ilqgames
A new real-time solver for large-scale differential games.
three_player_flat_overtaking_example.cpp
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34  * Authors: David Fridovich-Keil ( dfk@eecs.berkeley.edu )
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36 
37 ///////////////////////////////////////////////////////////////////////////////
38 //
39 // Three player *flat* overtaking 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_norm_cost.h>
51 #include <ilqgames/cost/quadratic_polyline2_cost.h>
52 #include <ilqgames/cost/route_progress_cost.h>
53 #include <ilqgames/cost/semiquadratic_cost.h>
54 #include <ilqgames/cost/semiquadratic_norm_cost.h>
55 #include <ilqgames/cost/semiquadratic_polyline2_cost.h>
56 #include <ilqgames/dynamics/concatenated_flat_system.h>
57 #include <ilqgames/dynamics/single_player_flat_car_6d.h>
58 #include <ilqgames/dynamics/single_player_flat_unicycle_4d.h>
59 #include <ilqgames/examples/three_player_flat_overtaking_example.h>
60 #include <ilqgames/geometry/polyline2.h>
61 #include <ilqgames/solver/problem.h>
62 #include <ilqgames/utils/solver_log.h>
63 #include <ilqgames/utils/strategy.h>
64 #include <ilqgames/utils/types.h>
65 
66 #include <math.h>
67 #include <memory>
68 #include <vector>
69 
70 namespace ilqgames {
71 
72 namespace {
73 
74 // Car inter-axle distance.
75 static constexpr float kInterAxleLength = 4.0; // m
76 
77 // Cost weights.
78 static constexpr float kCarAuxCostWeight = 5000.0;
79 
80 static constexpr float kP1NominalVCostWeight = 10.0;
81 static constexpr float kP2NominalVCostWeight = 1.0;
82 static constexpr float kP3NominalVCostWeight = 1.0;
83 
84 static constexpr float kLaneCostWeight = 25.0;
85 static constexpr float kLaneBoundaryCostWeight = 100.0;
86 
87 static constexpr float kMinProximity = 5.0;
88 static constexpr float kP1ProximityCostWeight = 100.0;
89 static constexpr float kP2ProximityCostWeight = 100.0;
90 static constexpr float kP3ProximityCostWeight = 100.0;
91 using ProxCost = ProximityCost;
92 
93 // Heading weight
94 static constexpr float kNominalHeadingCostWeight = 150.0;
95 
96 static constexpr bool kOrientedRight = true;
97 
98 // Lane width.
99 static constexpr float kLaneHalfWidth = 2.5; // m
100 
101 // Nominal speeds.
102 static constexpr float kP1NominalV = 15.0; // m/s
103 static constexpr float kP2NominalV = 10.0; // m/s
104 static constexpr float kP3NominalV = 10.0; // m/s
105 
106 // Nominal heading
107 static constexpr float kP1NominalHeading = M_PI_2; // rad
108 
109 // Initial state.
110 static constexpr float kP1InitialX = 2.5; // m
111 static constexpr float kP1InitialY = -10.0; // m
112 
113 static constexpr float kP2InitialX = -1.0; // m
114 static constexpr float kP2InitialY = -10.0; // m
115 
116 static constexpr float kP3InitialX = 2.5; // m
117 static constexpr float kP3InitialY = 10.0; // 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 = M_PI_2; // rad
122 
123 static constexpr float kP1InitialSpeed = 5.0; // m/s
124 static constexpr float kP2InitialSpeed = 5.0; // m/s
125 static constexpr float kP3InitialSpeed = 5.25; // m/s
126 
127 // State dimensions.
128 using P1 = SinglePlayerFlatCar6D;
129 using P2 = SinglePlayerFlatCar6D;
130 using P3 = SinglePlayerFlatCar6D;
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 static const Dimension kP1AIdx = P1::kAIdx;
138 static const Dimension kP1VxIdx = P1::kVxIdx;
139 static const Dimension kP1VyIdx = P1::kVyIdx;
140 static const Dimension kP1AxIdx = P1::kAxIdx;
141 static const Dimension kP1AyIdx = P1::kAyIdx;
142 
143 static const Dimension kP2XIdx = P1::kNumXDims + P2::kPxIdx;
144 static const Dimension kP2YIdx = P1::kNumXDims + P2::kPyIdx;
145 static const Dimension kP2HeadingIdx = P1::kNumXDims + P2::kThetaIdx;
146 static const Dimension kP2PhiIdx = P1::kNumXDims + P2::kPhiIdx;
147 static const Dimension kP2VIdx = P1::kNumXDims + P2::kVIdx;
148 static const Dimension kP2AIdx = P1::kNumXDims + P2::kAIdx;
149 static const Dimension kP2VxIdx = P1::kNumXDims + P2::kVxIdx;
150 static const Dimension kP2VyIdx = P1::kNumXDims + P2::kVyIdx;
151 static const Dimension kP2AxIdx = P1::kNumXDims + P2::kAxIdx;
152 static const Dimension kP2AyIdx = P1::kNumXDims + P2::kAyIdx;
153 
154 static const Dimension kP3XIdx = P1::kNumXDims + P2::kNumXDims + P3::kPxIdx;
155 static const Dimension kP3YIdx = P1::kNumXDims + P2::kNumXDims + P3::kPyIdx;
156 static const Dimension kP3HeadingIdx =
157  P1::kNumXDims + P2::kNumXDims + P3::kThetaIdx;
158 static const Dimension kP3VIdx = P1::kNumXDims + P2::kNumXDims + P3::kVIdx;
159 static const Dimension kP3VxIdx = P1::kNumXDims + P2::kNumXDims + P3::kVxIdx;
160 static const Dimension kP3VyIdx = P1::kNumXDims + P2::kNumXDims + P3::kVyIdx;
161 
162 // Control dimensions.
163 static const Dimension kP1OmegaIdx = 0;
164 static const Dimension kP1JerkIdx = 1;
165 static const Dimension kP2OmegaIdx = 0;
166 static const Dimension kP2JerkIdx = 1;
167 static const Dimension kP3OmegaIdx = 0;
168 static const Dimension kP3AIdx = 1;
169 
170 } // anonymous namespace
171 
172 void ThreePlayerFlatOvertakingExample::ConstructDynamics() {
173  dynamics_.reset(
174  new ConcatenatedFlatSystem({std::make_shared<P1>(kInterAxleLength),
175  std::make_shared<P2>(kInterAxleLength),
176  std::make_shared<P3>(kInterAxleLength)}));
177 }
178 
179 void ThreePlayerFlatOvertakingExample::ConstructInitialState() {
180  VectorXf x0 = VectorXf::Zero(dynamics_->XDim());
181  x0(kP1XIdx) = kP1InitialX;
182  x0(kP1YIdx) = kP1InitialY;
183  x0(kP1HeadingIdx) = kP1InitialHeading;
184  x0(kP1VIdx) = kP1InitialSpeed;
185  x0(kP2XIdx) = kP2InitialX;
186  x0(kP2YIdx) = kP2InitialY;
187  x0(kP2HeadingIdx) = kP2InitialHeading;
188  x0(kP2VIdx) = kP2InitialSpeed;
189  x0(kP3XIdx) = kP3InitialX;
190  x0(kP3YIdx) = kP3InitialY;
191  x0(kP3HeadingIdx) = kP3InitialHeading;
192  x0(kP3VIdx) = kP3InitialSpeed;
193 
194  x0_ = dynamics_->ToLinearSystemState(x0);
195 }
196 
197 void ThreePlayerFlatOvertakingExample::ConstructPlayerCosts() {
198  // Set up costs for all players.
199  player_costs_.emplace_back("P1");
200  player_costs_.emplace_back("P2");
201  player_costs_.emplace_back("P3");
202  auto& p1_cost = player_costs_[0];
203  auto& p2_cost = player_costs_[1];
204  auto& p3_cost = player_costs_[2];
205 
206  // Stay in lanes.
207  const Polyline2 lane1(
208  {Point2(kP2InitialX, kP2InitialY), Point2(kP2InitialX, 1000.0)});
209  const Polyline2 lane2(
210  {Point2(kP3InitialX, kP3InitialY), Point2(kP3InitialX, 1000.0)});
211 
212  const std::shared_ptr<QuadraticPolyline2Cost> p1_lane_cost(
213  new QuadraticPolyline2Cost(kLaneCostWeight, lane1, {kP1XIdx, kP1YIdx},
214  "LaneCenter"));
215  const std::shared_ptr<SemiquadraticPolyline2Cost> p1_lane_r_cost(
216  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
217  {kP1XIdx, kP1YIdx}, kLaneHalfWidth,
218  kOrientedRight, "LaneRightBoundary"));
219  const std::shared_ptr<SemiquadraticPolyline2Cost> p1_lane_l_cost(
220  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
221  {kP1XIdx, kP1YIdx}, -kLaneHalfWidth,
222  !kOrientedRight, "LaneLeftBoundary"));
223  p1_cost.AddStateCost(p1_lane_cost);
224  p1_cost.AddStateCost(p1_lane_r_cost);
225  p1_cost.AddStateCost(p1_lane_l_cost);
226 
227  const std::shared_ptr<QuadraticPolyline2Cost> p2_lane_cost(
228  new QuadraticPolyline2Cost(kLaneCostWeight, lane1, {kP2XIdx, kP2YIdx},
229  "LaneCenter"));
230  const std::shared_ptr<SemiquadraticPolyline2Cost> p2_lane_r_cost(
231  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
232  {kP2XIdx, kP2YIdx}, kLaneHalfWidth,
233  kOrientedRight, "LaneRightBoundary"));
234  const std::shared_ptr<SemiquadraticPolyline2Cost> p2_lane_l_cost(
235  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane1,
236  {kP2XIdx, kP2YIdx}, -kLaneHalfWidth,
237  !kOrientedRight, "LaneLeftBoundary"));
238  p2_cost.AddStateCost(p2_lane_cost);
239  p2_cost.AddStateCost(p2_lane_r_cost);
240  p2_cost.AddStateCost(p2_lane_l_cost);
241 
242  const std::shared_ptr<QuadraticPolyline2Cost> p3_lane_cost(
243  new QuadraticPolyline2Cost(kLaneCostWeight, lane2, {kP3XIdx, kP3YIdx},
244  "LaneCenter"));
245  const std::shared_ptr<SemiquadraticPolyline2Cost> p3_lane_r_cost(
246  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane2,
247  {kP3XIdx, kP3YIdx}, kLaneHalfWidth,
248  kOrientedRight, "LaneRightBoundary"));
249  const std::shared_ptr<SemiquadraticPolyline2Cost> p3_lane_l_cost(
250  new SemiquadraticPolyline2Cost(kLaneBoundaryCostWeight, lane2,
251  {kP3XIdx, kP3YIdx}, -kLaneHalfWidth,
252  !kOrientedRight, "LaneLeftBoundary"));
253  p3_cost.AddStateCost(p3_lane_cost);
254  p3_cost.AddStateCost(p3_lane_r_cost);
255  p3_cost.AddStateCost(p3_lane_l_cost);
256 
257  // Max/min/nominal speed costs.
258  const std::shared_ptr<RouteProgressCost> p1_progress_cost(
259  new RouteProgressCost(kP1NominalVCostWeight, kP1NominalV, lane1,
260  {kP1XIdx, kP1YIdx}, "RouteProgress",
261  kP1InitialY - kP2InitialY));
262  p1_cost.AddStateCost(p1_progress_cost);
263 
264  const std::shared_ptr<RouteProgressCost> p2_progress_cost(
265  new RouteProgressCost(kP2NominalVCostWeight, kP2NominalV, lane1,
266  {kP2XIdx, kP2YIdx}, "RouteProgress"));
267  p2_cost.AddStateCost(p2_progress_cost);
268 
269  const std::shared_ptr<RouteProgressCost> p3_progress_cost(
270  new RouteProgressCost(kP3NominalVCostWeight, kP3NominalV, lane2,
271  {kP3XIdx, kP3YIdx}, "RouteProgress"));
272  p3_cost.AddStateCost(p3_progress_cost);
273 
274  // Penalize control effort.
275  constexpr Dimension kApplyInAllDimensions = -1;
276  // const auto unicycle_aux_cost = std::make_shared<QuadraticCost>(
277  // kUnicycleAuxCostWeight, kApplyInAllDimensions, 0.0, "Auxiliary Input");
278  const auto car_aux_cost = std::make_shared<QuadraticCost>(
279  kCarAuxCostWeight, kApplyInAllDimensions, 0.0, "Auxiliary Input");
280  p1_cost.AddControlCost(0, car_aux_cost);
281  p2_cost.AddControlCost(1, car_aux_cost);
282  p3_cost.AddControlCost(2, car_aux_cost);
283 
284  // Pairwise proximity costs.
285  const std::shared_ptr<ProxCost> p1p2_proximity_cost(
286  new ProxCost(kP1ProximityCostWeight, {kP1XIdx, kP1YIdx},
287  {kP2XIdx, kP2YIdx}, kMinProximity, "ProximityP2"));
288  const std::shared_ptr<ProxCost> p1p3_proximity_cost(
289  new ProxCost(kP1ProximityCostWeight, {kP1XIdx, kP1YIdx},
290  {kP3XIdx, kP3YIdx}, kMinProximity, "ProximityP3"));
291  p1_cost.AddStateCost(p1p2_proximity_cost);
292  p1_cost.AddStateCost(p1p3_proximity_cost);
293 
294  const std::shared_ptr<ProxCost> p2p1_proximity_cost(
295  new ProxCost(kP2ProximityCostWeight, {kP2XIdx, kP2YIdx},
296  {kP1XIdx, kP1YIdx}, kMinProximity, "ProximityP1"));
297  const std::shared_ptr<ProxCost> p2p3_proximity_cost(
298  new ProxCost(kP2ProximityCostWeight, {kP2XIdx, kP2YIdx},
299  {kP3XIdx, kP3YIdx}, kMinProximity, "ProximityP3"));
300  p2_cost.AddStateCost(p2p1_proximity_cost);
301  p2_cost.AddStateCost(p2p3_proximity_cost);
302 
303  const std::shared_ptr<ProxCost> p3p1_proximity_cost(
304  new ProxCost(kP3ProximityCostWeight, {kP3XIdx, kP3YIdx},
305  {kP1XIdx, kP1YIdx}, kMinProximity, "ProximityP1"));
306  const std::shared_ptr<ProxCost> p3p2_proximity_cost(
307  new ProxCost(kP3ProximityCostWeight, {kP3XIdx, kP3YIdx},
308  {kP2XIdx, kP2YIdx}, kMinProximity, "ProximityP2"));
309  p3_cost.AddStateCost(p3p1_proximity_cost);
310  p3_cost.AddStateCost(p3p2_proximity_cost);
311 }
312 
313 inline std::vector<float> ThreePlayerFlatOvertakingExample::Xs(
314  const VectorXf& xi) const {
315  return {xi(kP1XIdx), xi(kP2XIdx), xi(kP3XIdx)};
316 }
317 
318 inline std::vector<float> ThreePlayerFlatOvertakingExample::Ys(
319  const VectorXf& xi) const {
320  return {xi(kP1YIdx), xi(kP2YIdx), xi(kP3YIdx)};
321 }
322 
323 inline std::vector<float> ThreePlayerFlatOvertakingExample::Thetas(
324  const VectorXf& xi) const {
325  const VectorXf x = dynamics_->FromLinearSystemState(xi);
326  return {x(kP1HeadingIdx), x(kP2HeadingIdx), x(kP3HeadingIdx)};
327 }
328 
329 } // namespace ilqgames
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