Towards reliable real-time trajectory optimization

TL;DR

The work tackles non-convex trajectory optimization for robotics by addressing initialization sensitivity and scalability with four algorithms. It introduces constraint remodeling to reveal hidden convex structures and leverages GPU acceleration for real-time performance; it then extends to batch optimization, projection-based guidance, and multi-agent coordination. Collectively, the methods deliver substantial gains in computation time, scalability, and robustness across static, dynamic, and multi-agent scenarios, with real-world demonstrations validating practicality. Together these contributions enable reliable, real-time motion planning in cluttered and dynamic environments, advancing robotic navigation capabilities at scale.

Abstract

Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations. However, current trajectory optimization approaches have two main challenges. Firstly, their solution heavily depends on the initial guess, and they are prone to get stuck in local minima. Secondly, they face scalability limitations by increasing the number of constraints. This thesis endeavors to tackle these challenges by introducing four innovative trajectory optimization algorithms to improve reliability, scalability, and computational efficiency. There are two novel aspects of the proposed algorithms. The first key innovation is remodeling the kinematic constraints and collision avoidance constraints. Another key innovation lies in the design of algorithms that effectively utilize parallel computation on GPU accelerators. By using reformulated constraints and leveraging the computational power of GPUs, the proposed algorithms of this thesis demonstrate significant improvements in efficiency and scalability compared to the existing methods. Parallelization enables faster computation times, allowing for real-time decision-making in dynamic environments. Moreover, the algorithms are designed to adapt to changes in the environment, ensuring robust performance. Extensive benchmarking for each proposed optimizer validates their efficacy. Overall, this thesis makes a significant contribution to the field of trajectory optimization algorithms. It introduces innovative solutions that specifically address the challenges faced by existing methods. The proposed algorithms pave the way for more efficient and robust motion planning solutions in robotics by leveraging parallel computation and specific mathematical structures.

Figures (43)

• Figure 1: Motion planning examples in a (a) mobile robot (the sequence of positions are shown as a blue trajectory). (b): manipulator ( the sequence of joint motions is shown in transparent color)
• Figure 3: Illustration of a convex and non-convex set. (a) The line segment between points $\xi_{1}$ and $\xi_{2}$ is entirely contained within the green set. (b) In contrast, a portion of the line segment connecting $\xi_{1}$ and $\xi_{2}$ extends outside of the green set.
• Figure 4: Illustration of a Convex and Non-Convex function. (a) The function remains below or on the line segment, connecting two points. (b) A a portion of $f(\xi)$ is situated above the line segment connecting $\xi_{1}$ and $\xi_{2}$.
• Figure 5: Local minima in a convex (a) and non-convex function(b)
• Figure 6: Demonstration of how initial guesses (red and purple points) can affect the solution of a convex and non-convex function. (a) In a convex function, both the purple and red points converge to the same global minimum. (b) In a non-convex function, distinct local minima are reached for each of these initial guesses.

Theorems & Definitions (6)

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