Safety-Critical Coordination of Legged Robots via Layered Controllers and Forward Reachable Set based Control Barrier Functions

This paper presents a safety-critical approach to the coordination of robots in dynamic environments. To this end, we leverage control barrier functions (CBFs) with the forward reachable set to guarantee the safe coordination of the robots while preserving a desired trajectory via a layered controller. The top-level planner generates a safety-ensured trajectory for each agent, accounting for the dynamic constraints in the environment. This planner leverages high-order CBFs based on the forward reachable set to ensure safety-critical coordination control, i.e., guarantee the safe coordination of the robots during locomotion. The middle-level trajectory planner employs single rigid body (SRB) dynamics to generate optimal ground reaction forces (GRFs) to track the safety-ensured trajectories from the top-level planner. The whole-body motions to adhere to the optimal GRFs while ensuring the friction cone condition at the end of each stance leg are generated from the low-level controller. The effectiveness of the approach is demonstrated through simulation and hardware experiments.

A Data-driven Method for Safety-critical Control: Designing Control Barrier Functions from State Constraints

This paper addresses the challenge of integrating explicit hard constraints into the control barrier function (CBF) framework for ensuring safety in autonomous systems, including robots. We propose a novel data-driven method to derive CBFs from these hard constraints in practical scenarios. Our approach assumes that the forward invariant safe set is either a subset or equal to the constrained set. The process consists of two main steps. First, we randomly sample states within the constraint boundaries and identify inputs meeting the time derivative criteria of the hard constraint; this iterative process converges using the Jaccard index. Next, we formulate CBFs that enclose the safe set using the sampled boundaries. This enables the creation of a control-invariant safe set, approaching the maximum attainable level of control invariance. This approach, therefore, addresses the complexities posed by complex autonomous systems with constrained control input spaces, culminating in a control-invariant safe set that closely approximates the maximal control invariant set.

Safety-critical Control of Quadrupedal Robots with Rolling Arms for Autonomous Inspection of Complex Environments

This paper presents a safety-critical control framework tailored for quadruped robots equipped with a roller arm, particularly when performing locomotive tasks such as autonomous robotic inspection in complex, multi-tiered environments. In this study, we consider the problem of operating a quadrupedal robot in distillation columns, locomoting on column trays and transitioning between these trays with a roller arm. To address this problem, our framework encompasses the following key elements: 1) Trajectory generation for seamless transitions between columns, 2) Foothold re-planning in regions deemed unsafe, 3) Safety-critical control incorporating control barrier functions, 4) Gait transitions based on safety levels, and 5) A low-level controller. Our comprehensive framework, comprising these components, enables autonomous and safe locomotion across multiple layers. We incorporate reduced-order and full-body models to ensure safety, integrating safety-critical control and footstep re-planning approaches. We validate the effectiveness of our proposed framework through practical experiments involving a quadruped robot equipped with a roller arm, successfully navigating and transitioning between different levels within the column tray structure.

Synthesizing Robust Walking Gaits via Discrete-Time Barrier Functions with Application to Multi-Contact Exoskeleton Locomotion

Successfully achieving bipedal locomotion remains challenging due to real-world factors such as model uncertainty, random disturbances, and imperfect state estimation. In this work, we propose the use of discrete-time barrier functions to certify hybrid forward invariance of reduced step-to-step dynamics. The size of these invariant sets can then be used as a metric for locomotive robustness. We demonstrate an application of this metric towards synthesizing robust nominal walking gaits using a simulation-in-the-loop approach. This procedure produces reference motions with step-to-step dynamics that are maximally forward-invariant with respect to the reduced representation of choice. The results demonstrate robust locomotion for both flat-foot walking and multi-contact walking on the Atalante lower-body exoskeleton.

Multi-Domain Walking with Reduced-Order Models of Locomotion

Drawing inspiration from human multi-domain walking, this work presents a novel reduced-order model based framework for realizing multi-domain robotic walking. At the core of our approach is the viewpoint that human walking can be represented by a hybrid dynamical system, with continuous phases that are fully-actuated, under-actuated, and over-actuated and discrete changes in actuation type occurring with changes in contact. Leveraging this perspective, we synthesize a multi-domain linear inverted pendulum (MLIP) model of locomotion. Utilizing the step-to-step dynamics of the MLIP model, we successfully demonstrate multi-domain walking behaviors on the bipedal robot Cassie -- a high degree of freedom 3D bipedal robot. Thus, we show the ability to bridge the gap between multi-domain reduced order models and full-order multi-contact locomotion. Additionally, our results showcase the ability of the proposed method to achieve versatile speed-tracking performance and robust push recovery behaviors.

Safety-Critical Control of Nonholonomic Vehicles in Dynamic Environments using Velocity Obstacles

This paper considers collision avoidance for vehicles with first-order nonholonomic constraints maintaining nonzero forward speeds, moving within dynamic environments. We leverage the concept of control barrier functions (CBFs) to synthesize control inputs that prioritize safety, where the safety criteria are derived from the velocity obstacle principle. Existing instantiations of CBFs for collision avoidance, e.g., based on maintaining a minimal distance, can result in control inputs that make the vehicle stop or even reverse. The proposed formulation effectively separates speed control from steering, allowing the vehicle to maintain a forward motion without compromising safety. This is beneficial for ensuring that the vehicle advances towards its desired destination, and it is moreover an underlying requirement for certain vehicles such as marine vessels and fixed-wing UAVs. Theoretical safety guarantees are provided, and numerical simulations demonstrate the efficiency of the strategy in environments containing moving obstacles.

PONG: Probabilistic Object Normals for Grasping via Analytic Bounds on Force Closure Probability

Classical approaches to grasp planning are deterministic, requiring perfect knowledge of an object's pose and geometry. In response, data-driven approaches have emerged that plan grasps entirely from sensory data. While these data-driven methods have excelled in generating parallel-jaw and power grasps, their application to precision grasps (those using the fingertips of a dexterous hand, e.g, for tool use) remains limited. Precision grasping poses a unique challenge due to its sensitivity to object geometry, which allows small uncertainties in the object's shape and pose to cause an otherwise robust grasp to fail. In response to these challenges, we introduce Probabilistic Object Normals for Grasping (PONG), a novel, analytic approach for calculating a conservative estimate of force closure probability in the case when contact locations are known but surface normals are uncertain. We then present a practical application where we use PONG as a grasp metric for generating robust grasps both in simulation and real-world hardware experiments. Our results demonstrate that maximizing PONG efficiently produces robust grasps, even for challenging object geometries, and that it can serve as a well-calibrated, uncertainty-aware metric of grasp quality.

Characterizing Smooth Safety Filters via the Implicit Function Theorem

Optimization-based safety filters, such as control barrier function (CBF) based quadratic programs (QPs), have demonstrated success in controlling autonomous systems to achieve complex goals. These CBF-QPs can be shown to be continuous, but are generally not smooth, let alone continuously differentiable. In this paper, we present a general characterization of smooth safety filters -- smooth controllers that guarantee safety in a minimally invasive fashion -- based on the Implicit Function Theorem. This characterization leads to families of smooth universal formulas for safety-critical controllers that quantify the conservatism of the resulting safety filter, the utility of which is demonstrated through illustrative examples.

Composing Control Barrier Functions for Complex Safety Specifications

The increasing complexity of control systems necessitates control laws that guarantee safety w.r.t. complex combinations of constraints. In this letter, we propose a framework to describe compositional safety specifications with control barrier functions (CBFs). The specifications are formulated as Boolean compositions of state constraints, and we propose an algorithmic way to create a single continuously differentiable CBF that captures these constraints and enables safety-critical control. We describe the properties of the proposed CBF, and we demonstrate its efficacy by numerical simulations.

On the Safety of Connected Cruise Control: Analysis and Synthesis with Control Barrier Functions

Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy these vehicles and leverage their benefits, the underlying algorithms must ensure their safe operation. In this paper, we address the safety of connected cruise control strategies for longitudinal car following using control barrier function (CBF) theory. In particular, we consider various safety measures such as minimum distance, time headway and time to conflict, and provide a formal analysis of these measures through the lens of CBFs. Additionally, motivated by how stability charts facilitate stable controller design, we derive safety charts for existing connected cruise controllers to identify safe choices of controller parameters. Finally, we combine the analysis of safety measures and the corresponding stability charts to synthesize safety-critical connected cruise controllers using CBFs. We verify our theoretical results by numerical simulations.