scholarly journals Kinodynamic motion planning: connecting exploration trees using trajectory optimization Methods

2004 ◽  
Author(s):  
F. Lamiraux ◽  
E. Ferre ◽  
E. Vallee
Keyword(s):  
Motion Planning ◽  
Trajectory Optimization ◽  
Optimization Methods

scholarly journals Creating Better Collision-Free Trajectory for Robot Motion Planning by Linearly Constrained Quadratic Programming

2021 ◽  
Vol 15 ◽  
Author(s):  
Yizhou Liu ◽  
Fusheng Zha ◽  
Mantian Li ◽  
Wei Guo ◽  
Yunxin Jia ◽  
...  
Keyword(s):  
Quadratic Programming ◽  
Motion Planning ◽  
Trajectory Optimization ◽  
Optimization Technique ◽  
Optimization Methods ◽  
Linear Constraints ◽  
Task Constraints ◽  
Probabilistic Sampling ◽  
Smooth Path ◽  
Linearly Constrained

Many algorithms in probabilistic sampling-based motion planning have been proposed to create a path for a robot in an environment with obstacles. Due to the randomness of sampling, they can efficiently compute the collision-free paths made of segments lying in the configuration space with probabilistic completeness. However, this property also makes the trajectories have some unnecessary redundant or jerky motions, which need to be optimized. For most robotics applications, the trajectories should be short, smooth and keep away from obstacles. This paper proposes a new trajectory optimization technique which transforms a polygon collision-free path into a smooth path, and can deal with trajectories which contain various task constraints. The technique removes redundant motions by quadratic programming in the parameter space of trajectory, and converts collision avoidance conditions to linear constraints to ensure absolute safety of trajectories. Furthermore, the technique uses a projection operator to realize the optimization of trajectories which are subject to some hard kinematic constraints, like keeping a glass of water upright or coordinating operation with dual robots. The experimental results proved the feasibility and effectiveness of the proposed method, when it is compared with other trajectory optimization methods.

Method to Calculate Aircraft VNAV Trajectory Cost Using a Performance Database

2014 ◽  
Author(s):  
Alejandro Murrieta-Mendoza ◽  
Ruxandra Botez
Keyword(s):  
Trajectory Optimization ◽  
Calculated Data ◽  
Optimization Methods ◽  
Fast Method ◽  
Computing Power ◽  
Flight Plan ◽  
Aerodynamic Model ◽  
The Given ◽  
Equations Of Motions ◽  
A Performance

Vertical Navigation (VNAV) trajectory optimization has been identified as a means to reduce fuel consumption. Due to the computing power limitations of devices such as Flight Management Systems (FMSs), it is very desirable to implement a fast method for calculating trajectory cost using optimization algorithms. Conventional trajectory optimization methods solve a set of differential equations called the aircraft equations of motions to find the optimal flight profile. Many FMSs do not use these equations, but rather a set of lookup tables with experimental, or pre-calculated data, called a Performance Database (PDB). This paper proposes a method to calculate a full trajectory flight cost using a PDB. The trajectory to be calculated is composed of climb, acceleration, cruise, descent and deceleration flight phases. The influence of the crossover altitude during climb and step climbs in cruise were considered for these calculations. Since the PDB is a set of discrete data, Lagrange linear interpolations were performed within the PDB to calculate the required values. Given a takeoff weight, the initial and final coordinates and the desired flight plan, the trajectory model provides the Top of Climb coordinates, the Top of Descent coordinates, the fuel burned and the flight time needed to follow the given flight plan. The accuracy of the trajectory costs calculated with the proposed method was validated for two aircraft; one with an aerodynamic model in FlightSIM, software developed by Presagis, and the other using the trajectory generated by the reference FMS.

Guidance Performance Benchmarking for Autonomous Rotorcraft

2014 ◽  
Vol 59 (4) ◽  
pp. 1-16 ◽  
Author(s):  
Bérénice Mettler ◽  
Zhaodan Kong ◽  
Chad Goerzen ◽  
Matthew Whalley
Keyword(s):  
Trajectory Optimization ◽  
Numerical Optimization ◽  
Performance Metrics ◽  
Optimization Methods ◽  
Urban Environments ◽  
Performance Benchmarking ◽  
Digital Terrain ◽  
Motion Primitive ◽  
Terrain Elevation ◽  
Methods Numerical

This paper describes a framework for performance evaluation of autonomous guidance systems. The elements of the framework consist of a set of spatial geometries, flight tasks, performance metrics, a flightdynamic model, and baseline solutions. The spatial benchmarks consist of six tasks in simple geometrical environments and 10 tasks in more complex urban environments based on a real digital terrain elevation map. The framework also includes a set of performance metrics used to compare trajectories. The performance baselines used in the proposed framework are near-optimal solutions computed using one of two trajectory optimization methods: numerical optimization based on nonlinear programming for the simple geometric environments and a motion primitive automaton for problems involving the urban environments. The paper concludes with a demonstration of the benchmarking framework using the Obstacle Field Navigation system developed by the Army Aeroflightdynamics Directorate.

scholarly journals Mediating Between Contact Feasibility and Robustness of Trajectory Optimization Through Chance Complementarity Constraints

2022 ◽  
Vol 8 ◽  
Author(s):  
Luke Drnach ◽  
John Z. Zhang ◽  
Ye Zhao
Keyword(s):  
Motion Planning ◽  
Constraint Satisfaction ◽  
Model Uncertainty ◽  
Trajectory Optimization ◽  
Chance Constraints ◽  
Complementarity Constraints ◽  
Trade Off ◽  
Block System ◽  
Risk Sensitive ◽  
Intermittent Contact

As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.

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