Amith Manoharan - Research

π -MPPI: A Projection-Based Model Predictive Path Integral Scheme for Smooth Optimal Control of Fixed-Wing Aerial Vehicles

Model Predictive Path Integral (MPPI) is a popular sampling-based Model Predictive Control (MPC) algorithm for nonlinear systems. It optimizes trajectories by sampling control sequences and averaging them. However, a key issue with MPPI is the non-smoothness of the optimal control sequence, leading to oscillations in systems like fixed-wing aerial vehicles (FWVs). Existing solutions use post-hoc smoothing, which fails to bound control derivatives. This letter introduces a new approach: we add a projection filter π to minimally correct control samples, ensuring bounds on control magnitude and higher-order derivatives. The filtered samples are then averaged using MPPI, leading to our π-MPPI approach. We minimize computational overhead by using a neural accelerated custom optimizer for the projection filter. π-MPPI offers a simple way to achieve arbitrary smoothness in control sequences. While we focus on FWVs, this projection filter can be integrated into any MPPI pipeline. Applied to FWVs, π-MPPI is easier to tune than the baseline, resulting in smoother, more robust performance.

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Bi-level Trajectory Optimization on Uneven Terrains with Differentiable Wheel-Terrain Interaction Model

Navigation of wheeled vehicles on uneven terrain necessitates going beyond the 2D approaches for trajectory planning. Specifically, it is essential to incorporate the full 6dof variation of vehicle pose and its associated stability cost in the planning process. To this end, most recent works aim to learn a neural network model to predict the vehicle evolution. However, such approaches are data-intensive and fraught with generalization issues. In this paper, we present a purely model-based approach that just requires the digital elevation information of the terrain. Specifically, we express the wheel-terrain interaction and 6dof pose prediction as a non-linear least squares (NLS) problem. As a result, trajectory planning can be viewed as a bi-level optimization. The inner optimization layer predicts the pose on the terrain along a given trajectory, while the outer layer deforms the trajectory itself to reduce the stability and kinematic costs of the pose. We improve the state-of-the-art in the following respects. First, we show that our NLS based pose prediction closely matches the output from a high-fidelity physics engine. This result coupled with the fact that we can query gradients of the NLS solver, makes our pose predictor, a differentiable wheel-terrain interaction model. We further leverage this differentiability to efficiently solve the proposed bi-level trajectory optimization problem. Finally, we perform extensive experiments, and comparison with a baseline to showcase the effectiveness of our approach in obtaining smooth, stable trajectories.

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Multi-agent Target Defense Game with Learned Defender to Attacker Assignment

This paper considers a variant of pursuit-evasion games where multiple attacker unmanned aerial vehicles (UAVs) are trying to converge on a target. The goal is to use a set of defender UAVs to save the target by ensuring they converge on the attackers before the latter converge to the target. The core challenge lies in appropriately assigning a particular defender to an attacker. The simple heuristic assignment based on Euclidean distance between the attacker and defender performs poorly. This paper presents a data-driven solution assuming that the attacker uses a known optimal control policy. We show how massive offline simulations can be leveraged to predict the optimal cost/value function incurred by the defender to converge on an attacker for a given target trajectory. We use this optimal cost/value function as a true measure of separation between an attacker and a defender. We use it as the guiding heuristic in the Hungarian algorithm for computing defender-attacker assignments. We perform extensive simulations to validate our approach wherein we couple the learned assignment with a non-linear model predictive controller to perform realistic simulations. We show that our assignment approach outperforms that based on the Euclidean heuristic in terms of the number of successful attempts by the defenders.

Learning-based NMPC Framework for Car Racing Cinematography Using Fixed-Wing UAV

A learning-based nonlinear model predictive control (L-NMPC) scheme is designed for the iterative task of filming a race-car using a gimbaled camera mounted on a fixed-wing autonomous aerial vehicle (AAV). The controller is capable of avoiding the environmental obstacles that block the path of the AAV. It also ensures that the car always lies in the field of view (FOV) of the camera while satisfying the control and state constraints. The controller is able to learn from the previous iterations and improve the tracking performance with the help of reinforcement learning (RL). Simulation results are given to demonstrate the efficacy of the proposed learning-based control scheme.

Cooperative Localization and Path planning using NMPC

Round the clock delivery of essential supplies like medicines from one location to another is an important application of unmanned vehicles. In order to perform this task, the vehicle needs to navigate from a source location (S) to a goal (G). Usually, GPS with inertial measurement is used for navigating the vehicle. However, there are many situations where GPS may not be available - primarily due to interference or lack of required number of available satellites at the desired location/region. Under such circumstances, the vehicle needs to localize using relative bearing or range measurements from known landmarks available in the area. If multiple vehicles are there, then the vehicles itself can be considered as landmarks for other vehicles. They can move cooperatively so as to form a connected graph including the landmarks and vehicles. So, we are proposing a Nonlinear Model Predictive Control (NMPC) approach for finding optimal control inputs for the vehicles such that the vehicles act in a cooperative fashion and move from a source point to a goal point, while choosing a path that will cover enough landmarks for localization. An Extended Kalman Filter (EKF) will be used for estimating vehicle positions using only relative bearing measurements.

NMPC Based Approach for Cooperative Target Defence

We consider a three-agent pursuit-evasion problem in which an attacker pursues to capture a target, while a defender tries to intercept the attacker to protect the target. The target and the defender cooperate with each other such that the defender can intercept the attacker while the target can escape capture. The target-defender team uses Nonlinear Model Predictive Control (NMPC) to compute their optimal control inputs while assuming the attacker to use conventional missile guidance laws. However, the attacker’s guidance law is not known to the target-defender team. Perfect knowledge of the attacker states is assumed to be unknown, hence an Extended Kalman Filter (EKF) is used to estimate the state of the attacker. Two cases of target maneuver are considered. In the first case, the target moves with a constant speed, and in the second case, the target does not move unless it is strictly necessary.

Three Dimensional UAV Path Following Using SDRE Guidance

Path following is an essential requirement for unmanned aerial vehicles. Typically, these paths are in three dimensions and the shape of the paths are application dependent. Mapping applications require stationary paths while moving target tracking with a stand-off distance involves moving reference paths. A path following strategy is required that can be used for stationary and moving path following applications and is robust to wind disturbances. In this paper, we propose an adaptive optimal guidance strategy using State Dependent Ricatti Equation (SDRE) approach. Comparison of the guidance law is ascertained and the approach is evaluated under different wind and target motion conditions. The guidance law shows robust performance up to 10 m/s wind speed and can follow different geometric reference paths.

Right of Way Rules based Collision Avoidance Approach Using Model Predictive Control

This paper presents a Model Predictive Control (MPC) based collision avoidance scheme for unmanned aerial vehicles (UAVs) in civilian airspace consisting of manned and unmanned aerial vehicles. The MPC formulation takes the Federal Aviation Regulations for collision avoidance mid-air collision scenarios into account. The optimal control inputs to the UAV in the form of angular velocities are computed by optimizing the MPC cost function for a finite prediction horizon. The algorithm is evaluated for pairwise and multi-UAV conflict scenarios and compared against inverse proportional navigation (IPN) collision avoidance approach. The results show that MPC has lower control effort than the IPN while achieving similar performance of IPN.

Geostationary Orbit Payload Improvement using Lunar Gravity Assist

While launching communication satellites, low inclined Geostationary Transfer Orbits (GTO) are preferred. Hohmann transfer is used to change the orbit from GTO to Geostationary orbit (GSO). The low inclined GTO design has limitations on launch vehicle configuration design. To avoid this specific issue, high inclined GTO can have optimum launch vehicle configuration design, which gives significant payload improvement. Orbital transfer from high inclined GTO to GSO demands higher incremental velocity. However, this penalty due to high inclined GTO to GSO transfer can be catered by lunar flyby technique. The orbital inclination change is done by using the gravity field of the Moon. In this project, advantage of lunar gravity assist technique over conventional method is investigated.