# US 8,571,727 B1 · Energy-angular momentum closed-loop guidance for launch vehicles > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 8,571,727 B1 - Document ID: US8571727B1 - Status: Granted - Kind: B1 - Application number: 13/760,189 - Filed: 2013-02-06 - Granted: 2013-10-29 - Earliest claimed: 2013-02-06 - Assignees: The Aerospace Corporation - Applicants: The Aerospace Corporation - Inventors: Russell Paul Patera - Web page: https://patentgrep.com/patent/US8571727B1 ## CPC - B64G 1/002: {Launch systems} - B64G 1/244: {Spacecraft control systems} - B64G 1/245: {Attitude control algorithms for spacecraft attitude control} - B64G: COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR ## Abstract An improved method for launch vehicle guidance is disclosed. A pre-computed energy-angular momentum (E-J) curve to place a launch vehicle into a target orbit is received and stored. An energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle are computed from state vector data while the launch vehicle is traveling to the target orbit. The pre-computed E-J curve and the computed energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle are used to determine pitch and pitch rate of the launch vehicle. ## Claims ### Claim 1 A computer program embodied on a computer-readable storage medium, the computer program configured to cause at least one processor to: receive and store a pre-computed energy-angular momentum (E-J) curve to place a launch vehicle into a target orbit; compute an energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle from state vector data while the launch vehicle is traveling to the target orbit; and use the pre-computed E-J curve and the computed energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle to determine pitch and pitch rate of the launch vehicle. ### Claim 2 (depends on 1) The computer program of claim 1, wherein when the launch vehicle deviates from the E-J curve, the program is further configured to cause the at least one processor to engage one or more motors of the launch vehicle to alter a pitch of the launch vehicle to a corrected slope to steer out energy deviations and return the launch vehicle to the E-J curve. ### Claim 3 (depends on 2) The computer program of claim 2, wherein the program is configured to cause the at least one processor to determine the corrected slope by δ ⁡ ( J ) = ( B ) ⁢ Δ ⁢ ⁢ E ( 1 + ɛ ) ⁢ J f - J where B is a constant gain or a function of J whose value can be adjusted as needed to ensure satisfactory performance, ΔE is a difference between actual vehicle energy and energy prescribed by the E-J curve, Jf refers to final angular momentum at orbit injection, and constant ε is a small positive non-dimensional number that ensures that a denominator of the equation does not become zero. ### Claim 4 (depends on 1) The computer program of claim 1, wherein the program is further configured to cause the at least one processor to receive and store a pre-computed inclination versus angular momentum (I-J) curve. ### Claim 5 (depends on 4) The computer program of claim 4, wherein when the launch vehicle deviates from the I-J curve, the program is further configured to cause the at least one processor to engage one or more motors of the launch vehicle to perform yaw corrections to steer out deviations from a desired inclination. ### Claim 6 (depends on 5) The computer program of claim 5, wherein the program is configured to cause the at least one processor to determine the yaw corrections by δ ⁢ ⁢ θ = - Δ ⁢ ⁢ IJB 1 ⁢ J f ar ⁢ ⁢ cos ⁡ ( ϕ ) ⁢ ( J f ⁡ ( 1 + ɛ 1 ) - J ) where ΔI is a change in inclination, J is angular momentum, Jf is angular momentum at orbit injection, B1 is a constant gain or a function of J, ε1 is a constant, r is a distance to a center of Earth or gravitational field, a is an acceleration, and φ is an argument of latitude. ### Claim 7 (depends on 1) The computer program of claim 1, wherein the E-J curve represents an optimum trajectory to reach the target orbit. ### Claim 8 (depends on 7) The computer program of claim 7, wherein the optimum trajectory is configured to deliver a largest mass to the target orbit with a smallest amount of fuel for the launch vehicle. ### Claim 9 (depends on 1) The computer program of claim 1, wherein the program is further configured to cause the at least one processor to continuously check for deviations by the launch vehicle from the E-J and I-J curves from launch of the launch vehicle until the launch vehicle reaches the target orbit. ### Claim 10 (depends on 1) The computer program of claim 1, wherein the program is further configured to cause the at least one processor to calculate inclination dispersions by taking a difference between pre-flight trajectory angular momentum and vehicle trajectory angular momentum and drive the difference to zero. ### Claim 11 A computer-implemented method, comprising: receiving and storing a pre-computed energy-angular momentum (E-J) curve to place a launch vehicle into a target orbit; computing an energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle from state vector data while the launch vehicle is traveling to the target orbit; and using the pre-computed E-J curve and the computed energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle to determine pitch and pitch rate of the launch vehicle. ### Claim 12 (depends on 11) The computer-implemented method of claim 11, wherein when the launch vehicle deviates from the E-J curve, the method further comprises engaging one or more motors of the launch vehicle to alter a pitch of the launch vehicle to a corrected slope to steer out energy deviations and return the launch vehicle to the desired E-J curve. ### Claim 13 (depends on 12) The computer-implemented method of claim 12, the corrected slope is determined by δ ⁡ ( J ) = ( B ) ⁢ Δ ⁢ ⁢ E ( 1 + ɛ ) ⁢ J f - J where B is a constant gain or a function of J whose value can be adjusted as needed to ensure satisfactory performance, ΔE is a difference between actual vehicle energy and energy prescribed by the E-J curve, Jf refers to final angular momentum at orbit injection, and constant ε is a small positive non-dimensional number that ensures that a denominator of the equation does not become zero. ### Claim 14 (depends on 11) The computer-implemented method of claim 11, further comprising: receiving and storing a pre-computed inclination versus angular momentum (I-J) curve. ### Claim 15 (depends on 14) The computer-implemented method of claim 14, wherein when the launch vehicle deviates from the I-J curve, the method further comprises engaging one or more motors of the launch vehicle to perform yaw corrections to steer out deviations from a desired inclination. ### Claim 16 (depends on 15) The computer program of claim 15, wherein the yaw corrections are determined by δ ⁢ ⁢ θ = - Δ ⁢ ⁢ IJB 1 ⁢ J f ar ⁢ ⁢ cos ⁡ ( ϕ ) ⁢ ( J f ⁡ ( 1 + ɛ 1 ) - J ) where ΔI is a change in inclination, J is angular momentum, Jf is angular momentum at orbit injection, B1 is a constant gain or a function of J, ε1 is a constant, r is a distance to a center of Earth or gravitational field, a is an acceleration, and φ is an argument of latitude. ### Claim 17 (depends on 11) The computer-implemented method of claim 11, wherein the E-J curve represents an optimum trajectory to reach the target orbit. ### Claim 18 (depends on 17) The computer-implemented method of claim 17, wherein the optimum trajectory is configured to deliver a largest mass to the target orbit with a smallest amount of fuel for the launch vehicle. ### Claim 19 (depends on 11) The computer-implemented method of claim 11, further comprising: continuously checking for deviations by the launch vehicle from the E-J and I-J curves from launch of the launch vehicle until the launch vehicle reaches the target orbit. ### Claim 20 (depends on 11) The computer-implemented method of claim 11, further comprising: calculating inclination dispersions by taking a difference between pre-flight trajectory angular momentum and vehicle trajectory angular momentum; and driving the difference to zero. ### Claim 21 An apparatus, comprising: physical memory comprising computer program instructions; and at least one processor configured to execute the computer program instructions, the at least one processor configured to: receive and store a pre-computed energy-angular momentum (E-J) curve to place a launch vehicle into a target orbit; compute an energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle from state vector data while the launch vehicle is traveling to the target orbit; and use the pre-computed E-J curve and the computed energy, angular momentum, radial distance, velocity magnitude, and flight path angle of the launch vehicle to determine pitch and pitch rate of the launch vehicle. ### Claim 22 (depends on 21) The apparatus of claim 21, wherein when the launch vehicle deviates from the E-J curve, the at least one processor is further configured to engage one or more motors of the launch vehicle to alter a pitch of the launch vehicle to a corrected slope to steer out energy deviations and return the launch vehicle to the E-J curve. ### Claim 23 (depends on 22) The apparatus of claim 22, wherein the at least one processor is configured to determine the corrected slope by δ ⁡ ( J ) = ( B ) ⁢ Δ ⁢ ⁢ E ( 1 + ɛ ) ⁢ J f - J where B is a constant gain or a function of J whose value can be adjusted as needed to ensure satisfactory performance, ΔE is a difference between actual vehicle energy and energy prescribed by the E-J curve, Jf refers to final angular momentum at orbit injection, and constant ε is a small positive non-dimensional number that ensures that a denominator of the equation does not become zero. ### Claim 24 (depends on 21) The apparatus of claim 21, wherein the at least one processor is further configured to receive and store a pre-computed inclination versus angular momentum (I-J) curve. ### Claim 25 (depends on 24) The apparatus of claim 24, wherein when the launch vehicle deviates from the I-J curve, the at least one processor is further configured to engage one or more motors of the launch vehicle to perform yaw corrections to steer out deviations from a desired inclination. ### Claim 26 (depends on 25) The apparatus of claim 25, wherein the at least one processor is configured to determine the yaw corrections by δ ⁢ ⁢ θ = - Δ ⁢ ⁢ IJB 1 ⁢ J f ar ⁢ ⁢ cos ⁡ ( ϕ ) ⁢ ( J f ⁡ ( 1 + ɛ 1 ) - J ) where ΔI is a change in inclination, J is angular momentum, Jf is angular momentum at orbit injection, B1 is a constant gain or a function of J, ε1 is a constant, r is a distance to a center of Earth or gravitational field, a is an acceleration, and φ is an argument of latitude. ### Claim 27 (depends on 21) The apparatus of claim 21, wherein the E-J curve represents an optimum trajectory to reach the target orbit. ### Claim 28 (depends on 27) The apparatus of claim 27, wherein the optimum trajectory is configured to deliver a largest mass to the target orbit with a smallest amount of fuel for the launch vehicle. ### Claim 29 (depends on 21) The apparatus of claim 21, wherein the at least one processor is further configured to continuously check for deviations by the launch vehicle from the E-J and I-J curves from launch of the launch vehicle until the launch vehicle reaches the target orbit. ### Claim 30 (depends on 21) The apparatus of claim 21, wherein the at least one processor is further configured to calculate inclination dispersions by taking a difference between pre-flight trajectory angular momentum and vehicle trajectory angular momentum and drive the difference to zero.