Safety-Critical and Distributed Nonlinear Predictive Controllers for Teams of Quadrupedal Robots

This paper presents a novel hierarchical, safety-critical control framework that integrates distributed nonlinear model predictive controllers (DNMPCs) with control barrier functions (CBFs) to enable cooperative locomotion of multi-agent quadrupedal robots in complex environments. While NMPC-based methods are widely adopted for enforcing safety constraints and navigating multi-robot systems (MRSs) through intricate environments, ensuring the safety of MRSs requires a formal definition grounded in the concept of invariant sets. CBFs, typically implemented via quadratic programs (QPs) at the planning layer, provide formal safety guarantees. However, their zero-control horizon limits their effectiveness for extended trajectory planning in inherently unstable, underactuated, and nonlinear legged robot models. Furthermore, the integration of CBFs into real-time NMPC for sophisticated MRSs, such as quadrupedal robot teams, remains underexplored. This paper develops computationally efficient, distributed NMPC algorithms that incorporate CBF-based collision safety guarantees within a consensus protocol, enabling longer planning horizons for safe cooperative locomotion under disturbances and rough terrain conditions. The optimal trajectories generated by the DNMPCs are tracked using full-order, nonlinear whole-body controllers at the low level. The proposed approach is validated through extensive numerical simulations with up to four Unitree A1 robots and hardware experiments involving two A1 robots subjected to external pushes, rough terrain, and uncertain obstacle information. Comparative analysis demonstrates that the proposed CBF-based DNMPCs achieve a 27.89% higher success rate than conventional NMPCs without CBF constraints.

Robust Adaptive Safe Robotic Grasping with Tactile Sensing

Robotic grasping requires safe force interaction to prevent a grasped object from being damaged or slipping out of the hand. In this vein, this paper proposes an integrated framework for grasping with formal safety guarantees based on Control Barrier Functions. We first design contact force and force closure constraints, which are enforced by a safety filter to accomplish safe grasping with finger force control. For sensory feedback, we develop a technique to estimate contact point, force, and torque from tactile sensors at each finger. We verify the framework with various safety filters in a numerical simulation under a two-finger grasping scenario. We then experimentally validate the framework by grasping multiple objects, including fragile lab glassware, in a real robotic setup, showing that safe grasping can be successfully achieved in the real world. We evaluate the performance of each safety filter in the context of safety violation and conservatism, and find that disturbance observer-based control barrier functions provide superior performance for safety guarantees with minimum conservatism. The demonstration video is available at https://youtu.be/Cuj47mkXRdg.

Safety-critical Locomotion of Biped Robots in Infeasible Paths: Overcoming Obstacles during Navigation toward Destination

This paper proposes a safety-critical locomotion control framework employed for legged robots exploring through infeasible path in obstacle-rich environments. Our research focus is on achieving safe and robust locomotion where robots confront unavoidable obstacles en route to their designated destination. Through the utilization of outcomes from physical interactions with unknown objects, we establish a hierarchy among the safety-critical conditions avoiding the obstacles. This hierarchy enables the generation of a safe reference trajectory that adeptly mitigates conflicts among safety conditions and reduce the risk while controlling the robot toward its destination without additional motion planning methods. In addition, robust bipedal locomotion is achieved by utilizing the Hybrid Linear Inverted Pendulum model, coupled with a disturbance observer addressing a disturbance from the physical interaction.

Dynamic Walking on Highly Underactuated Point Foot Humanoids: Closing the Loop between HZD and HLIP

Realizing bipedal locomotion on humanoid robots with point feet is especially challenging due to their highly underactuated nature, high degrees of freedom, and hybrid dynamics resulting from impacts. With the goal of addressing this challenging problem, this paper develops a control framework for realizing dynamic locomotion and implements it on a novel point foot humanoid: ADAM. To this end, we close the loop between Hybrid Zero Dynamics (HZD) and Hybrid linear inverted pendulum (HLIP) based step length regulation. To leverage the full-order hybrid dynamics of the robot, walking gaits are first generated offline by utilizing HZD. These trajectories are stabilized online through the use of a HLIP based regulator. Finally, the planned trajectories are mapped into the full-order system using a task space controller incorporating inverse kinematics. The proposed method is verified through numerical simulations and hardware experiments on the humanoid robot ADAM marking the first humanoid point foot walking. Moreover, we experimentally demonstrate the robustness of the realized walking via the ability to track a desired reference speed, robustness to pushes, and locomotion on uneven terrain.

Safety-critical Autonomous Inspection of Distillation Columns using Quadrupedal Robots Equipped with Roller Arms

This paper proposes a comprehensive framework designed for the autonomous inspection of complex environments, with a specific focus on multi-tiered settings such as distillation column trays. Leveraging quadruped robots equipped with roller arms, and through the use of onboard perception, we integrate essential motion components including: locomotion, safe and dynamic transitions between trays, and intermediate motions that bridge a variety of motion primitives. Given the slippery and confined nature of column trays, it is critical to ensure safety of the robot during inspection, therefore we employ a safety filter and footstep re-planning based upon control barrier function representations of the environment. Our framework integrates all system components into a state machine encoding the developed safety-critical planning and control elements to guarantee safety-critical autonomy, enabling autonomous and safe navigation and inspection of distillation columns. Experimental validation in an environment, consisting of industrial-grade chemical distillation trays, highlights the effectiveness of our multi-layered architecture.

Data-Driven Predictive Control for Robust Exoskeleton Locomotion

Exoskeleton locomotion must be robust while being adaptive to different users with and without payloads. To address these challenges, this work introduces a data-driven predictive control (DDPC) framework to synthesize walking gaits for lower-body exoskeletons, employing Hankel matrices and a state transition matrix for its data-driven model. The proposed approach leverages DDPC through a multi-layer architecture. At the top layer, DDPC serves as a planner employing Hankel matrices and a state transition matrix to generate a data-driven model that can learn and adapt to varying users and payloads. At the lower layer, our method incorporates inverse kinematics and passivity-based control to map the planned trajectory from DDPC into the full-order states of the lower-body exoskeleton. We validate the effectiveness of this approach through numerical simulations and hardware experiments conducted on the Atalante lower-body exoskeleton with different payloads. Moreover, we conducted a comparative analysis against the model predictive control (MPC) framework based on the reduced-order linear inverted pendulum (LIP) model. Through this comparison, the paper demonstrates that DDPC enables robust bipedal walking at various velocities while accounting for model uncertainties and unknown perturbations.

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.

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.

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.

Humanoid Robot Co-Design: Coupling Hardware Design with Gait Generation via Hybrid Zero Dynamics

Selecting robot design parameters can be challenging since these parameters are often coupled with the performance of the controller and, therefore, the resulting capabilities of the robot. This leads to a time-consuming and often expensive process whereby one iterates between designing the robot and manually evaluating its capabilities. This is particularly challenging for bipedal robots, where it can be difficult to evaluate the behavior of the system due to the underlying nonlinear and hybrid dynamics. Thus, in an effort to streamline the design process of bipedal robots, and maximize their performance, this paper presents a systematic framework for the co-design of humanoid robots and their associated walking gaits. To this end, we leverage the framework of hybrid zero dynamic (HZD) gait generation, which gives a formal approach to the generation of dynamic walking gaits. The key novelty of this paper is to consider both virtual constraints associated with the actuators of the robot, coupled with design virtual constraints that encode the associated parameters of the robot to be designed. These virtual constraints are combined in an HZD optimization problem which simultaneously determines the design parameters while finding a stable walking gait that minimizes a given cost function. The proposed approach is demonstrated through the design of a novel humanoid robot, ADAM, wherein its thigh and shin are co-designed so as to yield energy efficient bipedal locomotion.