In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation.

Abstract-This paper describes a real-time motion planning algorithm, based on the Rapidly-exploring Random Tree (RRT) approach, applicable to autonomous vehicles operating in an urban environment. Extensions to the standard RRT are predominantly motivated by: (i) the need to generate dynamically feasible plans in real-time, (ii) safety requirements, (iii) the constraints dictated by the uncertain operating (urban) environment. The primary novelty is in the use of closed-loop prediction in the framework of RRT. The proposed algorithm was at the core of the planning and control software for Team MIT's entry for the 2007 DARPA Urban Challenge, where the vehicle demonstrated the ability to complete a 60 mile simulated military supply mission, while safely interacting with other autonomous and human driven vehicles.

Abstract-Finding feasible, collision-free paths for multiagent systems can be challenging, particularly in noncommunicating scenarios where each agent's intent (e.g. goal) is unobservable to the others. In particular, finding time efficient paths often requires anticipating interaction with neighboring agents, the process of which can be computationally prohibitive. This work presents a decentralized multiagent collision avoidance algorithm based on a novel application of deep reinforcement learning, which effectively offloads the online computation (for predicting interaction patterns) to an offline learning procedure. Specifically, the proposed approach develops a value network that encodes the estimated time to the goal given an agent's joint configuration (positions and velocities) with its neighbors. Use of the value network not only admits efficient (i.e., real-time implementable) queries for finding a collisionfree velocity vector, but also considers the uncertainty in the other agents' motion. Simulation results show more than 26% improvement in paths quality (i.e., time to reach the goal) when compared with optimal reciprocal collision avoidance (ORCA), a state-of-the-art collision avoidance strategy.

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Abstract-For robotic vehicles to navigate safely and efficiently in pedestrian-rich environments, it is important to model subtle human behaviors and navigation rules (e.g., passing on the right). However, while instinctive to humans, socially compliant navigation is still difficult to quantify due to the stochasticity in people's behaviors. Existing works are mostly focused on using feature-matching techniques to describe and imitate human paths, but often do not generalize well since the feature values can vary from person to person, and even run to run. This work notes that while it is challenging to directly specify the details of what to do (precise mechanisms of human navigation), it is straightforward to specify what not to do (violations of social norms). Specifically, using deep reinforcement learning, this work develops a time-efficient navigation policy that respects common social norms. The proposed method is shown to enable fully autonomous navigation of a robotic vehicle moving at human walking speed in an environment with many pedestrians.

This paper presents a new approach to fuel-optimal path planning of multiple vehicles using a combination of linear and integer programming. The basic problem formulation is to have the vehicles move from an initial dynamic state to a final state without colliding with each other, while at the same time avoiding other stationary and moving obstacles. It is shown that this problem can be rewritten as a linear program with mixed integer/linear constraints that account for the collision avoidance. A key benefit of this approach is that the path optimization can be readily solved using the CPLEX optimization software with an AMPL/Matlab interface. An example is worked out to show that the framework of mixed integer/linear programming is well suited for path planning and collision avoidance problems. Implementation issues are also considered. In particular, we compare receding horizon strategies with fixed arrival time approaches.

Robots that navigate among pedestrians use collision avoidance algorithms to enable safe and efficient operation. Recent works present deep reinforcement learning as a framework to model the complex interactions and cooperation. However, they are implemented using key assumptions about other agents' behavior that deviate from reality as the number of agents in the environment increases. This work extends our previous approach to develop an algorithm that learns collision avoidance among a variety of types of dynamic agents without assuming they follow any particular behavior rules. This work also introduces a strategy using LSTM that enables the algorithm to use observations of an arbitrary number of other agents, instead of previous methods that have a fixed observation size. The proposed algorithm outperforms our previous approach in simulation as the number of agents increases, and the algorithm is demonstrated on a fully autonomous robotic vehicle traveling at human walking speed, without the use of a 3D Lidar.

A method for nding fuel-optimal trajectories for spacecraft subjected to avoidance requirements is introduced. These include avoidance of collisions with obstacles or other vehicles and prevention of thruster plumes from one spacecraft impinging on another spacecraft. The necessary logical constraints for avoidance are appended to a fuel-optimizing linear program by including binary variables in the optimization. The resulting problem is a mixedinteger linear program (MILP) that can be solved using available software. The logical constraints can also be used to express the con guration requirements for maneuvers where only the nal relative alignment of the vehicles is important and the assignment of spacecraft within the eet is not speci ed. The collision avoidance, trajectory optimization, and eet assignment problems can be combined into a single MILP to obtain the optimal solution for these maneuvers. The MILP problem formulation, including these various avoidance constraints, is presented, and then several examples of their application to spacecraft maneuvers, including recon guration of a satellite formation and close inspection of the International Space Station by a microsatellite, are shown. These examples clearly show that the trajectory design methods presented are particularly well suited to proposed formation ying missions that involve multiple vehicles operating in close proximity. Nomenclature