The curvature value of the trajectory output by the MPT algorithm exceeds the limit.

[JokerWhy233]

when i set max_steer_angle in param of MPT algorithm , something wrong . our vehicle max_steer_angle is 0.3755, However ,Using this parameter will result in abnormal algorithm results。

in our vehicle info ：
wheel_base : 5.52
max_steer_angle: 0.3755
curvature_limit_: 14

I am trying to optimize the following trajectory，there are points in the trajectory that exceed the limit，such like index: 71ref_k: -0.143847delta_ref_k: -0.671094 in < input trajectory >

The result of MPT optimization, Uex, did not exceed the limit, but there are many points that happen to be within the limit values such like Uex[50] = -0.3755 in <The result of MPT optimization, Uex: >

However, the trajectory obtained through the function getMPTPoints has many points that exceed the limit value，such like index: 77ref_k: -0.104724delta_ref_k: -0.524142 in

============================================================================
input trajectory ：

index: 1ref_k: -0.0223623delta_ref_k: -0.122819
index: 2ref_k: -0.0186476delta_ref_k: -0.102574
index: 3ref_k: -0.0137021delta_ref_k: -0.075492
index: 4ref_k: -0.00866801delta_ref_k: -0.0478109
index: 5ref_k: -0.00645125delta_ref_k: -0.0355959
index: 6ref_k: -0.00742327delta_ref_k: -0.0409535
index: 7ref_k: -0.0114595delta_ref_k: -0.0631721
index: 8ref_k: -0.0187874delta_ref_k: -0.103337
index: 9ref_k: -0.0285311delta_ref_k: -0.156209
index: 10ref_k: -0.0363998delta_ref_k: -0.198286
index: 11ref_k: -0.0424133delta_ref_k: -0.229979
index: 12ref_k: -0.0467293delta_ref_k: -0.252443
index: 13ref_k: -0.0489783delta_ref_k: -0.264048
index: 14ref_k: -0.049437delta_ref_k: -0.266406
index: 15ref_k: -0.0500547delta_ref_k: -0.269576
index: 16ref_k: -0.0507307delta_ref_k: -0.27304
index: 17ref_k: -0.0513493delta_ref_k: -0.276203
index: 18ref_k: -0.0519787delta_ref_k: -0.279416
index: 19ref_k: -0.052621delta_ref_k: -0.282689
index: 20ref_k: -0.0533015delta_ref_k: -0.286149
index: 21ref_k: -0.0540389delta_ref_k: -0.289892
index: 22ref_k: -0.0548572delta_ref_k: -0.294034
index: 23ref_k: -0.0557585delta_ref_k: -0.298585
index: 24ref_k: -0.0567372delta_ref_k: -0.303513
index: 25ref_k: -0.05779delta_ref_k: -0.308796
index: 26ref_k: -0.0589127delta_ref_k: -0.314411
index: 27ref_k: -0.060098delta_ref_k: -0.320317
index: 28ref_k: -0.0613394delta_ref_k: -0.326477
index: 29ref_k: -0.0626356delta_ref_k: -0.332882
index: 30ref_k: -0.0639178delta_ref_k: -0.339191
index: 31ref_k: -0.0651108delta_ref_k: -0.345034
index: 32ref_k: -0.0661479delta_ref_k: -0.350095
index: 33ref_k: -0.0669573delta_ref_k: -0.354032
index: 34ref_k: -0.0674603delta_ref_k: -0.356472
index: 35ref_k: -0.0677133delta_ref_k: -0.357698
index: 36ref_k: -0.0677878delta_ref_k: -0.358059
index: 37ref_k: -0.067747delta_ref_k: -0.357862
index: 38ref_k: -0.067666delta_ref_k: -0.357469
index: 39ref_k: -0.0676211delta_ref_k: -0.357252
index: 40ref_k: -0.067621delta_ref_k: -0.357251
index: 41ref_k: -0.0676667delta_ref_k: -0.357473
index: 42ref_k: -0.0677608delta_ref_k: -0.357928
index: 43ref_k: -0.0679055delta_ref_k: -0.358629
index: 44ref_k: -0.068078delta_ref_k: -0.359464
index: 45ref_k: -0.0682169delta_ref_k: -0.360135
index: 46ref_k: -0.0682444delta_ref_k: -0.360268
index: 47ref_k: -0.0680911delta_ref_k: -0.359527
index: 48ref_k: -0.0676769delta_ref_k: -0.357522
index: 49ref_k: -0.0669765delta_ref_k: -0.354125
index: 50ref_k: -0.0660417delta_ref_k: -0.349578
index: 51ref_k: -0.06496delta_ref_k: -0.344297
index: 52ref_k: -0.0638094delta_ref_k: -0.338658
index: 53ref_k: -0.0626757delta_ref_k: -0.33308
index: 54ref_k: -0.0616174delta_ref_k: -0.327853
index: 55ref_k: -0.0606536delta_ref_k: -0.323077
index: 56ref_k: -0.0597868delta_ref_k: -0.318768
index: 57ref_k: -0.0590185delta_ref_k: -0.314939
index: 58ref_k: -0.0583578delta_ref_k: -0.311639
index: 59ref_k: -0.057809delta_ref_k: -0.308892
index: 60ref_k: -0.0573188delta_ref_k: -0.306434
index: 61ref_k: -0.057276delta_ref_k: -0.306219
index: 62ref_k: -0.0581956delta_ref_k: -0.310827
index: 63ref_k: -0.0605681delta_ref_k: -0.322653
index: 64ref_k: -0.064963delta_ref_k: -0.344312
index: 65ref_k: -0.0721102delta_ref_k: -0.378823
index: 66ref_k: -0.0819039delta_ref_k: -0.424607
index: 67ref_k: -0.0939499delta_ref_k: -0.47842
index: 68ref_k: -0.108123delta_ref_k: -0.538092
index: 69ref_k: -0.122787delta_ref_k: -0.595659
index: 70ref_k: -0.135352delta_ref_k: -0.64167
index: 71ref_k: -0.143847delta_ref_k: -0.671094
index: 72ref_k: -0.146547delta_ref_k: -0.68017
index: 73ref_k: -0.141379delta_ref_k: -0.662682
index: 74ref_k: -0.128938delta_ref_k: -0.618561
index: 75ref_k: -0.111416delta_ref_k: -0.551388
index: 76ref_k: -0.0907198delta_ref_k: -0.464266
index: 77ref_k: -0.0687805delta_ref_k: -0.362857
index: 78ref_k: -0.0476301delta_ref_k: -0.2571
index: 79ref_k: -0.0277995delta_ref_k: -0.152265
index: 80ref_k: -0.00837091delta_ref_k: -0.0461746
index: 81ref_k: -0.00837091delta_ref_k: -0.0461746
index: 82ref_k: -0.00837091delta_ref_k: -0.0461746

The result of MPT optimization, Uex:
Uex[0] = 0.0154528
Uex[1] = -0.0406416
Uex[2] = -0.0498725
Uex[3] = -0.0911338
Uex[4] = -0.127853
Uex[5] = -0.157029
Uex[6] = -0.178296
Uex[7] = -0.194006
Uex[8] = -0.189243
Uex[9] = -0.138981
Uex[10] = -0.102044
Uex[11] = -0.120173
Uex[12] = -0.152137
Uex[13] = -0.18237
Uex[14] = -0.204703
Uex[15] = -0.218627
Uex[16] = -0.228667
Uex[17] = -0.237592
Uex[18] = -0.246545
Uex[19] = -0.255258
Uex[20] = -0.263492
Uex[21] = -0.27128
Uex[22] = -0.278658
Uex[23] = -0.285611
Uex[24] = -0.291946
Uex[25] = -0.297576
Uex[26] = -0.302529
Uex[27] = -0.306878
Uex[28] = -0.31071
Uex[29] = -0.314088
Uex[30] = -0.317012
Uex[31] = -0.319409
Uex[32] = -0.321294
Uex[33] = -0.322974
Uex[34] = -0.326051
Uex[35] = -0.33064
Uex[36] = -0.334929
Uex[37] = -0.338317
Uex[38] = -0.340605
Uex[39] = -0.341712
Uex[40] = -0.3418
Uex[41] = -0.341004
Uex[42] = -0.339475
Uex[43] = -0.337547
Uex[44] = -0.336203
Uex[45] = -0.337887
Uex[46] = -0.346984
Uex[47] = -0.365915
Uex[48] = -0.3755
Uex[49] = -0.3755
Uex[50] = -0.3755
Uex[51] = -0.3755
Uex[52] = -0.3755
Uex[53] = -0.3755
Uex[54] = -0.3755
Uex[55] = -0.3755
Uex[56] = -0.3755
Uex[57] = -0.3755
Uex[58] = -0.3755
Uex[59] = -0.3755
Uex[60] = -0.3755
Uex[61] = -0.3755
Uex[62] = -0.3755
Uex[63] = -0.3755
Uex[64] = -0.3755
Uex[65] = -0.3755
Uex[66] = -0.3755
Uex[67] = -0.3755
Uex[68] = -0.3755
Uex[69] = -0.3755
Uex[70] = -0.3755
Uex[71] = -0.3755
Uex[72] = -0.321819
Uex[73] = -0.17508
Uex[74] = -0.163766
Uex[75] = -0.222929
Uex[76] = -0.279167
Uex[77] = -0.311037
Uex[78] = -0.312836
Uex[79] = -0.29125
Uex[80] = -0.262125
Uex[81] = -0.239572

=========================================================
MPT output
index: 0ref_k: 0.00488671delta_ref_k: 0.0269681
index: 1ref_k: 0.00488671delta_ref_k: 0.0269681
index: 2ref_k: 0.00488671delta_ref_k: 0.0269681
index: 3ref_k: 0.00488671delta_ref_k: 0.0269681
index: 4ref_k: 0.00488671delta_ref_k: 0.0269681
index: 5ref_k: 0.00488671delta_ref_k: 0.0269681
index: 6ref_k: 0.00488671delta_ref_k: 0.0269681
index: 7ref_k: 0.00230673delta_ref_k: 0.0127324
index: 8ref_k: -0.00056496delta_ref_k: -0.00311857
index: 9ref_k: -0.00348273delta_ref_k: -0.0192223
index: 10ref_k: -0.00637905delta_ref_k: -0.0351978
index: 11ref_k: -0.009351delta_ref_k: -0.0515717
index: 12ref_k: -0.012296delta_ref_k: -0.0677699
index: 13ref_k: -0.0151905delta_ref_k: -0.0836557
index: 14ref_k: -0.0193335delta_ref_k: -0.106318
index: 15ref_k: -0.0236268delta_ref_k: -0.129688
index: 16ref_k: -0.0274843delta_ref_k: -0.150565
index: 17ref_k: -0.031348delta_ref_k: -0.171344
index: 18ref_k: -0.0351356delta_ref_k: -0.19157
index: 19ref_k: -0.0363561delta_ref_k: -0.198055
index: 20ref_k: -0.0369565delta_ref_k: -0.201238
index: 21ref_k: -0.0377212delta_ref_k: -0.205288
index: 22ref_k: -0.0384043delta_ref_k: -0.208899
index: 23ref_k: -0.0390804delta_ref_k: -0.212468
index: 24ref_k: -0.0409813delta_ref_k: -0.222472
index: 25ref_k: -0.0431361delta_ref_k: -0.233758
index: 26ref_k: -0.0451796delta_ref_k: -0.244406
index: 27ref_k: -0.0471151delta_ref_k: -0.254439
index: 28ref_k: -0.0489275delta_ref_k: -0.263786
index: 29ref_k: -0.0506515delta_ref_k: -0.272634
index: 30ref_k: -0.0523244delta_ref_k: -0.281179
index: 31ref_k: -0.0539516delta_ref_k: -0.289449
index: 32ref_k: -0.0555066delta_ref_k: -0.297315
index: 33ref_k: -0.056964delta_ref_k: -0.304652
index: 34ref_k: -0.0583097delta_ref_k: -0.311398
index: 35ref_k: -0.0595355delta_ref_k: -0.317517
index: 36ref_k: -0.0606382delta_ref_k: -0.323001
index: 37ref_k: -0.0616266delta_ref_k: -0.327899
index: 38ref_k: -0.0625258delta_ref_k: -0.332341
index: 39ref_k: -0.0633118delta_ref_k: -0.336212
index: 40ref_k: -0.0639868delta_ref_k: -0.339529
index: 41ref_k: -0.0645735delta_ref_k: -0.342406
index: 42ref_k: -0.0650806delta_ref_k: -0.344887
index: 43ref_k: -0.0654912delta_ref_k: -0.346893
index: 44ref_k: -0.0658842delta_ref_k: -0.34881
index: 45ref_k: -0.0662765delta_ref_k: -0.350721
index: 46ref_k: -0.0666407delta_ref_k: -0.352493
index: 47ref_k: -0.0669517delta_ref_k: -0.354005
index: 48ref_k: -0.0671926delta_ref_k: -0.355174
index: 49ref_k: -0.0673103delta_ref_k: -0.355745
index: 50ref_k: -0.0673208delta_ref_k: -0.355796
index: 51ref_k: -0.0673413delta_ref_k: -0.355895
index: 52ref_k: -0.0675935delta_ref_k: -0.357118
index: 53ref_k: -0.0682376delta_ref_k: -0.360235
index: 54ref_k: -0.0692905delta_ref_k: -0.365315
index: 55ref_k: -0.0706731delta_ref_k: -0.371956
index: 56ref_k: -0.0721902delta_ref_k: -0.379204
index: 57ref_k: -0.0734626delta_ref_k: -0.385251
index: 58ref_k: -0.0742538delta_ref_k: -0.388995
index: 59ref_k: -0.0745882delta_ref_k: -0.390575
index: 60ref_k: -0.0745829delta_ref_k: -0.39055
index: 61ref_k: -0.0743679delta_ref_k: -0.389534
index: 62ref_k: -0.0741518delta_ref_k: -0.388513
index: 63ref_k: -0.0740577delta_ref_k: -0.388068
index: 64ref_k: -0.0740721delta_ref_k: -0.388136
index: 65ref_k: -0.0741485delta_ref_k: -0.388498
index: 66ref_k: -0.0742662delta_ref_k: -0.389054
index: 67ref_k: -0.0744125delta_ref_k: -0.389745
index: 68ref_k: -0.0745213delta_ref_k: -0.390259
index: 69ref_k: -0.074464delta_ref_k: -0.389988
index: 70ref_k: -0.0745644delta_ref_k: -0.390462
index: 71ref_k: -0.0751003delta_ref_k: -0.392989
index: 72ref_k: -0.0763588delta_ref_k: -0.398903
index: 73ref_k: -0.0788delta_ref_k: -0.41029
index: 74ref_k: -0.0830739delta_ref_k: -0.429956
index: 75ref_k: -0.0889543delta_ref_k: -0.456444
index: 76ref_k: -0.0963406delta_ref_k: -0.488763
index: 77ref_k: -0.104724delta_ref_k: -0.524142
index: 78ref_k: -0.110437delta_ref_k: -0.547458
index: 79ref_k: -0.110859delta_ref_k: -0.549153
index: 80ref_k: -0.105673delta_ref_k: -0.528059
index: 81ref_k: -0.0949187delta_ref_k: -0.482624
index: 82ref_k: -0.079578delta_ref_k: -0.413895
index: 83ref_k: -0.0654628delta_ref_k: -0.346754
index: 84ref_k: -0.055117delta_ref_k: -0.295348

[takayuki5168]

@JokerWhy233
You are right. Currently, due to the heavy calculation of MPT, the max steering angle constraint is not applied to MPT.
https://github.com/autowarefoundation/autoware_launch/blob/80a387e10c6a2615d3cb45854fecc5137c5a68f4/autoware_launch/config/planning/scenario_planning/lane_driving/motion_planning/autoware_path_optimizer/path_optimizer.param.yaml#L39-L40

I guess the implementation has some bugs that cause the heavy calculation.