Vivek K. Adajania

Vivek Kantilal Adajania, Houman Masnavi, Fatemeh Rastgar et al.

Most commercially available fixed-wing aerial vehicles (FWV) can carry only small, lightweight computing hardware such as Jetson TX2 onboard. Solving non-linear trajectory optimization on these computing resources is computationally challenging even while considering only the kinematic motion model. Most importantly, the computation time increases sharply as the environment becomes more cluttered. In this paper, we take a step towards overcoming this bottleneck and propose a trajectory optimizer that achieves online performance on both conventional laptops/desktops and Jetson TX2 in a typical urban environment setting. Our optimizer builds on the novel insight that the seemingly non-linear trajectory optimization problem for FWV has an implicit multi-convex structure. Our optimizer exploits these computational structures by bringing together diverse concepts from Alternating Minimization, Bregman iteration, and Alternating Direction Method of Multipliers. We show that our optimizer outperforms the state-of-the-art implementation of sequential quadratic programming approach in optimal control solver ACADO in computation time and solution quality measured in terms of control and goal reaching cost.

Vivek K. Adajania, Aditya Sharma, Anish Gupta et al.

Standard Model Predictive Control (MPC) or trajectory optimization approaches perform only a local search to solve a complex non-convex optimization problem. As a result, they cannot capture the multi-modal characteristic of human driving. A global optimizer can be a potential solution but is computationally intractable in a real-time setting. In this paper, we present a real-time MPC capable of searching over different driving modalities. Our basic idea is simple: we run several goal-directed parallel trajectory optimizations and score the resulting trajectories based on user-defined meta cost functions. This allows us to perform a global search over several locally optimal motion plans. Although conceptually straightforward, realizing this idea in real-time with existing optimizers is highly challenging from technical and computational standpoints. With this motivation, we present a novel batch non-holonomic trajectory optimization whose underlying matrix algebra is easily parallelizable across problem instances and reduces to computing large batch matrix-vector products. This structure, in turn, is achieved by deriving a linearization-free multi-convex reformulation of the non-holonomic kinematics and collision avoidance constraints. We extensively validate our approach using both synthetic and real data sets (NGSIM) of traffic scenarios. We highlight how our algorithm automatically takes lane-change and overtaking decisions based on the defined meta cost function. Our batch optimizer achieves trajectories with lower meta cost, up to 6x faster than competing baselines.