A Constructive Method for Designing Safe Multirate Controllers for Differentially-Flat Systems

We present a multi-rate control architecture that leverages fundamental properties of differential flatness to synthesize controllers for safety-critical nonlinear dynamical systems. We propose a two-layer architecture, where the high-level generates reference trajectories using a linear Model Predictive Controller, and the low-level tracks this reference using a feedback controller. The novelty lies in how we couple these layers, to achieve formal guarantees on recursive feasibility of the MPC problem, and safety of the nonlinear system. Furthermore, using differential flatness, we provide a constructive means to synthesize the multi-rate controller, thereby removing the need to search for suitable Lyapunov or barrier functions, or to approximately linearize/discretize nonlinear dynamics. We show the synthesized controller is a convex optimization problem, making it amenable to real-time implementations. The method is demonstrated experimentally on a ground rover and a quadruped robotic system.

Feasible Space Monitoring for Multiple Control Barrier Functions with application to Large Scale Indoor Navigation

Quadratic programs (QP) subject to multiple time-dependent control barrier function (CBF) based constraints have been used to design safety-critical controllers. However, ensuring the existence of a solution at all times to the QP subject to multiple CBF constraints is non-trivial. We quantify the feasible solution space of the QP in terms of its volume. We introduce a novel feasible space volume monitoring control barrier function that promotes compatibility of barrier functions and, hence, existence of a solution at all times. We show empirically that our approach not only enhances feasibility but also exhibits reduced sensitivity to changes in the hyperparameters such as gains of nominal controller. Finally, paired with a global planner, we evaluate our controller for navigation among humans in the AWS Hospital gazebo environment. The proposed controller is demonstrated to outperform the standard CBF-QP controller in maintaining feasibility.

The Dilemma of Choice: Addressing Constraint Selection for Autonomous Robotic Agents

The tasks that an autonomous agent is expected to perform are often optional or are incompatible with each other owing to the agent's limited actuation capabilities, specifically the dynamics and control input bounds. We encode tasks as time-dependent state constraints and leverage the advances in multi-objective optimization to formulate the problem of choosing tasks as selection of a feasible subset of constraints that can be satisfied for all time and maximizes a performance metric. We show that this problem, although amenable to reachability or mixed integer model predictive control-based analysis in the offline phase, is NP-Hard in general and therefore requires heuristics to be solved efficiently. When incompatibility in constraints is observed under a given policy that imposes task constraints at each time step in an optimization problem, we assign a Lagrange score to each of these constraints based on the variation in the corresponding Lagrange multipliers over the compatible time horizon. These scores are then used to decide the order in which constraints are dropped in a greedy strategy. We further employ a genetic algorithm to improve upon the greedy strategy. We evaluate our method on a robot waypoint following task when the low-level controllers that impose state constraints are described by Control Barrier Function-based Quadratic Programs and provide a comparison with waypoint selection based on knowledge of backward reachable sets.

Rate-Tunable Control Barrier Functions: Methods and Algorithms for Online Adaptation

Control Barrier Functions offer safety certificates by dictating controllers that enforce safety constraints. However, their response depends on the classK function that is used to restrict the rate of change of the barrier function along the system trajectories. This paper introduces the notion of Rate Tunable Control Barrier Function (RT-CBF), which allows for online tuning of the response of CBF-based controllers. In contrast to the existing CBF approaches that use a fixed (predefined) classK function to ensure safety, we parameterize and adapt the classK function parameters online. Furthermore, we discuss the challenges associated with multiple barrier constraints, namely ensuring that they admit a common control input that satisfies them simultaneously for all time. In practice, RT-CBF enables designing parameter dynamics for (1) a better-performing response, where performance is defined in terms of the cost accumulated over a time horizon, or (2) a less conservative response. We propose a model-predictive framework that computes the sensitivity of the future states with respect to the parameters and uses Sequential Quadratic Programming for deriving an online law to update the parameters in the direction of improving the performance. When prediction is not possible, we also provide point-wise sufficient conditions to be imposed on any user-given parameter dynamics so that multiple CBF constraints continue to admit common control input with time. Finally, we introduce RT-CBFs for decentralized uncooperative multi-agent systems, where a trust factor, computed based on the instantaneous ease of constraint satisfaction, is used to update parameters online for a less conservative response.

FORESEE: Model-based Reinforcement Learning using Unscented Transform with application to Tuning of Control Barrier Functions

In this paper, we introduce a novel online model-based reinforcement learning algorithm that uses Unscented Transform to propagate uncertainty for the prediction of the future reward. Previous approaches either approximate the state distribution at each step of the prediction horizon with a Gaussian, or perform Monte Carlo simulations to estimate the rewards. Our method, depending on the number of sigma points employed, can propagate either mean and covariance with minimal points, or higher-order moments with more points similarly to Monte Carlo. The whole framework is implemented as a computational graph for online training. Furthermore, in order to prevent explosion in the number of sigma points when propagating through a generic state-dependent uncertainty model, we add sigma-point expansion and contraction layers to our graph, which are designed using the principle of moment matching. Finally, we propose gradient descent inspired by Sequential Quadratic Programming to update policy parameters in the presence of state constraints. We demonstrate the proposed method with two applications in simulation. The first one designs a stabilizing controller for the cart-pole problem when the dynamics is known with state-dependent uncertainty. The second example, following up on our previous work, tunes the parameters of a control barrier function-based Quadratic Programming controller for a leader-follower problem in the presence of input constraints.

Trust-based Rate-Tunable Control Barrier Functions for Non-Cooperative Multi-Agent Systems

For efficient and robust task accomplishment in multi-agent systems, an agent must be able to distinguish cooperative agents from non-cooperative agents, i.e., uncooperative and adversarial agents. Task descriptions capturing safety and collaboration can often be encoded as Control Barrier Functions (CBFs). In this work, we first develop a trust metric that each agent uses to form its own belief of how cooperative other agents are. The metric is used to adjust the rate at which the CBFs allow the system trajectories to approach the boundaries of the safe region. Then, based on the presented notion of trust, we propose a Rate-Tunable CBF framework that leads to less conservative performance compared to an identity-agnostic implementation, where cooperative and non-cooperative agents are treated similarly. Finally, in presence of non-cooperating agents, we show the application of our control algorithm to heterogeneous multi-agent system through simulations.

Recursive Feasibility Guided Optimal Parameter Adaptation of Differential Convex Optimization Policies for Safety-Critical Systems

Quadratic programs (QPs) that enforce control barrier functions (CBFs) have become popular for safety-critical control synthesis, in part due to their ease of implementation and constraint specification. 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.