Hardik Parwana

Keyvan Majd, Hardik Parwana, Bardh Hoxha et al.

Articulated vehicles such as tractor-trailers, yard trucks, and similar platforms must often reverse and maneuver in cluttered spaces where pedestrians are present. We present how Barrier-Rate guided Model Predictive Path Integral (BR-MPPI) control can solve navigation in such challenging environments. BR-MPPI embeds Control Barrier Function (CBF) constraints directly into the path-integral update. By steering the importance-sampling distribution toward collision-free, dynamically feasible trajectories, BR-MPPI enhances the exploration strength of MPPI and improves robustness of resulting trajectories. The method is evaluated in the high-fidelity CarMaker simulator on a 12 [m] tractor-trailer tasked with reverse and forward parking in a parking lot. BR-MPPI computes control inputs in above 100 [Hz] on a single GPU (for scenarios with eight obstacles) and maintains better parking clearance than a standard MPPI baseline and an MPPI with collision cost baseline.

Hardik Parwana, Dimitra Panagou

Propagating state distributions through a generic, uncertain nonlinear dynamical model is known to be intractable and usually begets numerical or analytical approximations. We introduce a method for state prediction, called the Expansion-Compression Unscented Transform, and use it to solve a class of online policy optimization problems. Our proposed algorithm propagates a finite number of sigma points through a state-dependent distribution, which dictates an increase in the number of sigma points at each time step to represent the resulting distribution; this is what we call the expansion operation. To keep the algorithm scalable, we augment the expansion operation with a compression operation based on moment matching, thereby keeping the number of sigma points constant across predictions over multiple time steps. Its performance is empirically shown to be comparable to Monte Carlo but at a much lower computational cost. Under state and control input constraints, the state prediction is subsequently used in tandem with a proposed variant of constrained gradient-descent for online update of policy parameters in a receding horizon fashion. The framework is implemented as a differentiable computational graph for policy training. We showcase our framework for a quadrotor stabilization task as part of a benchmark comparison in safe-control-gym and for optimizing the parameters of a Control Barrier Function based controller in a leader-follower problem.

Hardik Parwana, Dimitra Panagou

Quadratic Program(QP) based state-feedback controllers, whose inequality constraints bound the rate of change of control barrier(CBFs) and lyapunov function with a class-$\mathcal{K}$ function of their values, are sensitive to the parameters of these class-$\mathcal{K}$ functions. The construction of valid CBFs, however, is not straightforward, and for arbitrarily chosen parameters of the QP, the system trajectories may enter states at which the QP either eventually becomes infeasible, or may not achieve desired performance. In this work, we pose the control synthesis problem as a differential policy whose parameters are optimized for performance over a time horizon at high level, thus resulting in a bi-level optimization routine. In the absence of knowledge of the set of feasible parameters, we develop a Recursive Feasibility Guided Gradient Descent approach for updating the parameters of QP so that the new solution performs at least as well as previous solution. By considering the dynamical system as a directed graph over time, this work presents a novel way of optimizing performance of a QP controller over a time horizon for multiple CBFs by (1) using the gradient of its solution with respect to its parameters by employing sensitivity analysis, and (2) backpropagating these as well as system dynamics gradients to update parameters while maintaining feasibility of QPs.

Hardik Parwana, Mangal Kothari

The attitude space has been parameterized in various ways for practical purposes. Different representations gain preferences over others based on their intuitive understanding, ease of implementation, formulaic simplicity, and physical as well as mathematical complications involved in using them. This technical note gives a brief overview and discusses the quaternions, which are fourth dimensional extended complex numbers and used to represent orientation. Their relationship to other modes of attitude representation such as Euler angles and Axis-Angle representation is also explored and conversion from one representation to another is explained. The conventions, intuitive understanding and formulas most frequently used and indispensable to any quaternion application are stated and wherever possible, derived.