This paper presents a novel approach to improve the Model Predictive Path Integral (MPPI) control by using a transformer to initialize the mean control sequence. Traditional MPPI methods often struggle with sample efficiency and computational costs due to suboptimal initial rollouts. We propose TransformerMPPI, which uses a transformer trained on historical control data to generate informed initial mean control sequences. TransformerMPPI combines the strengths of the attention mechanism in transformers and sampling-based control, leading to improved computational performance and sample efficiency. The ability of the transformer to capture long-horizon patterns in optimal control sequences allows TransformerMPPI to start from a more informed control sequence, reducing the number of samples required, and accelerating convergence to optimal control sequence. We evaluate our method on various control tasks, including avoidance of collisions in a 2D environment and autonomous racing in the presence of static and dynamic obstacles. Numerical simulations demonstrate that TransformerMPPI consistently outperforms traditional MPPI algorithms in terms of overall average cost, sample efficiency, and computational speed in the presence of static and dynamic obstacles.

We present an approach to ensure safe and deadlock-free navigation for decentralized multi-robot systems operating in constrained environments, including doorways and intersections. Although many solutions have been proposed to ensure safety, preventing deadlocks in a decentralized fashion with global consensus remains an open problem. We first formalize the objective as a non-cooperative, non-communicative, partially observable multi-robot navigation problem in constrained spaces with multiple conflicting agents, which we term as \emph{social mini-games}. Our approach to ensuring liveness rests on two novel insights: $(i)$ there exists a mixed-strategy Nash equilibrium that allows decentralized robots to perturb their state onto \textit{liveness sets} i.e. states where robots are deadlock-free and $(ii)$ forward invariance of liveness sets can be achieved identical to how control barrier functions (CBFs) guarantee forward invariance of safety sets. We evaluate our approach in simulation as well on physical robots using F$1/10$ robots, a Clearpath Jackal, as well as a Boston Dynamics Spot in a doorway and corridor intersection scenario. Compared to both fully decentralized and centralized approaches with and without deadlock resolution capabilities, we demonstrate that our approach results in safer, more efficient, and smoother navigation, based on a comprehensive set of metrics including success rate, collision rate, stop time, change in velocity, path deviation, time-to-goal, and flow rate.

In this paper, we consider the motion planning problem in Gaussian belief space for minimum sensing navigation. Despite the extensive use of sampling-based algorithms and their rigorous analysis in the deterministic setting, there has been little formal analysis of the quality of their solutions returned by sampling algorithms in Gaussian belief space. This paper aims to address this lack of research by examining the asymptotic behavior of the cost of solutions obtained from Gaussian belief space based sampling algorithms as the number of samples increases. To that end, we propose a sampling based motion planning algorithm termed Information Geometric PRM* (IG-PRM*) for generating feasible paths that minimize a weighted sum of the Euclidean and an information-theoretic cost and show that the cost of the solution that is returned is guaranteed to approach the global optimum in the limit of large number of samples. Finally, we consider an obstacle-free scenario and compute the optimal solution using the "move and sense" strategy in literature. We then verify that the cost returned by our proposed algorithm converges to this optimal solution as the number of samples increases.