
111  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
112  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
113  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.25, v.Acc(time),epsilon);
114 
115  // end of ramp up
116  time = 4;
117  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Pos(time),epsilon);
118  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Vel(time),epsilon);
119  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
120 
121  // middle of flat velocity
122  time = 6;
123  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Pos(time),epsilon);
124  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Vel(time),epsilon);
125  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
126 
127  // end of flat velocity
128  time = 8;
129  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
130  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Vel(time),epsilon);
131  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.25, v.Acc(time),epsilon);
132 
133  // middle of ramp down
134  time = 10;
135  CPPUNIT_ASSERT_DOUBLES_EQUAL(9.5, v.Pos(time),epsilon);
136  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.5, v.Vel(time),epsilon);
137  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.25, v.Acc(time),epsilon);
138 
139  // end
140  time = 12;
141  CPPUNIT_ASSERT_DOUBLES_EQUAL(10.0, v.Pos(time),epsilon);
142  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
143  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.25, v.Acc(time),epsilon);
144 }
145 
146 void VelocityProfileTest::TestTrapHalf_SetProfile_Start()
147 {
148  // 2 second ramp up (cover 2 distance),
149  // 2 second flat velocity (cover 4 distance)
150  VelocityProfile_TrapHalf v(2, 1, true);
151  double time;
152  v.SetProfile(2, 2+6);
153  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Duration(),epsilon);
154 
155  // start
156  time = 0;
157  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
158  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
159  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Acc(time),epsilon);
160 
161  // end of ramp up
162  time = 2;
163  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Pos(time),epsilon);
164  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
165  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
166 
167  // middle of flat velocity
168  time = 3;
169  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.0, v.Pos(time),epsilon);
170  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
171  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
172 
173  // end
174  time = 4;
175  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
176  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
177  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
178 
179  // fenceposts - before and after
180  time = -1;
181  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
182  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
183  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
184  time = 5;
185  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
186  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
187  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
188 }
189 
190 void VelocityProfileTest::TestTrapHalf_SetProfile_End()
191 {
192  // 2 second flat velocity (cover 4 distance)
193  // 2 second ramp up (cover 2 distance),
194  VelocityProfile_TrapHalf v(2, 1, false);
195  double time;
196  v.SetProfile(9, 9-6);
197  CPPUNIT_ASSERT_DOUBLES_EQUAL(4.0, v.Duration(),epsilon);
198 
199  // start - flat velocity
200  time = 0;
201  CPPUNIT_ASSERT_DOUBLES_EQUAL(9.0, v.Pos(time),epsilon);
202  CPPUNIT_ASSERT_DOUBLES_EQUAL(-2.0, v.Vel(time),epsilon);
203  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
204 
205  // end of flat velocity
206  time = 2;
207  CPPUNIT_ASSERT_DOUBLES_EQUAL(5.0, v.Pos(time),epsilon);
208  CPPUNIT_ASSERT_DOUBLES_EQUAL(-2.0, v.Vel(time),epsilon);
209  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Acc(time),epsilon);
210 
211  // middle of ramp down
212  time = 3;
213  CPPUNIT_ASSERT_DOUBLES_EQUAL(3.5, v.Pos(time),epsilon);
214  CPPUNIT_ASSERT_DOUBLES_EQUAL(-1.0, v.Vel(time),epsilon);
215  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Acc(time),epsilon);
216 
217  // end
218  time = 4;
219  CPPUNIT_ASSERT_DOUBLES_EQUAL(3.0, v.Pos(time),epsilon);
220  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
221  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
222 
223  // fenceposts - before and after
224  time = -1;
225  CPPUNIT_ASSERT_DOUBLES_EQUAL(9.0, v.Pos(time),epsilon);
226  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
227  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
228  time = 5;
229  CPPUNIT_ASSERT_DOUBLES_EQUAL(3.0, v.Pos(time),epsilon);
230  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
231  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
232 }
233 
234 void VelocityProfileTest::TestTrapHalf_SetDuration_Start()
235 {
236  // same as TestTrapHalf__SetProfile_Start() but twice as slow
237  // Lingers at start position with zero velocity for a period of time,
238  // as does not scale the velocity; only scales the acceleration!?
239  VelocityProfile_TrapHalf v(2, 1, true);
240  double time;
241  v.SetProfileDuration(2, 2+6, 8);
242  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Duration(),epsilon);
243 
244  // start - no motion
245  time = 0;
246  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
247  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
248  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
249 
250  // no motion
251  time = 1.9;
252  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
253  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
254  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
255 
256  // begin ramp at scaled acceleration
257  time = 2;
258  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time), 0.001);
259  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
260  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.333, v.Acc(time), 0.001);
261 
262  // middle of ramp up
263  time = 5;
264  CPPUNIT_ASSERT_DOUBLES_EQUAL(3.5, v.Pos(time), 0.001);
265  CPPUNIT_ASSERT_DOUBLES_EQUAL(1.0, v.Vel(time), 0.001);
266  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.3333, v.Acc(time), 0.001);
267 
268  // end - continue with given velocity
269  time = 8;
270  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
271  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Vel(time),epsilon);
272  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
273 
274  // fenceposts - before and after
275  time = -1;
276  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
277  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
278  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
279  time = 9;
280  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
281  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
282  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
283 
284 }
285 
286 void VelocityProfileTest::TestTrapHalf_SetDuration_End()
287 {
288  // same as TestTrapHalf__SetProfile_Start() but twice as slow
289  // Lingers at start position with zero velocity for a period of time,
290  // as does not scale the velocity; only scales the acceleration!?
291  VelocityProfile_TrapHalf v(2, 1, true);
292  double time;
293  v.SetProfileDuration(2+6, 2, 8);
294  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Duration(),epsilon);
295 
296  // start - no motion
297  time = 0;
298  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
299  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
300  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
301 
302  // no motion
303  time = 1.9;
304  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
305  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
306  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
307 
308  // begin ramp at scaled acceleration
309  time = 2;
310  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time), 0.001);// WRONG, backwards!
311  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
312  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.333, v.Acc(time), 0.001);
313 
314  // middle of ramp up
315  time = 5;
316  CPPUNIT_ASSERT_DOUBLES_EQUAL(6.5, v.Pos(time), 0.001);
317  CPPUNIT_ASSERT_DOUBLES_EQUAL(-1.0, v.Vel(time), 0.001);
318  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.3333, v.Acc(time), 0.001);
319 
320  // end - continue with given velocity
321  time = 8;
322  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
323  CPPUNIT_ASSERT_DOUBLES_EQUAL(-2.0, v.Vel(time),epsilon);
324  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
325 
326  // fenceposts - before and after
327  time = -1;
328  CPPUNIT_ASSERT_DOUBLES_EQUAL(8.0, v.Pos(time),epsilon);
329  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
330  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
331  time = 9;
332  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.0, v.Pos(time),epsilon);
333  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Vel(time),epsilon);
334  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, v.Acc(time),epsilon);
335 
336 }
337 
338 void VelocityProfileTest::TestDirac_SetProfile()
339 {
340  double time;
341  double pos1 = 10.0;
342  double pos2 = -1.0;
343 
344  VelocityProfile_Dirac v;
345  v.SetProfile(pos1, pos2);
346 
347  time = 0;
348  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos1, v.Pos(time), epsilon);
349 
350  time = 1.0;
351  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos2, v.Pos(time), epsilon);
352 
353  time = -1.0;
354  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos1, v.Pos(time), epsilon);
355 }
356 
357 void VelocityProfileTest::TestDirac_SetProfileDuration()
358 {
359  double time;
360  double pos1 = 10.0;
361  double pos2 = -1.0;
362  double duration = 5.0;
363  VelocityProfile_Dirac v;
364  v.SetProfileDuration(pos1, pos2, duration);
365 
366  time = -1.0;
367  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos1, v.Pos(time), epsilon);
368 
369  time = duration/2;
370  CPPUNIT_ASSERT_DOUBLES_EQUAL((pos1 + pos2)/2, v.Pos(time), epsilon);
371  CPPUNIT_ASSERT_DOUBLES_EQUAL((pos2-pos1)/duration, v.Vel(time), epsilon);
372 
373  time = duration;
374  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos2, v.Pos(time), epsilon);
375 
376  time = duration + 1.0;
377  CPPUNIT_ASSERT_DOUBLES_EQUAL(pos2, v.Pos(time), epsilon);
378 }
KDL::VelocityProfile_TrapHalf::Pos
virtual double Pos(double time) const
Definition: velocityprofile_traphalf.cpp:144
KDL::VelocityProfile_Trap::Vel
virtual double Vel(double time) const
Definition: velocityprofile_trap.cpp:152
KDL::VelocityProfile_TrapHalf::Duration
virtual double Duration() const
Definition: velocityprofile_traphalf.cpp:140
KDL::VelocityProfile_Trap::Pos
virtual double Pos(double time) const
Definition: velocityprofile_trap.cpp:139
KDL::VelocityProfile_Trap
Definition: velocityprofile_trap.hpp:60
frames_io.hpp
KDL::VelocityProfile_Dirac::Vel
virtual double Vel(double time) const
Definition: velocityprofile_dirac.cpp:67
KDL::VelocityProfile_Dirac::SetProfile
void SetProfile(double pos1, double pos2)
Definition: velocityprofile_dirac.cpp:34
KDL::VelocityProfile_Trap::SetProfileDuration
virtual void SetProfileDuration(double pos1, double pos2, double newduration)
Definition: velocityprofile_trap.cpp:91
KDL::VelocityProfile_Dirac::Pos
virtual double Pos(double time) const
Definition: velocityprofile_dirac.cpp:55
KDL::epsilon
double epsilon
default precision while comparing with Equal(..,..) functions. Initialized at 0.0000001.
KDL::VelocityProfile_TrapHalf::Acc
virtual double Acc(double time) const
Definition: velocityprofile_traphalf.cpp:171
KDL::VelocityProfile_TrapHalf
Definition: velocityprofile_traphalf.hpp:63
KDL::VelocityProfile_Dirac::SetProfileDuration
virtual void SetProfileDuration(double pos1, double pos2, double duration)
Definition: velocityprofile_dirac.cpp:45
KDL::VelocityProfile_Trap::Acc
virtual double Acc(double time) const
Definition: velocityprofile_trap.cpp:166
KDL::VelocityProfile_TrapHalf::SetProfile
virtual void SetProfile(double pos1, double pos2)
Definition: velocityprofile_traphalf.cpp:82
KDL::VelocityProfile_TrapHalf::Vel
virtual double Vel(double time) const
Definition: velocityprofile_traphalf.cpp:157
CPPUNIT_TEST_SUITE_REGISTRATION
CPPUNIT_TEST_SUITE_REGISTRATION(VelocityProfileTest)
KDL::VelocityProfile_Trap::Duration
virtual double Duration() const
Definition: velocityprofile_trap.cpp:135
KDL::VelocityProfile_Trap::SetProfile
virtual void SetProfile(double pos1, double pos2)
Definition: velocityprofile_trap.cpp:61
KDL::VelocityProfile_TrapHalf::SetProfileDuration
virtual void SetProfileDuration(double pos1, double pos2, double newduration)
Definition: velocityprofile_traphalf.cpp:100
KDL::VelocityProfile_Dirac
Definition: velocityprofile_dirac.hpp:48

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autogenerated on Sat Jun 15 2019 19:07:36