Trajectory opimization: Fast preview algorithm

In summary, the person is interested in trajectory optimization and has read papers and bought a book on the topic. They are looking to start programming and are considering different approaches such as analytical solutions, direct transcription with nonlinear programming, particle swarm algorithms, and evolutionary/genetic algorithms. They are looking for a fast solution that does not necessarily find the global minima, but a good enough one. They are unsure of which approach to take and are seeking advice. They mention the use of heuristics in algorithms and suggest looking into sources from game AI programming for more information.
  • #1
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Hello everyone,

I have been interested in trajectory optimization for a while now and I have read a few papers on that topic and bought the book "Spacecraft trajectory optimization" from Cambridge University Press and want to start programming with the goal to optimize a trajectory in a simplified solar system, not in real time but as close as possible, without the need of an exact solution but a preview of a good one.

The books and papers propose different approaches like
  • Analytical solutions with the primer vector
  • Direct transcription + nonlinear programming
  • particle swarm algorithms
  • evolutionary/genetic algorithms

From what I have understood so far genetic algorithms (GA's) are pretty good for finding global minima of the cost function even with a bad first guess but are pretty slow. I am looking for a solution that is as fast as possible but where finding the global minima is not required - a 'good' solution is fine. So I am still unsure of which approach to take; as mentioned before it should be consider a preview.
Particle swarm algorithms have been suggested to me as well and seem to be faster than GA's but converge slower towards the optimum, which is fine to me but I could not find any papers on the topic of speed comparisons regrading these optimal control problems.

If this is the wrong forum for questions like mine please move this post; I was unsure because this question is related to computer science an engineering as well.

Thanks for your help!
 
  • #3
I am by no means an expert, but I figured a reply from someone similarly interested would be better than no reply at all.
Heuristics in algorithms is entirely about defining the metrics of "good enough," how often those metrics are calculated, and the "time" wasted making those calculations. While an effective heuristic algorithm will come up with an equitable answer faster than a precise algorithm, they take longer to code. In a sense, you're adding three new dimensions of complexity to test. The reason to turn to heuristics is when and only when a precise algorithm takes too long to complete, and you have plenty of time to experiment.

These types of problems are addressed in real time game AI programming, specifically in path-finding algorithms, so sources from that field may also be helpful.
 

1. What is trajectory optimization?

Trajectory optimization is a process that involves finding the optimal path or trajectory for a moving object based on a set of constraints and objectives. This is typically used in fields such as robotics, aerospace engineering, and physics.

2. How does the fast preview algorithm work?

The fast preview algorithm is a method used to quickly generate a rough estimate of the optimal trajectory for a moving object. It works by first creating a simplified model of the object and its environment, and then using that model to predict the best path. This allows for faster processing and less computation compared to traditional trajectory optimization methods.

3. What are the benefits of using trajectory optimization?

Trajectory optimization can help improve the performance and efficiency of moving objects by finding the most optimal path. This can result in cost savings, increased accuracy, and reduced risk in various applications such as robot motion planning, spacecraft trajectory planning, and vehicle navigation.

4. What are some common constraints used in trajectory optimization?

Some common constraints used in trajectory optimization include physical limitations such as maximum velocity and acceleration, environmental factors like wind or obstacles, and mission requirements such as reaching a specific destination or avoiding certain areas.

5. How is trajectory optimization related to machine learning?

Trajectory optimization is often used as a component in machine learning algorithms to help improve the performance of autonomous systems. By optimizing the trajectory of a moving object, machine learning models can learn to make more accurate predictions and decisions based on the given constraints and objectives.

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