Trajectory optimization with inter-sample obstacle avoidance via successive convexification

Dueri, Daniel; Mao, Yuanqi; Mian, Zohaib; Ding, Jerry; Açıkmeşe, Behçet

doi:10.1109/cdc.2017.8263811

Cited by 25 publications

(15 citation statements)

References 19 publications

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“…If the temporal grid is too sparse, the constraints related to the pointing objectives, maximum wheel momentum or spacecraft angular rates could be violated during the intersample period. More sophisticated methods such as the one presented in [33] could be employed to guarantee that the conditions hold even in the intersample time. For this paper however, the motor torque within each subinterval is linearly interpolated between the endpoints.…”

Section: Remarkmentioning

confidence: 99%

Optimal Science-time Reorientation Policy for the Comet Interceptor Flyby via Sequential Convex Programming

Preda¹,

Hyslop²,

Bennani³

2021

Preprint

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This paper introduces an algorithm to perform optimal reorientation of a spacecraft during a high speed flyby mission that maximizes the time a certain target is kept within the field of view of scientific instruments. The method directly handles the nonlinear dynamics of the spacecraft, sun exclusion constraint, torque and momentum limits on the reaction wheels as well as potential faults in these actuators. A sequential convex programming approach was used to reformulate non-convex pointing objectives and other constraints in terms of a series of novel convex cardinality minimization problems. These subproblems were then efficiently solved even on limited hardware resources using convex programming solvers implementing second-order conic constraints. The proposed method was applied to a scenario that involved maximizing the science time for the upcoming Comet Interceptor flyby mission developed by the European Space Agency. Extensive simulation results demonstrate the capability of the approach to generate viable trajectories even in the presence of reaction wheel failures or prior dust particle impacts.

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Section: Remarkmentioning

confidence: 99%

Optimal Science-time Reorientation Policy for the Comet Interceptor Flyby via Sequential Convex Programming

Preda¹,

Hyslop²,

Bennani³

2021

Preprint

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“…The kinematics of quadrotors are discretized using the trapezoidal method [11]. The obstacle-avoidance constraints p(t) / ∈ m are discretized as p[k] / ∈ m , which are still concave constraints [29].…”

Section: A Convex Quadratic Programming Formulationmentioning

confidence: 99%

“…In the field of convex-optimization-based quadrotor realtime trajectory planning, Auguglizro et al [28] first proposed a sequential convex programming (SCP) method to enhance the computational efficiency. Dueri et al [29] combined SCP with inter-sample obstacle avoidance methods to ensure that the generated trajectories do not cross obstacles between discrete states. Chen et al [30] developed an incremental SCP (iSCP) to incrementally add the collision-avoidance constraints during the iterative process of SCP, which leads to significant improvement in computational tractability.…”

Section: Introductionmentioning

confidence: 99%

Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning

Wang

et al. 2019

IEEE Access

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Sequential convex programming (SCP) has been recently employed in various trajectory planning problems, including entry flight, planetary landing, and aircraft formation. In SCP, convex programming subproblems are sequentially solved to obtain the optimum of original nonconvex problems. For SCPbased quadrotor trajectory planning, this paper proposes a matrix-structure-driven interior point method (MSD-IPM) to improve the efficiency of solving search directions in convex programming. In MSD-IPM, primal-dual systems for solving search directions are derived from the Karush-Kuhn-Tucher (KKT) conditions of quadrotor trajectory planning subproblems. Then, the successive elimination technique is used to solve the inverse of large-scale coefficient matrices of primal-dual systems by more efficient operations on small-scale matrices. In successive elimination, the positive definiteness of several small-scale matrices is used to enhance the numerical stability of computing search directions, and the specific diagonal structures of small-scale matrices are exploited to efficiently compute the search directions. The complexity analysis shows that the efficiency of the proposed method is about one order of magnitude higher than that of the standard IPM. The comparative studies on simulation experiments demonstrate that the MSD-IPM generally outperforms several well-known optimizers (e.g., MOSEK, SDPT3, and SeDuMi) in terms of efficiency and robustness. Finally, the indoor trajectory tracking experiments indicate that the proposed method can generate smooth trajectories for real-world applications.

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“…The inter-sampling safety can be improved by increasing the number of samples at the expense of computation, which works well in practice but lacks a formal continuous-time guarantee [5], [6], [7]. Other works addressing the gap between discrete and continuoustime system trajectories include [8], [9], [10]; for example, [8] predicts when safety will be violated during each intersample time interval, but it relies on finite violations derived from polynomial dynamics systems. Another body of literature exploits the differential flatness property of quadcopters and the convexity property of B-spline basis functions to generate Victor Freire and Xiangru Xu are with the Department of Mechanical Engineering, University of Wisconsin-Madison, Madison, WI, USA.…”

Section: Introductionmentioning

confidence: 99%

Flatness-based Quadcopter Trajectory Planning and Tracking with Continuous-time Safety Guarantees

Freire

2021

Preprint

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This work presents a convex optimization framework for the planning and tracking of quadcopter trajectories with continuous-time safety guarantees. Using B-spline basis functions and the differential flatness property of quadcopters, a second-order cone program is formulated to generate optimal trajectories that respect safe state and input constraints in the continuous-time sense. A quadratic program (QP) based on control barrier functions is proposed to guarantee bounded trajectory tracking in continuous time by filtering a nominal controller, where the QP is shown to be always feasible. Furthermore, conditions that ensure the safe tracking controller respects thrust, roll angle, and pitch angle constraints are also proposed. The effectiveness of the proposed framework is demonstrated by real-world experiments using a Crazyflie2.1 nano quadcopter.The video for the experiments of Section VI is available at https://xu.me.wisc.edu/wp-content/uploads/sites/1196/2021/10/ continuous-safety.mp4.

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Trajectory optimization with inter-sample obstacle avoidance via successive convexification

Cited by 25 publications

References 19 publications

Optimal Science-time Reorientation Policy for the Comet Interceptor Flyby via Sequential Convex Programming

Optimal Science-time Reorientation Policy for the Comet Interceptor Flyby via Sequential Convex Programming

Matrix Structure Driven Interior Point Method for Quadrotor Real-Time Trajectory Planning

Flatness-based Quadcopter Trajectory Planning and Tracking with Continuous-time Safety Guarantees

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