2020/01/21 by P. S. Naga Jyotish, Jyotish, P. S. Naga, Bharath Gopalakrishnan +10
Computer Science · Engineering · #Adaptive Control of Nonlinear Systems #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #Robotic Path Planning Algorithms #Robotics (cs.RO) #Systems and Control (eess.SY) #Target Tracking and Data Fusion in Sensor Networks #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2001.09007
openalex publication_date 2020/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The probabilistic velocity obstacle (PVO) extends the concept of velocity\nobstacle (VO) to work in uncertain dynamic environments. In this paper, we show\nhow a robust model predictive control (MPC) with PVO constraints under\nnon-parametric uncertainty can be made computationally tractable. At the core\nof our formulation is a novel yet simple interpretation of our robust MPC as a\nproblem of matching the distribution of PVO with a certain desired\ndistribution. To this end, we propose two methods. Our first baseline method is\nbased on approximating the distribution of PVO with a Gaussian Mixture Model\n(GMM) and subsequently performing distribution matching using Kullback Leibler\n(KL) divergence metric. Our second formulation is based on the possibility of\nrepresenting arbitrary distributions as functions in Reproducing Kernel Hilbert\nSpace (RKHS). We use this foundation to interpret our robust MPC as a problem\nof minimizing the distance between the desired distribution and the\ndistribution of the PVO in the RKHS. Both the RKHS and GMM based formulation\ncan work with any uncertainty distribution and thus allowing us to relax the\nprevalent Gaussian assumption in the existing works. We validate our\nformulation by taking an example of 2D navigation of quadrotors with a\nrealistic noise model for perception and ego-motion uncertainty. In particular,\nwe present a systematic comparison between the GMM and the RKHS approach and\nshow that while both approaches can produce safe trajectories, the former is\nhighly conservative and leads to poor tracking and control costs. Furthermore,\nRKHS based approach gives better computational times that are up to one order\nof magnitude lesser than the computation time of the GMM based approach.\n