Smooth polynomial interpolation for point-to-point trajectories with vibration avoidance

Sencer, Burak; Ishizaki, Kosuke

doi:10.1109/iecon.2015.7392406

Cited by 6 publications

(5 citation statements)

References 14 publications

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“…Trajectory generation must not only describe the desired trajectory accurately, but must also have smooth kinematics profiles for increasing the precision and the durability of the system, maintaining higher tracking accuracy while avoiding exciting natural modes of the mechanical structure or servo control system [35]. To do so, the trajectory must satisfy certain constraints such as the vehicle's physical limits, safety regulations and sensor specifications.…”

Section: Velocity and Acceleration Constraintsmentioning

confidence: 99%

“…Theorem 1. Consider the rigid body dynamics (20) with the control law (27) resulting in the closed loop attitude dynamics given by (34) and (35). Then, under assumptions of the lemma, the trajectories of (34) and (35) converges to the following subsets S 3 × R 3 , given by Θ 1 = (±1, 0, 0) and Θ 2 = {(0, ±v 1 , 0), (0, ±v 2 , 0), (0, ±v 3 , 0)}, where v i (i = 1, 2, 3) are unit eigenvectors of W ρ .…”

Section: Stability Analysis Of the Proposed Control Lawmentioning

confidence: 99%

See 1 more Smart Citation

Guidance, Navigation and Control for Autonomous Quadrotor Flight in an Agricultural Field: The Case of Vineyards

Mokrane

Benallègue

Choukchou-Braham

et al. 2022

Sensors

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In this paper, we present a complete and efficient solution of guidance, navigation and control for a quadrotor platform to accomplish 3D coverage flight missions in mapped vineyard terrains. Firstly, an occupancy grid map of the terrain is used to generate a safe guiding coverage path using an Iterative Structured Orientation planning algorithm. Secondly, way-points are extracted from the generated path and added to them trajectory’s velocities and accelerations constraints. The constrained way-points are fed into a Linear Quadratic Regulator algorithm so as to generate global minimum snap optimal trajectory while satisfying both the pointing and the corridor constraints. Then, when facing unexpected obstacles, the quadrotor tends to re-plan its path in real-time locally using an Improved Artificial Potential Field algorithm. Finally, a geometric trajectory tracking controller is developed on the Special Euclidean group SE(3). The aim of this controller is to track the generated trajectory while pointing towards predetermined direction using the vector measurements provided by the inertial unit. The performance of the proposed method is demonstrated through several simulation results. In particular, safe guiding paths are achieved. Obstacle-free optimal trajectories that satisfy the way-point position, the pointing direction, and the corridor constraints, are successfully generated with optimized platform snap. Besides, the implemented geometric controller can achieve higher trajectory tracking accuracy with an absolute value of the maximum error in the order of 10−3 m.

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Section: Velocity and Acceleration Constraintsmentioning

confidence: 99%

Section: Stability Analysis Of the Proposed Control Lawmentioning

confidence: 99%

Guidance, Navigation and Control for Autonomous Quadrotor Flight in an Agricultural Field: The Case of Vineyards

Mokrane

Benallègue

Choukchou-Braham

et al. 2022

Sensors

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show abstract

“…To suppress the vibration quickly, the jerk should be continuous. However, planning the higher order curves directly may increase computation load (Sencer and Ishizaki, 2016). The general input shaping can lower the abrupt change value, while it cannot guarantee the continuous jerk.…”

Section: Principle Of Vibration Suppressionmentioning

confidence: 99%

Combined S-curve feedrate profiling and input shaping for glass substrate transfer robot vibration suppression

Liu

Chen

2018

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Purpose The glass substrate transfer robot uses flexible arm and fork to transport the glass substrate which will generate vibration. To reduce the settling time and increase productivity, the authors proposed a vibration suppression method that integrated the continuous input shaping into the S-curve feedrate profiling. Design/methodology/approach The quasi-optimal S-curve feedrate profiling is achieved by the robot model. Then the outputs of the S-curve are shaped by the continuous input shaper, which can greatly lower the vibration and shorten the settling time. Findings The robot produces vibrations because of the flexibility of the belt system and the forks; the vibration of the robot is especially obvious in the acceleration and deceleration stage and the low-speed operation stage. Because the fork fingers are flexible, vibration at the end of the fork is enlarged. Originality/value The effectiveness of the proposed method is verified by the comparative experiments conducted on a glass substrate transfer robot.

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“…For complex, nonlinear systems, feedforward motion planning or trajectory planning with minimum vibration can be determined by employing various optimization algorithms, like particle swarm optimization (PSO), and genetic algorithm (GA) [16][17][18] . In those investigations, the motion profiles are generated using polynomial functions, trapezoidal profiles, or spline curves [19,20] . On the other hand, a large number of investigations toward feedback vibration control have also been conducted by using smart materials, like piezoelectric actuators, PVDF [21] .…”

Section: Introductionmentioning

confidence: 99%

Finite-time hybrid motion/deformation terminal control for rigid/compliant systems using acceleration-based quadratic objective function

Li,

Wang,

Wang

et al. 2024

Preprint

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Nowadays, new concepts of active compliant structures employing smart materials are receiving increasing attention to design high-precision lightweight mechanisms, however, bring a new challenge to deformation control system design, especially considering the coupling with rigid motion control. An important issue for such a rigid/compliant system is to realize a fast, smooth hybrid motion/deformation control effect with minimized structural vibration in a given time interval. A rotating compliant manipulator actuated by an electric motor and distributed piezocomposite patches is utilized for investigation towards motion/deformation control. Open-loop simulations imply that structural vibration can be excited by both rigid motion control and deformation control. A finite-time terminal control design approach is developed using a new quadratic objective function which is formulated by (generalized) acceleration, instead of the state (composed of generalized displacement and velocity) and input of the system in regular formulation, to improve the terminal control effect without sharp change in the input profiles. The time-varying control law is obtained by solving a set of DREs. Pure and hybrid motion/deformation control with conventional and new objective functions are presented and discussed. The results imply that more smooth dynamic responses for hybrid motion/deformation control performance with minimized residual vibration can be obtained by using the new acceleration-based objective function, while the state and input at the terminal point are the approximate analytical steady-state. The new objective function also has unique merit in that the associated weighting matrix can be intuitively chosen with better robustness. Hybrid objective functions with a combination of the conventional and new acceleration-based terms can be employed to obtain favorable comprehensive control performance and bring a wider margin for the designers.

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Smooth polynomial interpolation for point-to-point trajectories with vibration avoidance

Cited by 6 publications

References 14 publications

Guidance, Navigation and Control for Autonomous Quadrotor Flight in an Agricultural Field: The Case of Vineyards

Guidance, Navigation and Control for Autonomous Quadrotor Flight in an Agricultural Field: The Case of Vineyards

Combined S-curve feedrate profiling and input shaping for glass substrate transfer robot vibration suppression

Finite-time hybrid motion/deformation terminal control for rigid/compliant systems using acceleration-based quadratic objective function

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