scholarly journals Time-Optimal Trajectory Generation for Path Following with Bounded Acceleration and Velocity

2012 ◽  
Author(s):  
Tobias Kunz ◽  
Mike Stilman
Keyword(s):  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Path Following ◽  
Time Optimal

Time-Optimal Trajectory Generation of Rotary Cranes with Load Sway Reduction Using Only Horizontal Boom Motion

2021 ◽  
Author(s):  
Abdallah Farrage ◽  
Hideki Takahashi ◽  
Kenichi Terauchi ◽  
Shintaro Sasai ◽  
Hitoshi Sakurai ◽  
...  
Keyword(s):  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Time Optimal

A Time-optimal Trajectory Generation Approach with Non-uniform B-splines

2021 ◽  
Vol 19 (12) ◽  
pp. 3947-3955
Author(s):  
Thanh Phan-Huu ◽  
Vo Hoang Nguyen ◽  
Ulrich Konigorski
Keyword(s):  
Optimal Trajectory ◽  
Trajectory Generation ◽  
B Splines ◽  
Time Optimal

An Efficient Approach of Time-Optimal Trajectory Generation for the Fully Autonomous Navigation of the Quadrotor

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Wei Dong ◽  
Ye Ding ◽  
Jie Huang ◽  
Xiangyang Zhu ◽  
Han Ding
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Trajectory Tracking ◽  
Linear Programming Problem ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Nurbs Curve ◽  
Tracking Controller ◽  
Time Optimal ◽  
Trajectory Tracking Controller

In this work, a time-optimal trajectory generation approach is developed for the multiple way-point navigation of the quadrotor based on the nonuniform rational B-spline (NURBS) curve and linear programming. To facilitate this development, the dynamic model of the quadrotor is formulated first. Then, the geometric trajectory regarding multiple way-point navigation is constructed based on the NURBS curve. With the constructed geometric trajectory, a time-optimal interpolation problem is imposed considering the velocity, acceleration, and jerk constraints. This optimization problem is solved in two steps. In the first step, a preliminary result is obtained by solving a linear programming problem without jerk constraints. Then by introducing properly relaxed jerk constraints, a second linear programming problem is formulated based on the preliminarily obtained result, and the time-optimal problem can be fully solved in this way. Subsequently, a nonlinear trajectory tracking controller is developed to track the generated trajectory. The feasibilities of the proposed trajectory generation approach as well as the tracking controller are verified through both simulations and real-time experiments. With enhanced computational efficiency, the proposed approach can generate trajectory for an indoor environment with the smooth acceleration profile and moderate velocity V≈1 m/s in real-time, while guaranteeing velocity, acceleration, and jerk constraints: Vmax=1 m/s, Amax=2 m/s2, and Jmax=5 m/s3. In such a case, the trajectory tracking controller can closely track the reference trajectory with cross-tracking error less than 0.05 m.

Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully Specified Paths With G1-Discontinuities

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Eric Barnett ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Optimal Solution ◽  
Test System ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Cable Tension ◽  
Time Optimal ◽  
Optimal Trajectory Planning

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is converted to a dynamic technique and adapted for use with cable-driven parallel robots, which exhibit cable tension and motor torque constraints. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the cable-tension constraints are imposed directly and fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. MTTS is applied to a test system and path, and compared to the bang–bang technique. With the same constraints, the results obtained with both techniques are found to be very close. However, MTTS can be applied to a wider variety of paths, and accepts constraints on jerk and total acceleration that would be difficult to apply using the bang–bang approach.

Time-Optimal Trajectory Planning of Cable-Driven Parallel Mechanisms for Fully-Specified Paths With G1 Discontinuities

2013 ◽  
Author(s):  
Eric Barnett ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Optimal Trajectory ◽  
Trajectory Generation ◽  
Optimal Solution ◽  
Vertical Direction ◽  
Parallel Robots ◽  
Parallel Mechanisms ◽  
Time Optimal ◽  
Time Required ◽  
Optimal Trajectory Planning

Time-optimal trajectory planning (TOTP) is a well-studied problem in robotics and manufacturing, which involves the minimization of the time required for the operation point of a mechanism to follow a path, subject to a set of constraints. A TOTP technique, designed for fully-specified paths that include abrupt changes in direction, was previously introduced by the first author of this paper: an incremental approach called minimum-time trajectory shaping (MTTS) was used. In the current paper, MTTS is adapted for use with cable-driven parallel robots, which exhibit the additional constraint that all cable tensions remain positive along a path to be followed. For many applications, cable tensions along a path are verified after trajectory generation, rather than imposed during trajectory generation. For the technique proposed in this paper, the minimum-tension constraint is imposed directly and is fully integrated with MTTS, during trajectory generation, thus maintaining a time-optimal solution. This approach is relevant for cable-driven mechanism applications that involve high accelerations, particularly in the vertical direction.

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