#!/usr/bin/env python3 import os import numpy as np from common.realtime import sec_since_boot from common.numpy_fast import clip, interp from selfdrive.swaglog import cloudlog from selfdrive.modeld.constants import index_function from selfdrive.controls.lib.radar_helpers import _LEAD_ACCEL_TAU if __name__ == '__main__': # generating code from pyextra.acados_template import AcadosModel, AcadosOcp, AcadosOcpSolver else: # from pyextra.acados_template import AcadosOcpSolver as AcadosOcpSolverFast from selfdrive.controls.lib.longitudinal_mpc_lib.c_generated_code.acados_ocp_solver_pyx import AcadosOcpSolverFast # pylint: disable=no-name-in-module, import-error from casadi import SX, vertcat LONG_MPC_DIR = os.path.dirname(os.path.abspath(__file__)) EXPORT_DIR = os.path.join(LONG_MPC_DIR, "c_generated_code") JSON_FILE = "acados_ocp_long.json" SOURCES = ['lead0', 'lead1', 'cruise'] X_DIM = 3 U_DIM = 1 COST_E_DIM = 4 COST_DIM = COST_E_DIM + 1 CONSTR_DIM = 4 X_EGO_OBSTACLE_COST = 3. V_EGO_COST = 0. X_EGO_COST = 0. A_EGO_COST = 0. J_EGO_COST = 10. DANGER_ZONE_COST = 100. CRASH_DISTANCE = .5 LIMIT_COST = 1e6 # Less timestamps doesn't hurt performance and leads to # much better convergence of the MPC with low iterations N = 12 MAX_T = 10.0 T_IDXS_LST = [index_function(idx, max_val=MAX_T, max_idx=N+1) for idx in range(N+1)] T_IDXS = np.array(T_IDXS_LST) T_DIFFS = np.diff(T_IDXS, prepend=[0.]) MIN_ACCEL = -3.5 T_REACT = 1.8 MAX_BRAKE = 9.81 def get_stopped_equivalence_factor(v_lead): return T_REACT * v_lead + (v_lead*v_lead) / (2 * MAX_BRAKE) def get_safe_obstacle_distance(v_ego): return 2 * T_REACT * v_ego + (v_ego*v_ego) / (2 * MAX_BRAKE) + 4.0 def desired_follow_distance(v_ego, v_lead): return get_safe_obstacle_distance(v_ego) - get_stopped_equivalence_factor(v_lead) def gen_long_model(): model = AcadosModel() model.name = 'long' # set up states & controls x_ego = SX.sym('x_ego') v_ego = SX.sym('v_ego') a_ego = SX.sym('a_ego') model.x = vertcat(x_ego, v_ego, a_ego) # controls j_ego = SX.sym('j_ego') model.u = vertcat(j_ego) # xdot x_ego_dot = SX.sym('x_ego_dot') v_ego_dot = SX.sym('v_ego_dot') a_ego_dot = SX.sym('a_ego_dot') model.xdot = vertcat(x_ego_dot, v_ego_dot, a_ego_dot) # live parameters x_obstacle = SX.sym('x_obstacle') a_min = SX.sym('a_min') a_max = SX.sym('a_max') model.p = vertcat(a_min, a_max, x_obstacle) # dynamics model f_expl = vertcat(v_ego, a_ego, j_ego) model.f_impl_expr = model.xdot - f_expl model.f_expl_expr = f_expl return model def gen_long_mpc_solver(): ocp = AcadosOcp() ocp.model = gen_long_model() Tf = T_IDXS[-1] # set dimensions ocp.dims.N = N # set cost module ocp.cost.cost_type = 'NONLINEAR_LS' ocp.cost.cost_type_e = 'NONLINEAR_LS' QR = np.zeros((COST_DIM, COST_DIM)) Q = np.zeros((COST_E_DIM, COST_E_DIM)) ocp.cost.W = QR ocp.cost.W_e = Q x_ego, v_ego, a_ego = ocp.model.x[0], ocp.model.x[1], ocp.model.x[2] j_ego = ocp.model.u[0] a_min, a_max = ocp.model.p[0], ocp.model.p[1] x_obstacle = ocp.model.p[2] ocp.cost.yref = np.zeros((COST_DIM, )) ocp.cost.yref_e = np.zeros((COST_E_DIM, )) desired_dist_comfort = get_safe_obstacle_distance(v_ego) # The main cost in normal operation is how close you are to the "desired" distance # from an obstacle at every timestep. This obstacle can be a lead car # or other object. In e2e mode we can use x_position targets as a cost # instead. costs = [((x_obstacle - x_ego) - (desired_dist_comfort)) / (v_ego + 10.), x_ego, v_ego, a_ego, j_ego] ocp.model.cost_y_expr = vertcat(*costs) ocp.model.cost_y_expr_e = vertcat(*costs[:-1]) # Constraints on speed, acceleration and desired distance to # the obstacle, which is treated as a slack constraint so it # behaves like an assymetrical cost. constraints = vertcat((v_ego), (a_ego - a_min), (a_max - a_ego), ((x_obstacle - x_ego) - (3/4) * (desired_dist_comfort)) / (v_ego + 10.)) ocp.model.con_h_expr = constraints ocp.model.con_h_expr_e = vertcat(np.zeros(CONSTR_DIM)) x0 = np.zeros(X_DIM) ocp.constraints.x0 = x0 ocp.parameter_values = np.array([-1.2, 1.2, 0.0]) # We put all constraint cost weights to 0 and only set them at runtime cost_weights = np.zeros(CONSTR_DIM) ocp.cost.zl = cost_weights ocp.cost.Zl = cost_weights ocp.cost.Zu = cost_weights ocp.cost.zu = cost_weights ocp.constraints.lh = np.zeros(CONSTR_DIM) ocp.constraints.lh_e = np.zeros(CONSTR_DIM) ocp.constraints.uh = 1e4*np.ones(CONSTR_DIM) ocp.constraints.uh_e = 1e4*np.ones(CONSTR_DIM) ocp.constraints.idxsh = np.arange(CONSTR_DIM) # The HPIPM solver can give decent solutions even when it is stopped early # Which is critical for our purpose where the compute time is strictly bounded # We use HPIPM in the SPEED_ABS mode, which ensures fastest runtime. This # does not cause issues since the problem is well bounded. ocp.solver_options.qp_solver = 'PARTIAL_CONDENSING_HPIPM' ocp.solver_options.hessian_approx = 'GAUSS_NEWTON' ocp.solver_options.integrator_type = 'ERK' ocp.solver_options.nlp_solver_type = 'SQP_RTI' ocp.solver_options.qp_solver_cond_N = N//4 # More iterations take too much time and less lead to inaccurate convergence in # some situations. Ideally we would run just 1 iteration to ensure fixed runtime. ocp.solver_options.qp_solver_iter_max = 10 # set prediction horizon ocp.solver_options.tf = Tf ocp.solver_options.shooting_nodes = T_IDXS ocp.code_export_directory = EXPORT_DIR return ocp class LongitudinalMpc(): def __init__(self, e2e=False): self.e2e = e2e self.reset() self.accel_limit_arr = np.zeros((N+1, 2)) self.accel_limit_arr[:,0] = -1.2 self.accel_limit_arr[:,1] = 1.2 self.source = SOURCES[2] def reset(self): self.solver = AcadosOcpSolverFast('long', N, EXPORT_DIR) self.v_solution = [0.0 for i in range(N+1)] self.a_solution = [0.0 for i in range(N+1)] self.j_solution = [0.0 for i in range(N)] self.yref = np.zeros((N+1, COST_DIM)) for i in range(N): self.solver.cost_set(i, "yref", self.yref[i]) self.solver.cost_set(N, "yref", self.yref[N][:COST_E_DIM]) self.x_sol = np.zeros((N+1, X_DIM)) self.u_sol = np.zeros((N,1)) self.params = np.zeros((N+1,3)) for i in range(N+1): self.solver.set(i, 'x', np.zeros(X_DIM)) self.last_cloudlog_t = 0 self.status = False self.crash_cnt = 0.0 self.solution_status = 0 self.x0 = np.zeros(X_DIM) self.set_weights() def set_weights(self): if self.e2e: self.set_weights_for_xva_policy() else: self.set_weights_for_lead_policy() def set_weights_for_lead_policy(self): W = np.asfortranarray(np.diag([X_EGO_OBSTACLE_COST, X_EGO_COST, V_EGO_COST, A_EGO_COST, J_EGO_COST])) for i in range(N): self.solver.cost_set(i, 'W', W) # Setting the slice without the copy make the array not contiguous, # causing issues with the C interface. self.solver.cost_set(N, 'W', np.copy(W[:COST_E_DIM, :COST_E_DIM])) # Set L2 slack cost on lower bound constraints Zl = np.array([LIMIT_COST, LIMIT_COST, LIMIT_COST, DANGER_ZONE_COST]) for i in range(N): self.solver.cost_set(i, 'Zl', Zl) def set_weights_for_xva_policy(self): W = np.asfortranarray(np.diag([0., 10., 1., 10., 1.])) for i in range(N): self.solver.cost_set(i, 'W', W) # Setting the slice without the copy make the array not contiguous, # causing issues with the C interface. self.solver.cost_set(N, 'W', np.copy(W[:COST_E_DIM, :COST_E_DIM])) # Set L2 slack cost on lower bound constraints Zl = np.array([LIMIT_COST, LIMIT_COST, LIMIT_COST, 0.0]) for i in range(N): self.solver.cost_set(i, 'Zl', Zl) def set_cur_state(self, v, a): if abs(self.x0[1] - v) > 1.: self.x0[1] = v self.x0[2] = a for i in range(0, N+1): self.solver.set(i, 'x', self.x0) else: self.x0[1] = v self.x0[2] = a def extrapolate_lead(self, x_lead, v_lead, a_lead, a_lead_tau): a_lead_traj = a_lead * np.exp(-a_lead_tau * (T_IDXS**2)/2.) v_lead_traj = np.clip(v_lead + np.cumsum(T_DIFFS * a_lead_traj), 0.0, 1e8) x_lead_traj = x_lead + np.cumsum(T_DIFFS * v_lead_traj) lead_xv = np.column_stack((x_lead_traj, v_lead_traj)) return lead_xv def process_lead(self, lead): v_ego = self.x0[1] if lead is not None and lead.status: x_lead = lead.dRel v_lead = lead.vLead a_lead = lead.aLeadK a_lead_tau = lead.aLeadTau else: # Fake a fast lead car, so mpc can keep running in the same mode x_lead = 50.0 v_lead = v_ego + 10.0 a_lead = 0.0 a_lead_tau = _LEAD_ACCEL_TAU # MPC will not converge if immediate crash is expected # Clip lead distance to what is still possible to brake for min_x_lead = ((v_ego + v_lead)/2) * (v_ego - v_lead) / (-MIN_ACCEL * 2) x_lead = clip(x_lead, min_x_lead, 1e8) v_lead = clip(v_lead, 0.0, 1e8) a_lead = clip(a_lead, -10., 5.) lead_xv = self.extrapolate_lead(x_lead, v_lead, a_lead, a_lead_tau) return lead_xv def set_accel_limits(self, min_a, max_a): self.cruise_min_a = min_a self.cruise_max_a = max_a def update(self, carstate, radarstate, v_cruise): v_ego = self.x0[1] self.status = radarstate.leadOne.status or radarstate.leadTwo.status lead_xv_0 = self.process_lead(radarstate.leadOne) lead_xv_1 = self.process_lead(radarstate.leadTwo) # set accel limits in params self.params[:,0] = interp(float(self.status), [0.0, 1.0], [self.cruise_min_a, MIN_ACCEL]) self.params[:,1] = self.cruise_max_a # To estimate a safe distance from a moving lead, we calculate how much stopping # distance that lead needs as a minimum. We can add that to the current distance # and then treat that as a stopped car/obstacle at this new distance. lead_0_obstacle = lead_xv_0[:,0] + get_stopped_equivalence_factor(lead_xv_0[:,1]) lead_1_obstacle = lead_xv_1[:,0] + get_stopped_equivalence_factor(lead_xv_1[:,1]) # Fake an obstacle for cruise, this ensures smooth acceleration to set speed # when the leads are no factor. cruise_lower_bound = v_ego + (3/4) * self.cruise_min_a * T_IDXS cruise_upper_bound = v_ego + (3/4) * self.cruise_max_a * T_IDXS v_cruise_clipped = np.clip(v_cruise * np.ones(N+1), cruise_lower_bound, cruise_upper_bound) cruise_obstacle = T_IDXS*v_cruise_clipped + get_safe_obstacle_distance(v_cruise_clipped) x_obstacles = np.column_stack([lead_0_obstacle, lead_1_obstacle, cruise_obstacle]) self.source = SOURCES[np.argmin(x_obstacles[0])] self.params[:,2] = np.min(x_obstacles, axis=1) self.run() if (np.any(lead_xv_0[:,0] - self.x_sol[:,0] < CRASH_DISTANCE) and radarstate.leadOne.modelProb > 0.9): self.crash_cnt += 1 else: self.crash_cnt = 0 def update_with_xva(self, x, v, a): self.yref[:,1] = x self.yref[:,2] = v self.yref[:,3] = a for i in range(N): self.solver.cost_set(i, "yref", self.yref[i]) self.solver.cost_set(N, "yref", self.yref[N][:COST_E_DIM]) self.accel_limit_arr[:,0] = -10. self.accel_limit_arr[:,1] = 10. x_obstacle = 1e5*np.ones((N+1)) self.params = np.concatenate([self.accel_limit_arr, x_obstacle[:,None]], axis=1) self.run() def run(self): for i in range(N+1): self.solver.set(i, 'p', self.params[i]) self.solver.constraints_set(0, "lbx", self.x0) self.solver.constraints_set(0, "ubx", self.x0) self.solution_status = self.solver.solve() for i in range(N+1): self.x_sol[i] = self.solver.get(i, 'x') for i in range(N): self.u_sol[i] = self.solver.get(i, 'u') self.v_solution = self.x_sol[:,1] self.a_solution = self.x_sol[:,2] self.j_solution = self.u_sol[:,0] t = sec_since_boot() if self.solution_status != 0: if t > self.last_cloudlog_t + 5.0: self.last_cloudlog_t = t cloudlog.warning("Long mpc reset, solution_status: %s" % ( self.solution_status)) self.reset() if __name__ == "__main__": ocp = gen_long_mpc_solver() AcadosOcpSolver.generate(ocp, json_file=JSON_FILE, build=False)