Damaged Airplane Trajectory Planning Based on Flight Envelope and Motion Primitives Davood Asadi * and Mehdi Sabzehparvar † Amirkabir University of Technology, 15875-4413 Tehran, Iran Ella M. Atkins ‡ University of Michigan, Ann Arbor, Michigan 48109 and Heidar A. Talebi § Amirkabir University of Technology, 15875-4413 Tehran, Iran DOI: 10.2514/1.C032422 This paper presents an efficient approach for safe landing trajectory generation of an airplane with structural damage to its wing flying in proximity to local terrain. A damaged airplane maneuvering flight envelope is estimated by analyzing the local stability and flying quality at each trim condition. Trim state distance to a flight envelope boundary provides a novel criterion defined as the safety value index to prioritize choice of trim conditions for postdamage flight. A library of trajectory segments including trim states and transition maneuvers between trim conditions in the local neighborhood are generated using a linear quadratic regulator controller. A potential field strategy is used to rapidly define emergency landing trajectories composed as trim state sequences based on criteria including terrain avoidance, safety value index, and safe landing requirements such as touchdown heading and position, airspeed, glide slope, and bank angle. Cost criteria are balanced by adjusting weights. Landing scenarios are presented to demonstrate the capability of the proposed approach to autonomously plan safe landing trajectories. Nomenclature A = state matrix B = input matrix C = controllability matrix D = matrix of variables in data library DR = Dutch roll mode d T = airplane distance to terrain g = function of equality constraints h = flight altitude, m J = cost function K = state feedback gain of the controller k = gain value M = maneuvers Ph = Phugoid mode p, q, r = roll, pitch, and yaw rates, respectively, rad∕s Q = weighting matrix R = roll mode S = spiral mode s = inequality constraint function T = trim trajectories T r = roll mode time constant T 2 = minimum time to double the amplitude V = total velocity in body axes, m∕s W = weighting factor in heuristic function z = airplane state vector α, β, γ = angle of attack, sideslip angle, and flight path angle, rad Δx, Δy, Δz = variation in airplane position in each trajectory segment, m Δs = length of each trajectory segment δ th , δ a , δ e , δ r = engine throttle (%), aileron, elevator, and rudder deflections, deg μ = vector of control inputs ξ = damping ratio ψ , θ, φ = yaw, pitch, and roll angles, respectively, rad Subscript L = landing condition I. Introduction I N MODERN aviation, flight safety and risk reduction are important issues for manufacturers and passengers. Although triple-redundancy architectures have reduced the likelihood of incidents induced by damage or failures, loss of control remains the leading cause of accidents in transport aircraft. Damage or in-flight failures in a transport aircraft can lead to significant performance degradation, which can in turn cause loss of control. To prevent such situations, researchers are working on automation enhancement to safely recover a damaged airplane. Automation can assist by char- acterizing and adapting to the failure or damage situation. Once postfailure performance is characterized, a new landing flight plan can be generated that respects new constraints associated with the airplane’ s degraded performance and stability characteristics. There are several challenges in safely landing an aircraft after a failure or damage event. The first challenge is the requirement to characterize the airplane’ s new flight envelope and kinematic con- straints, which requires identification of the damaged airplane and estimation of the resulting flight envelope based on the effects of system degradation on airplane performance and stability. The next challenge is to safely guide and control the damaged airplane to a safe landing. An enhanced automation strategy addressing these challenges is illustrated in Fig. 1. In this architecture, first, the control subsystem helps the pilot retain control of the airplane. While this is happening, a terrain elevation map and a motion primitives database containing reference trim states are loaded based on failure or damage scenario identification. Fault detection and identification (FDI) identifies degraded aircraft behavior along with parameters used by Received 7 May 2013; revision received 22 June 2014; accepted for publication 18 July 2014; published online 31 October 2014. Copyright © 2014 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1542-3868/14 and $10.00 in correspondence with the CCC. *Ph.D. Student, Department of Aerospace Engineering; davoodasadi@aut .ac.ir. † Associate Professor, Department of Aerospace Engineering; sabzeh@aut .ac.ir. ‡ Associate Professor, Department of Aerospace Engineering; ematkins@ umich.edu. Associate Fellow AIAA. § Professor, Department of Electrical Engineering; alit@aut.ac.ir. AIAA Early Edition / 1 JOURNAL OF AIRCRAFT Downloaded by University of Newcastle on November 25, 2014 | http://arc.aiaa.org | DOI: 10.2514/1.C032422