We present Residual Descent Differential Dynamic Game (RD3G), a Newton-based solver for constrained multiagent game-control problems. The proposed solver seeks a local Nash equilibrium for games where agents are coupled through their rewards and state constraints. By maintaining a dynamic set of active constraints, combined with a barrier function on satisfied constraints and a backtracking line search, the proposed method is able to satisfy state constraints while keeping the dimension of the Newton descent direction problem to a minimum. We compare the proposed method against state-of-the-art techniques and showcase the computational benefits of the RD3G algorithm on several example problems. The RD3G is up to$\mathbf{4 X}$faster and has$\mathbf{2 X}$higher convergence rate than existing approaches in higher dimensional games.

We present BuzzRacer, a palm-sized autonomous vehicle platform suitable for multi-agent autonomous racing. BuzzRacer consists of two parts. First, a software framework with multiple racetrack environments, dynamic simulation, visualization, and control pipelines. Second, a miniature autonomous vehicle platform capable of 1g acceleration and 3.5m/s top speed. BuzzRacer is an open-source project currently used at Georgia Tech in a project-based robotics course and research projects for experimental validation and benchmarking of novel planning and control algorithms.

A new belief space planning algorithm, called covariance steering Belief RoadMap (CS-BRM), is introduced, analyzed, and numerically and experimentally tested. CS-BRM is a multi-query algorithm for motion planning for dynamical systems under simultaneous motion and observation uncertainties. CS-BRM extends the probabilistic roadmap (PRM) approach to belief spaces based on the recently developed theory of covariance steering (CS) that enables guaranteed satisfaction of terminal belief constraints in finite time. The nodes in the CS-BRM are sampled in the belief space and represent distributions of the system states. A covariance steering controller steers the system from one BRM node to another, thus acting as an edge controller of the corresponding belief graph that ensures belief constraint satisfaction. After the edge controller is computed, a specific edge cost is assigned to that edge. The CS-BRM algorithm allows the sampling of non-stationary belief nodes and thus is able to explore the velocity space and find much more efficient trajectories than previous BRM methods. The performance of CS-BRM is evaluated and compared to previous belief space planning approaches using several numerical examples and experimental demonstrations, illustrating the benefits of the proposed approach.

In this paper, we present a novel Model Predictive Control method for autonomous robot planning and control subject to arbitrary forms of uncertainty. The proposed Risk-Aware Model Predictive Path Integral (RA-MPPI) control utilizes the Conditional Value-at-Risk (CVaR) measure to generate optimal control actions for safety-critical robotic applications. Different from most existing Stochastic MPCs and CVaR optimization methods that linearize the original dynamics and formulate control tasks as convex programs, the proposed method directly uses the original dynamics without restricting the form of the cost functions or the noise. We apply the novel RA-MPPI controller to an autonomous vehicle to perform aggressive driving maneuvers in cluttered environments. Our simulations and experiments show that the proposed RA-MPPI controller can achieve similar lap times with the baseline MPPI controller while encountering significantly fewer collisions. The proposed controller performs online computation at an update frequency of up to 80 Hz, utilizing modern Graphics Processing Units (GPUs) to multi-thread the generation of trajectories as well as the CVaR values.

This paper presents a novel control approach for autonomous systems operating under uncertainty. We combine Model Predictive Path Integral (MPPI) control with Covariance Steering (CS) theory to obtain a robust controller for general nonlinear systems. The proposed Covariance-Controlled Model Predictive Path Integral (CC-MPPI) controller addresses the performance degradation observed in some MPPI implementations owing to unexpected disturbances and uncertainties. Namely, in cases where the environment changes too fast or the simulated dynamics during the MPPI rollouts do not capture the noise and uncertainty in the actual dynamics, the baseline MPPI implementation may lead to divergence. The proposed CC-MPPI controller avoids divergence by controlling the dispersion of the rollout trajectories at the end of the prediction horizon. Furthermore, the CC-MPPI has adjustable trajectory sampling distributions that can be changed according to the environment to achieve efficient sampling. Numerical examples using a ground vehicle navigating in challenging environments demonstrate the proposed approach.