Traditional learning approaches proposed for controlling quadrotors or helicopters have focused on improving performance specific trajectories by iteratively upon a nominal controller, example from demonstrations, iterative learning, and reinforcement learning. In these schemes, however, it is not clear how the information gathered training can be used to synthesize controllers more general trajectories. Recently, efficacy of deep in inferring helicopter dynamics has been shown. Motivated...

.We present the concept of a generalized feedback Nash equilibrium (GFNE) in dynamic games, extending to games which players are subject state and input constraints. We formalize necessary sufficient conditions for (local) GFNE solutions at trajectory level, enable development efficient numerical methods their computation. Specifically, we propose Newton-style method finding game trajectories satisfy an equilibrium, can then be checked against sufficiency conditions. show that evaluation...

Contingency planning, wherein an agent generates a set of possible plans conditioned on the outcome uncertain event, is increasingly popular way for robots to act under uncertainty. In this work we take game-theoretic perspective contingency tailored multi-agent scenarios in which robot's actions impact decisions other agents and vice versa. The resulting <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">contingency game</i> allows robot...

Collision detection is a critical functionality for robotics. The degree to which objects collide cannot be represented as continuously differentiable function any shapes other than spheres. This paper proposes framework handling collision between polyhedral shapes. We frame the signed distance two bodies optimal value of convex optimization, and consider constraining in bilevel optimization problem. To avoid relying on specialized solvers, our method exploits fact that minimal point region...

We present a novel method for handling uncertainty about the intentions of non-ego players in trajectory games, with application to motion planning autonomous vehicles. Our models intention other agents by constructing multiple hypotheses objectives and constraints scene. For each candidate hypothesis, we associate Bernoulli random variable representing probability that which may or not be independent hypotheses. leverage constraint asymmetries feedback information patterns incorporate...

A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The explicitly determines an affine relationship between control and state variables, in standard Riccati recursion, giving rise feedback policies that account Since linearly-constrained LQR arises commonly robotic trajectory optimization, having a can efficiently compute these solutions important....

Mathematical Program Networks (MPNs) are introduced in this work. A MPN is a collection of interdependent Programs (MPs) which to be solved simultaneously, while respecting the connectivity pattern network defining their relationships. The structure an impacts decision variables each constituent mathematical program can influence, either directly or indirectly via solution graph constraints representing optimal decisions for decedents. This framework unifies many existing problem...

With dynamic pricing on the rise, firms are using sophisticated algorithms for price determination. These often non-interpretable and there has been a recent interest in their seemingly emergent ability to tacitly collude with each other without any prior communication whatsoever. Most of previous works investigate algorithmic collusion simple reinforcement learning (RL) based operating basic market model. Instead, we explore collusive tendencies Proximal Policy Optimization (PPO),...

We present the concept of a Generalized Feedback Nash Equilibrium (GFNE) in dynamic games, extending to games which players are subject state and input constraints. formalize necessary sufficient conditions for (local) GFNE solutions at trajectory level, enable development efficient numerical methods their computation. Specifically, we propose Newton-style method finding game trajectories satisfy an equilibrium, can then be checked against sufficiency conditions. show that evaluation general...

A method is presented for parallelizing the computation of solutions to discrete-time, linear dynamic, quadratic objective, finite-horizon optimal control problems, which we refer as LQR problems. For many applications, size these problems can be large enough that computing solution prohibitively slow when using a single processor. In this work, present novel across multiple processors. As byproduct computation, generates feedback policies are useful nonlinear and in autonomous systems. The...

A common design pattern in cyber-physical systems features a continuous plant and discrete controller feedback loop. Sampled data analysis attempts to take into consideration both the time elements of such design. In this paper we adapt an earlier algorithm for efficient ellipsoidal approximation robust sampled finite horizon viability kernels compute capture basins with linear dynamics. Using these basins, construct hybrid automaton which can verify if necessary modify exogenous input...

Stackelberg games originate where there are market leaders and followers, the actions of influence behavior followers. Mathematical modelling such results in what's called a Bilevel Optimization problem. There is an entire area research dedicated to analyzing solving problems which often complex, finding solutions for known be NP-Hard. A generalization Multilevel game we may have nested that follower is, turn, leader all lower-level players. These much more difficult solve, existing solution...

In multi-agent settings, game theory is a natural framework for describing the strategic interactions of agents whose objectives depend upon one another's behavior.Trajectory games capture these complex effects by design.In competitive this makes them more faithful interaction model than traditional "predict then plan" approaches.However, current game-theoretic planning methods have important limitations.In work, we propose two main contributions.First, introduce an offline training phase...

Two-vehicle racing is natural example of a competitive dynamic game. As with most games, there are many ways in which the underlying information pattern can be structured, resulting different equilibrium concepts. For particular, assumed plays large impact type behaviors that emerge from two interacting players. example, blocking behavior something cannot static Nash play, but could presumably leader-follower play. In this work, we develop novel model for two-player vehicle racing, complete...

Gig economy consists of two market groups connected via an intermediary. Popular examples are rideshares where passengers and drivers mediated platforms such as Uber Lyft. In a duopoly market, the must compete to attract not only by providing lower rate but also better wages. While this should indicate driver payout, pool, real world statistics does such. This goes completely against intuition that worker side gig economy, given their importance, always earn better. We attempt answer low...

Equilibrium problems representing interaction in physical environments typically require continuous strategies which satisfy opponent-dependent constraints, such as those modeling collision avoidance. However, with finite games, mixed are often desired, both from an equilibrium existence perspective well a competitive perspective. To that end, this work investigates chance-constraint-based approach to coupled constraints generalized Nash solved over pure and mixing weights simultaneously. We...

A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The explicitly determines an affine relationship between control and state variables, in standard Riccati recursion, giving rise feedback policies that account Since linearly-constrained LQR arises commonly robotic trajectory optimization, having a can efficiently compute these solutions important....

A framework is presented for handling a potential loss of observability dynamical system in provably safe way.Inspired by the fragility data-driven perception systems used autonomous vehicles, we formulate problem that arises when sensing modality fails or found to be untrustworthy during operation.We cast this as differential game played between being controlled and external factor(s) which observations are lost.The zero-sum Stackelberg (leader) trying find trajectory maximizes function...

With the growth of industrial risks and multiplication CBRNe (Chemical Biological Radiological explosive) attacks through toxic chemicals, biological or radiological threats, public services military authorities face with increasingly critical situations, whose management is strongly conditioned by fast reliable establishment an informative diagnostic. Right after attack, five first minutes are crucial to define various scenarii most dangerous for a human intervention. Therefore use robots...

A framework is presented for handling a potential loss of observability dynamical system in provably-safe way. Inspired by the fragility data-driven perception systems used autonomous vehicles, we formulate problem that arises when sensing modality fails or found to be untrustworthy during operation. We cast this as differential game played between being controlled and external factor(s) which observations are lost. The zero-sum Stackelberg (leader) trying find trajectory maximizes function...