We address the problem of synthesizing a controller for nonlinear systems with reach-avoid requirements. Our controller consists of a reference controller and a tracking controller which drives the actual trajectory to follow the reference trajectory. We identify a type of reference trajectory such that the tracking error between the actual trajectory of the closed-loop system and the reference trajectory can be bounded. Moreover, such a bound on the tracking error is independent of the reference trajectory. Using such bounds on the tracking error, we propose a method that can find a reference trajectory by solving a satisfiability problem over linear constraints. Our overall algorithm guarantees that the resulting controller can make sure every trajectory from the initial set of the system satisfies the given reach-avoid requirement. We also implement our technique in a tool FACTEST. We show that FACTEST can find controllers for four vehicle models (3–6 dimensional state space and 2–4 dimensional input space) across eight scenarios (with up to 22 obstacles), all with running time at the sub-second range.
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Model Error Propagation via Learned Contraction Metrics for Safe Feedback Motion Planning of Unknown Systems
We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset, our method learns a deep control-affine approximation of the dynamics. To find a trusted domain where this model can be used for planning, we obtain an estimate of the Lipschitz constant of the model error, which is valid with a given probability, in a region around the training data, providing a local, spatially-varying model error bound. We derive a trajectory tracking error bound for a contraction based controller that is subjected to this model error, and then learn a controller that optimizes this tracking bound. With a given probability, we verify the correctness of the controller and tracking error bound in the trusted domain. We then use the trajectory error bound together with the trusted domain to guide a sampling-based planner to return trajectories that can be robustly tracked in execution. We show results on a 4D car, a 6D quadrotor, and a 22D deformable object manipulation task, showing our method plans safely with learned models of highdimensional underactuated systems, while baselines that plan without considering the tracking error bound or the trusted domain can fail to stabilize the system and become unsafe.
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- NSF-PAR ID:
- 10315848
- Date Published:
- Journal Name:
- 2021 60th IEEE Conference on Decision and Control (CDC)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract A safety-critical measure of legged locomotion performance is a robot's ability to track its desired time-varying position trajectory in an environment, which is herein termed as “global-position tracking.” This paper introduces a nonlinear control approach that achieves asymptotic global-position tracking for three-dimensional (3D) bipedal robots. Designing a global-position tracking controller presents a challenging problem due to the complex hybrid robot model and the time-varying desired global-position trajectory. Toward tackling this problem, the first main contribution is the construction of impact invariance to ensure all desired trajectories respect the foot-landing impact dynamics, which is a necessary condition for realizing asymptotic tracking of hybrid walking systems. Thanks to their independence of the desired global position, these conditions can be exploited to decouple the higher-level planning of the global position and the lower-level planning of the remaining trajectories, thereby greatly alleviating the computational burden of motion planning. The second main contribution is the Lyapunov-based stability analysis of the hybrid closed-loop system, which produces sufficient conditions to guide the controller design for achieving asymptotic global-position tracking during fully actuated walking. Simulations and experiments on a 3D bipedal robot with twenty revolute joints confirm the validity of the proposed control approach in guaranteeing accurate tracking.more » « less
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null (Ed.)Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.more » « less
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Introduction Individuals who have suffered a cervical spinal cord injury prioritize the recovery of upper limb function for completing activities of daily living. Hybrid FES-exoskeleton systems have the potential to assist this population by providing a portable, powered, and wearable device; however, realization of this combination of technologies has been challenging. In particular, it has been difficult to show generalizability across motions, and to define optimal distribution of actuation, given the complex nature of the combined dynamic system.
Methods In this paper, we present a hybrid controller using a model predictive control (MPC) formulation that combines the actuation of both an exoskeleton and an FES system. The MPC cost function is designed to distribute actuation on a single degree of freedom to favor FES control effort, reducing exoskeleton power consumption, while ensuring smooth movements along different trajectories. Our controller was tested with nine able-bodied participants using FES surface stimulation paired with an upper limb powered exoskeleton. The hybrid controller was compared to an exoskeleton alone controller, and we measured trajectory error and torque while moving the participant through two elbow flexion/extension trajectories, and separately through two wrist flexion/extension trajectories.
Results The MPC-based hybrid controller showed a reduction in sum of squared torques by an average of 48.7 and 57.9% on the elbow flexion/extension and wrist flexion/extension joints respectively, with only small differences in tracking accuracy compared to the exoskeleton alone.
Discussion To realize practical implementation of hybrid FES-exoskeleton systems, the control strategy requires translation to multi-DOF movements, achieving more consistent improvement across participants, and balancing control to more fully leverage the muscles' capabilities.
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Abstract Biological musculature employs variable recruitment of muscle fibers from smaller to larger units as the load increases. This orderly recruitment strategy has certain physiological advantages like minimizing fatigue and providing finer motor control. Recently fluidic artificial muscles (FAM) are gaining popularity as actuators due to their increased efficiency by employing bio-inspired recruitment strategies such as active variable recruitment (AVR). AVR systems use a multi-valve system (MVS) configuration to selectively recruit individual FAMs depending on the load. However, when using an MVS configuration, an increase in the number of motor units in a bundle corresponds to an increase in the number of valves in the system. This introduces greater complexity and weight. The objective of this paper is to propose, analyze, and demonstrate an orderly recruitment valve (ORV) concept that enables orderly recruitment of multiple FAMs in the system using a single valve. A mathematical model of an ORV-controlled FAM bundle is presented and validated by experiments performed on a proof-of-concept ORV experiment. The modeling is extended to explore a case study of a 1-DOF robot arm system consisting of an electrohydraulic pressurization system, ORV, and a FAM-actuated rotating arm plant and its dynamics are simulated to further demonstrate the capabilities of an ORV-controlled closed-loop system. An orderly recruitment strategy was implemented through a model-based feed forward controller. To benchmark the performance of the ORV, a conventional MVS with equivalent dynamics and controller was also implemented. Trajectory tracking simulations on both the systems revealed lower tracking error for the ORV controlled system compared to the MVS controlled system due to the unique cross-flow effects present in the ORV. However, the MVS, due to its independent and multiple valve setup, proved to be more adaptable for performance. For example, modifications to the recruitment thresholds of the MVS demonstrated improvement in tracking error, albeit with a sacrifice in efficiency. In the ORV, tracking performance remained insensitive to any variation in recruitment threshold. The results show that compared to the MVS, the ORV offers a simpler and more compact valving architecture at the expense of moderate losses in control flexibility and performance.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/CDC45484.2021.9683354
