ilqgames
A new real-time solver for large-scale differential games.
modified_three_player_intersection_example.cpp
1 /*
2  * Copyright (c) 2019, The Regents of the University of California (Regents).
3  * All rights reserved.
4  *
5  * Redistribution and use in source and binary forms, with or without
6  * modification, are permitted provided that the following conditions are
7  * met:
8  *
9  * 1. Redistributions of source code must retain the above copyright
10  * notice, this list of conditions and the following disclaimer.
11  *
12  * 2. Redistributions in binary form must reproduce the above
13  * copyright notice, this list of conditions and the following
14  * disclaimer in the documentation and/or other materials provided
15  * with the distribution.
16  *
17  * 3. Neither the name of the copyright holder nor the names of its
18  * contributors may be used to endorse or promote products derived
19  * from this software without specific prior written permission.
20  *
21  * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
22  * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
24  * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
25  * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
26  * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
27  * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
28  * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
29  * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
30  * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
31  * POSSIBILITY OF SUCH DAMAGE.
32  *
33  * Please contact the author(s) of this library if you have any questions.
34  * Authors: David Fridovich-Keil ( dfk@eecs.berkeley.edu )
35  */
36 
37 ///////////////////////////////////////////////////////////////////////////////
38 //
39 // Three player intersection example. Ordering is given by the following:
40 // (P1, P2, P3) = (Car 1, Car 2, Pedestrian).
41 //
42 ///////////////////////////////////////////////////////////////////////////////
43 
44 #include <ilqgames/cost/curvature_cost.h>
45 #include <ilqgames/cost/final_time_cost.h>
46 #include <ilqgames/cost/locally_convex_proximity_cost.h>
47 #include <ilqgames/cost/nominal_path_length_cost.h>
48 #include <ilqgames/cost/proximity_cost.h>
49 #include <ilqgames/cost/quadratic_cost.h>
50 #include <ilqgames/cost/quadratic_polyline2_cost.h>
51 #include <ilqgames/cost/semiquadratic_cost.h>
52 #include <ilqgames/cost/semiquadratic_polyline2_cost.h>
53 #include <ilqgames/cost/weighted_convex_proximity_cost.h>
54 #include <ilqgames/dynamics/concatenated_dynamical_system.h>
55 #include <ilqgames/dynamics/single_player_car_5d.h>
56 #include <ilqgames/dynamics/single_player_car_6d.h>
57 #include <ilqgames/dynamics/single_player_unicycle_4d.h>
58 #include <ilqgames/examples/modified_three_player_intersection_example.h>
59 #include <ilqgames/geometry/polyline2.h>
60 #include <ilqgames/solver/ilq_solver.h>
61 #include <ilqgames/solver/lq_feedback_solver.h>
62 #include <ilqgames/solver/problem.h>
63 #include <ilqgames/solver/solver_params.h>
64 #include <ilqgames/utils/solver_log.h>
65 #include <ilqgames/utils/strategy.h>
66 #include <ilqgames/utils/types.h>
67 
68 #include <math.h>
69 #include <memory>
70 #include <vector>
71 
72 namespace ilqgames {
73 
74 namespace {
75 
76 // Car inter-axle distance.
77 static constexpr float kInterAxleLength = 4.0; // m
78 
79 // Cost weights.
80 static constexpr float kStateRegularization = 10.0;
81 static constexpr float kControlRegularization = 10.0;
82 
83 static constexpr float kOmegaCostWeight = 0.1;
84 static constexpr float kACostWeight = 0.1;
85 
86 static constexpr float kLaneCostWeight = 25.0;
87 static constexpr float kLaneBoundaryCostWeight = 100.0;
88 
89 static constexpr float kProximityCostWeight = 0.0;
90 static constexpr float kMinProximity = 6.0; // m
91 using ProxCost = ProximityCost;
92 
93 static constexpr bool kOrientedRight = true;
94 
95 // Lane width.
96 static constexpr float kLaneHalfWidth = 2.5; // m
97 
98 // Nominal and max speed.
99 static constexpr float kMaxVCostWeight = 100.0;
100 static constexpr float kP1MaxV = 12.0; // m/s
101 static constexpr float kP2MaxV = 12.0; // m/s
102 static constexpr float kP3MaxV = 2.0; // m/s
103 static constexpr float kMinV = 1.0; // m/s
104 
105 static constexpr float kNominalVCostWeight = 10.0;
106 static constexpr float kP1NominalV = 8.0; // m/s
107 static constexpr float kP2NominalV = 6.0; // m/s
108 static constexpr float kP3NominalV = 1.5; // m/s
109 
110 // Initial state.
111 static constexpr float kP1InitialX = -2.0; // m
112 static constexpr float kP2InitialX = -10.0; // m
113 static constexpr float kP3InitialX = -11.0; // m
114 
115 static constexpr float kP1InitialY = -30.0; // m
116 static constexpr float kP2InitialY = 45.0; // m
117 static constexpr float kP3InitialY = 16.0; // m
118 
119 static constexpr float kP1InitialHeading = M_PI_2; // rad
120 static constexpr float kP2InitialHeading = -M_PI_2; // rad
121 static constexpr float kP3InitialHeading = 0.0; // rad
122 
123 static constexpr float kP1InitialSpeed = 4.0; // m/s
124 static constexpr float kP2InitialSpeed = 3.0; // m/s
125 static constexpr float kP3InitialSpeed = 1.25; // m/s
126 
127 // State dimensions.
128 using P1 = SinglePlayerCar5D;
129 using P2 = SinglePlayerCar5D;
130 using P3 = SinglePlayerUnicycle4D;
131 
132 static const Dimension kP1XIdx = P1::kPxIdx;
133 static const Dimension kP1YIdx = P1::kPyIdx;
134 static const Dimension kP1HeadingIdx = P1::kThetaIdx;
135 static const Dimension kP1PhiIdx = P1::kPhiIdx;
136 static const Dimension kP1VIdx = P1::kVIdx;
137 
138 static const Dimension kP2XIdx = P1::kNumXDims + P2::kPxIdx;
139 static const Dimension kP2YIdx = P1::kNumXDims + P2::kPyIdx;
140 static const Dimension kP2HeadingIdx = P1::kNumXDims + P2::kThetaIdx;
141 static const Dimension kP2PhiIdx = P1::kNumXDims + P2::kPhiIdx;
142 static const Dimension kP2VIdx = P1::kNumXDims + P2::kVIdx;
143 
144 static const Dimension kP3XIdx = P1::kNumXDims + P2::kNumXDims + P3::kPxIdx;
145 static const Dimension kP3YIdx = P1::kNumXDims + P2::kNumXDims + P3::kPyIdx;
146 static const Dimension kP3HeadingIdx =
147  P1::kNumXDims + P2::kNumXDims + P3::kThetaIdx;
148 static const Dimension kP3VIdx = P1::kNumXDims + P2::kNumXDims + P3::kVIdx;
149 
150 // Control dimensions.
151 static const Dimension kP1OmegaIdx = 0;
152 static const Dimension kP1AIdx = 1;
153 static const Dimension kP2OmegaIdx = 0;
154 static const Dimension kP2AIdx = 1;
155 static const Dimension kP3OmegaIdx = 0;
156 static const Dimension kP3AIdx = 1;
157 
158 } // anonymous namespace
159 
160 void ModifiedThreePlayerIntersectionExample::ConstructDynamics() {
161  dynamics_.reset(new ConcatenatedDynamicalSystem(
162  {std::make_shared<P1>(kInterAxleLength),
163  std::make_shared<P2>(kInterAxleLength), std::make_shared<P3>()}));
164 }
165 
166 void ModifiedThreePlayerIntersectionExample::ConstructInitialState() {
167  x0_ = VectorXf::Zero(dynamics_->XDim());
168  x0_(kP1XIdx) = kP1InitialX;
169  x0_(kP1YIdx) = kP1InitialY;
170  x0_(kP1HeadingIdx) = kP1InitialHeading;
171  x0_(kP1VIdx) = kP1InitialSpeed;
172  x0_(kP2XIdx) = kP2InitialX;
173  x0_(kP2YIdx) = kP2InitialY;
174  x0_(kP2HeadingIdx) = kP2InitialHeading;
175  x0_(kP2VIdx) = kP2InitialSpeed;
176  x0_(kP3XIdx) = kP3InitialX;
177  x0_(kP3YIdx) = kP3InitialY;
178  x0_(kP3HeadingIdx) = kP3InitialHeading;
179  x0_(kP3VIdx) = kP3InitialSpeed;
180 }
181 
182 void ModifiedThreePlayerIntersectionExample::ConstructPlayerCosts() {
183  // Set up costs for all players.
184  player_costs_.emplace_back("P1", kStateRegularization,
185  kControlRegularization);
186  player_costs_.emplace_back("P2", kStateRegularization,
187  kControlRegularization);
188  player_costs_.emplace_back("P3", kStateRegularization,
189  kControlRegularization);
190  auto& p1_cost = player_costs_[0];
191  auto& p2_cost = player_costs_[1];
192  auto& p3_cost = player_costs_[2];
193 
194  // Stay in lanes.
195  const Polyline2 lane1(
196  {Point2(kP1InitialX, -1000.0), Point2(kP1InitialX, 1000.0)});
197  const Polyline2 lane2(
198  {Point2(kP2InitialX, 1000.0), Point2(kP2InitialX, 28.0),
199  Point2(kP2InitialX + 0.5, 25.0), Point2(kP2InitialX + 1.0, 24.0),
200  Point2(kP2InitialX + 3.0, 22.5), Point2(kP2InitialX + 6.0, 22.0),
201  Point2(1000.0, 22.0)});
202  const Polyline2 lane3(
203  {Point2(-1000.0, kP3InitialY), Point2(1000.0, kP3InitialY)});
204 
205  const std::shared_ptr<QuadraticPolyline2Cost> p1_lane_cost(
206  new QuadraticPolyline2Cost(kLaneCostWeight, lane1, {kP1XIdx, kP1YIdx},
207  "LaneCenter"));
208  const std::shared_ptr<SemiquadraticPolyline2Cost> p1_lane_r_cost(
209  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
210  {kP1XIdx, kP1YIdx}, kLaneHalfWidth,
211  kOrientedRight, "LaneRightBoundary"));
212  const std::shared_ptr<SemiquadraticPolyline2Cost> p1_lane_l_cost(
213  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
214  {kP1XIdx, kP1YIdx}, -kLaneHalfWidth,
215  !kOrientedRight, "LaneLeftBoundary"));
216  p1_cost.AddStateCost(p1_lane_cost);
217  p1_cost.AddStateCost(p1_lane_r_cost);
218  p1_cost.AddStateCost(p1_lane_l_cost);
219 
220  const std::shared_ptr<QuadraticPolyline2Cost> p2_lane_cost(
221  new QuadraticPolyline2Cost(kLaneCostWeight, lane2, {kP2XIdx, kP2YIdx},
222  "LaneCenter"));
223  const std::shared_ptr<SemiquadraticPolyline2Cost> p2_lane_r_cost(
224  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane2,
225  {kP2XIdx, kP2YIdx}, kLaneHalfWidth,
226  kOrientedRight, "LaneRightBoundary"));
227  const std::shared_ptr<SemiquadraticPolyline2Cost> p2_lane_l_cost(
228  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane2,
229  {kP2XIdx, kP2YIdx}, -kLaneHalfWidth,
230  !kOrientedRight, "LaneLeftBoundary"));
231  p2_cost.AddStateCost(p2_lane_cost);
232  p2_cost.AddStateCost(p2_lane_r_cost);
233  p2_cost.AddStateCost(p2_lane_l_cost);
234 
235  const std::shared_ptr<QuadraticPolyline2Cost> p3_lane_cost(
236  new QuadraticPolyline2Cost(kLaneCostWeight, lane3, {kP3XIdx, kP3YIdx},
237  "LaneCenter"));
238  const std::shared_ptr<SemiquadraticPolyline2Cost> p3_lane_r_cost(
239  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane3,
240  {kP3XIdx, kP3YIdx}, kLaneHalfWidth,
241  kOrientedRight, "LaneRightBoundary"));
242  const std::shared_ptr<SemiquadraticPolyline2Cost> p3_lane_l_cost(
243  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane3,
244  {kP3XIdx, kP3YIdx}, -kLaneHalfWidth,
245  !kOrientedRight, "LaneLeftBoundary"));
246  p3_cost.AddStateCost(p3_lane_cost);
247  p3_cost.AddStateCost(p3_lane_r_cost);
248  p3_cost.AddStateCost(p3_lane_l_cost);
249 
250  // Max/min/nominal speed costs.
251  const auto p1_min_v_cost = std::make_shared<SemiquadraticCost>(
252  kMaxVCostWeight, kP1VIdx, kMinV, !kOrientedRight, "MinV");
253  const auto p1_max_v_cost = std::make_shared<SemiquadraticCost>(
254  kMaxVCostWeight, kP1VIdx, kP1MaxV, kOrientedRight, "MaxV");
255  const auto p1_nominal_v_cost = std::make_shared<QuadraticCost>(
256  kNominalVCostWeight, kP1VIdx, kP1NominalV, "NominalV");
257  p1_cost.AddStateCost(p1_min_v_cost);
258  p1_cost.AddStateCost(p1_max_v_cost);
259  p1_cost.AddStateCost(p1_nominal_v_cost);
260 
261  const auto p2_min_v_cost = std::make_shared<SemiquadraticCost>(
262  kMaxVCostWeight, kP2VIdx, kMinV, !kOrientedRight, "MinV");
263  const auto p2_max_v_cost = std::make_shared<SemiquadraticCost>(
264  kMaxVCostWeight, kP2VIdx, kP2MaxV, kOrientedRight, "MaxV");
265  const auto p2_nominal_v_cost = std::make_shared<QuadraticCost>(
266  kNominalVCostWeight, kP2VIdx, kP2NominalV, "NominalV");
267  p2_cost.AddStateCost(p2_min_v_cost);
268  p2_cost.AddStateCost(p2_max_v_cost);
269  p2_cost.AddStateCost(p2_nominal_v_cost);
270 
271  const auto p3_min_v_cost = std::make_shared<SemiquadraticCost>(
272  kMaxVCostWeight, kP3VIdx, kMinV, !kOrientedRight, "MinV");
273  const auto p3_max_v_cost = std::make_shared<SemiquadraticCost>(
274  kMaxVCostWeight, kP3VIdx, kP3MaxV, kOrientedRight, "MaxV");
275  const auto p3_nominal_v_cost = std::make_shared<QuadraticCost>(
276  kNominalVCostWeight, kP3VIdx, kP3NominalV, "NominalV");
277  p3_cost.AddStateCost(p3_min_v_cost);
278  p3_cost.AddStateCost(p3_max_v_cost);
279  p3_cost.AddStateCost(p3_nominal_v_cost);
280 
281  // Penalize control effort.
282  const auto p1_omega_cost = std::make_shared<QuadraticCost>(
283  kOmegaCostWeight, kP1OmegaIdx, 0.0, "Steering");
284  const auto p1_jerk_cost =
285  std::make_shared<QuadraticCost>(kACostWeight, kP1AIdx, 0.0, "A");
286  p1_cost.AddControlCost(0, p1_omega_cost);
287  p1_cost.AddControlCost(0, p1_jerk_cost);
288 
289  const auto p2_omega_cost = std::make_shared<QuadraticCost>(
290  kOmegaCostWeight, kP2OmegaIdx, 0.0, "Steering");
291  const auto p2_jerk_cost = std::make_shared<QuadraticCost>(
292  kACostWeight, kP2AIdx, 0.0, "Acceleration");
293  p2_cost.AddControlCost(1, p2_omega_cost);
294  p2_cost.AddControlCost(1, p2_jerk_cost);
295 
296  const auto p3_omega_cost = std::make_shared<QuadraticCost>(
297  kOmegaCostWeight, kP3OmegaIdx, 0.0, "Steering");
298  const auto p3_a_cost = std::make_shared<QuadraticCost>(kACostWeight, kP3AIdx,
299  0.0, "Acceleration");
300  p3_cost.AddControlCost(2, p3_omega_cost);
301  p3_cost.AddControlCost(2, p3_a_cost);
302 
303  // Collision-avoidance costs.
304  const std::shared_ptr<ProxCost> p1p2_proximity_cost(
305  new ProxCost(kProximityCostWeight, {kP1XIdx, kP1YIdx}, {kP2XIdx, kP2YIdx},
306  kMinProximity, "ProxCostP2"));
307  const std::shared_ptr<ProxCost> p1p3_proximity_cost(
308  new ProxCost(kProximityCostWeight, {kP1XIdx, kP1YIdx}, {kP3XIdx, kP3YIdx},
309  kMinProximity, "ProxCostP3"));
310  p1_cost.AddStateCost(p1p2_proximity_cost);
311  p1_cost.AddStateCost(p1p3_proximity_cost);
312 
313  const std::shared_ptr<ProxCost> p2p1_proximity_cost(
314  new ProxCost(kProximityCostWeight, {kP2XIdx, kP2YIdx}, {kP1XIdx, kP1YIdx},
315  kMinProximity, "ProxCostP1"));
316  const std::shared_ptr<ProxCost> p2p3_proximity_cost(
317  new ProxCost(kProximityCostWeight, {kP2XIdx, kP2YIdx}, {kP3XIdx, kP3YIdx},
318  kMinProximity, "ProxCostP3"));
319  p2_cost.AddStateCost(p2p1_proximity_cost);
320  p2_cost.AddStateCost(p2p3_proximity_cost);
321 
322  const std::shared_ptr<ProxCost> p3p1_proximity_cost(
323  new ProxCost(kProximityCostWeight, {kP3XIdx, kP3YIdx}, {kP1XIdx, kP1YIdx},
324  kMinProximity, "ProxCostP1"));
325  const std::shared_ptr<ProxCost> p3p2_proximity_cost(
326  new ProxCost(kProximityCostWeight, {kP3XIdx, kP3YIdx}, {kP2XIdx, kP2YIdx},
327  kMinProximity, "ProxCostP2"));
328  p3_cost.AddStateCost(p3p1_proximity_cost);
329  p3_cost.AddStateCost(p3p2_proximity_cost);
330 }
331 
332 inline std::vector<float> ModifiedThreePlayerIntersectionExample::Xs(
333  const VectorXf& x) const {
334  return {x(kP1XIdx), x(kP2XIdx), x(kP3XIdx)};
335 }
336 
337 inline std::vector<float> ModifiedThreePlayerIntersectionExample::Ys(
338  const VectorXf& x) const {
339  return {x(kP1YIdx), x(kP2YIdx), x(kP3YIdx)};
340 }
341 
342 inline std::vector<float> ModifiedThreePlayerIntersectionExample::Thetas(
343  const VectorXf& x) const {
344  return {x(kP1HeadingIdx), x(kP2HeadingIdx), x(kP3HeadingIdx)};
345 }
346 
347 } // namespace ilqgames
Generated by   doxygen 1.8.11