Towards reliable real-time trajectory optimization

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.