In this article, we propose a nonlinear receding horizon game-theoretic planner for autonomous cars in competitive scenarios with other cars. The online planner is specifically formulated for a multiple-car autonomous racing game, in which each car tries to advance along a given track as far as possible with respect to the other cars. The algorithm extends previous work on game-theoretic planning for single-integrator agents to be suitable for autonomous cars in the following ways: 1) by representing the trajectory as a piecewise polynomial; 2) incorporating bicycle kinematics into the trajectory; and 3) enforcing constraints on path curvature and acceleration. The game-theoretic planner iteratively plans a trajectory for the ego vehicle and then the other vehicles in sequence until convergence. Crucially, the trajectory optimization includes a sensitivity term that allows the ego vehicle to reason about how much the other vehicles will yield to the ego vehicle to avoid collisions. The resulting trajectories for the ego vehicle exhibit rich game strategies such as blocking, faking, and opportunistic overtaking. The game-theoretic planner is shown to significantly outperform a baseline planner using model-predictive control, which does not take interaction into account. The performance is validated in high-fidelity numerical simulations with three cars, in experiments with two small-scale autonomous cars, and in experiments with a full-scale autonomous car racing against a simulated vehicle (video is available at https://youtube.com/playlist?list=PLmIcLEh8KMje4rYBqRANDuKvqFvj7LCRp).

We propose a scalable cooperative control approach which coordinates a group of rigidly connected autonomous surface vessels to track desired trajectories in a planar water environment as a single floating modular structure. Our approach leverages the implicit information of the structure's motion for force and torque allocation without explicit communication among the robots. In our system, a leader robot steers the entire group by adjusting its force and torque according to the structure's deviation from the desired trajectory, while follower robots run distributed consensus-based controllers to match their inputs to amplify the leader's intent using only onboard sensors as feedback. To cope with the nonlinear system dynamics in the water, the leader robot employs a nonlinear model predictive controller (NMPC), where we experimentally estimated the dynamics model of the floating modular structure in order to achieve superior performance for leader-following control. Our method has a wide range of potential applications in transporting humans and goods in many of today's existing waterways. We conducted trajectory and orientation tracking experiments in hardware with three custom-built autonomous modular robotic boats, called Roboat, which are capable of holonomic motions and onboard state estimation. Simulation results with up to 65 robots also prove the scalability of our proposed approach.

In this article, we propose an online 3-D planning algorithm for a drone to race competitively against a single adversary drone. The algorithm computes an approximation of the Nash equilibrium in the joint space of trajectories of the two drones at each time step, and proceeds in a receding horizon fashion. The algorithm uses a novel sensitivity term, within an iterative best response computational scheme, to approximate the amount by which the adversary will yield to the ego drone to avoid a collision. This leads to racing trajectories that are more competitive than without the sensitivity term. We prove that the fixed point of this sensitivity enhanced iterative best response satisfies the first-order optimality conditions of a Nash equilibrium. We present results of a simulation study of races with 2-D and 3-D race courses, showing that our game theoretic planner significantly outperforms a model predictive control (MPC) racing algorithm. We also present results of multiple drone racing experiments on a 3-D track in which drones sense each others' relative position with onboard vision. The proposed game theoretic planner again outperforms the MPC opponent in these experiments where drones reach speeds up to 1.25 m/s.

In this paper, we propose a control algorithm to collectively transport an object using a group of relatively low-cost robots. We address this problem using the robust caging, which features reliable object closure with minimum number of robots, and requires no high-precision control capability on the individual robot. Given a 2-D convex object, the proposed method uses the quality of complete robustness to first optimize the number of robots in the initial formation, and then reorient and move the formation. The method is free of force analysis, and therefore less prone to sensor errors and failures. Compared with state-of-the-art multirobot object transport approaches, which require more robots and rely heavily on high-precision control, such as force and torque feedback control, our method uses fewer robots and has high tolerance to control noises. We performed both simulation and real-time experiments to demonstrate the performance of our method. We conclude that the proposed robust caging is promising under reduced number of robots and a certain level of control noises in multirobot object transport tasks.

We present a framework to enable a fleet of rigidly attached quadrotor aerial robots to transport heavy objects along a known reference trajectory without inter-robot communication or centralized coordination. Leveraging a distributed wrench controller, we provide exponential stability guarantees for the entire assembly, under a mild geometric condition. This is achieved by each quadrotor independently solving a local optimization problem to counteract the biased torque effects from each robot in the assembly. We rigorously analyze the controllability of the object, design a distributed compensation scheme to address these challenges, and show that the resulting strategy collectively guarantees full group control authority. To ensure feasibility for online implementation, we derive bounds on the net desired control wrench, characterize the output wrench space of each quadrotor, and perform subsequent trajectory optimization under these input constraints. We thoroughly validate our method in simulation with eight quadrotors transporting a heavy object in a cluttered environment subject to various sources of uncertainty, and demonstrate the algorithm's resilience.

This paper introduces the Buffered Input Cell as a reciprocal collision avoidance method for multiple vehicles with high-order linear dynamics, extending recently proposed methods based on the Buffered Voronoi Cell [1] and generalized Voronoi diagrams [2]. We prove that if each vehicle's control input remains in its Buffered Input Cell at each time step, collisions will be avoided indefinitely. The method is fast, reactive, and only requires that each vehicle measures the relative position of neighboring vehicles. We incorporate this collision avoidance method as one layer of a complete lane change control stack for autonomous cars in a freeway driving scenario. The lane change control stack comprises a decision-making layer, a trajectory planning layer, a trajectory following feedback controller, and the Buffered Input Cell for collision avoidance. We show in simulations that collisions are avoided with multiple vehicles simultaneously changing lanes on a freeway. We also show in simulations that autonomous cars using the BIC method effectively avoid collisions with an aggressive human-driven car.

This paper presents a method for controlling a swarm of quadrotors to perform agile interleaved maneuvers while holding a fixed relative formation, or transitioning between different formations. The method prevents collisions within the swarm, as well as between the quadrotors and static obstacles in the environment. The method is built upon the existing notion of a virtual structure, which serves as a framework with which to plan and execute complex interleaved trajectories, and also gives a simple, intuitive interface for a single human operator to control an arbitrarily large aerial swarm in real time. The virtual structure concept is integrated with differential flatness-based feedback control to give an end-to-end integrated swarm teleoperation system. Collision avoidance is achieved by using multiple layered potential fields. Our method is demonstrated in hardware experiments with groups of 3-5 quadrotors teleoperated by a single human operator, and simulations of 200 quadrotors teleoperated by a single human operator.

This paper proposes a novel decentralized algorithm that coordinates the forces of a group of robots during a cooperative manipulation task. The highlight of our approach is that no communication is needed between any two robots. Our underlying intuition is that every follower robot can measure the direction of the movement of the object and then applies its force along that direction to reinforce the movement. We prove that using our algorithm, all followers' forces will synchronize to the direction of the force applied by one leader robot, who guides the robotic fleet to its destination. We first verify our algorithm by simulation in a physics engine, where 20 robots transport a chair collectively. We then validate our algorithm in hardware experiments by building four low-cost robots, equipped with force and velocity sensors, to transport a cardboard box in a laboratory environment. In addition, our algorithm allows the leader to be a human, and we also demonstrate the human-swarm cooperation in our manipulation experiments.