Convex computation of the reachable set for controlled polynomial hybrid systems

Shia, Victor; Vasudevan, Ram; Bajcsy, Růžena; Tedrake, Russ

doi:10.1109/cdc.2014.7039612

Cited by 38 publications

(32 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Furthermore, a natural extension of this work would be to include elastic impacts, where many models exist which are amenable to complementarity formulations such as in [51]. Recent work on the computation of regions of attraction for polynomial systems has included convex, moment based approaches [16], with extensions to hybrid systems [46] and control design [30]. A similar approach here might eliminate the requirement for numerically challenging bilinear alternations and allow the problem to be posed as a single convex optimization program.…”

Section: Discussionmentioning

confidence: 99%

Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction

Posa

Tobenkin

Tedrake

2016

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

Abstract-Many critical tasks in robotics, such as locomotion or manipulation, involve collisions between a rigid body and the environment or between multiple bodies. Methods based on sums-of-squares (SOS) for numerical computation of Lyapunov certificates are a powerful tool for analyzing the stability of continuous nonlinear systems, and can additionally be used to automatically synthesize stabilizing feedback controllers. Here, we present a method for applying sums-of-squares verification to rigid bodies with Coulomb friction undergoing discontinuous, inelastic impact events. The proposed algorithm explicitly generates Lyapunov certificates for stability, positive invariance, and safety over admissible (non-penetrating) states and contact forces. We leverage the complementarity formulation of contact, which naturally generates the semialgebraic constraints that define this admissible region. The approach is demonstrated on multiple robotics examples, including simple models of a walking robot, a perching aircraft, and control design of a balancing robot.

show abstract

Section: Discussionmentioning

confidence: 99%

Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction

Posa

Tobenkin

Tedrake

2016

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This section describes a method to compute an indicator function on the set of times and points that the robot could reach (i.e. the FRS) using SOS programming based on [18], [22], [23]. We construct a time-varying FRS since we are concerned with dynamic environments.…”

Section: Relating Predictions To Trajectoriesmentioning

confidence: 99%

Towards Provably Not-At-Fault Control of Autonomous Robots in Arbitrary Dynamic Environments

Vaskov¹,

Kousik²,

Larson³

et al. 2019

Robotics: Science and Systems XV

Self Cite

View full text Add to dashboard Cite

As autonomous robots increasingly become part of daily life, they will often encounter dynamic environments while only having limited information about their surroundings. Unfortunately, due to the possible presence of malicious dynamic actors, it is infeasible to develop an algorithm that can guarantee collision-free operation. Instead, one can attempt to design a control technique that guarantees the robot is not-at-fault in any collision. In the literature, making such guarantees in real time has been restricted to static environments or specific dynamic models. To ensure not-at-fault behavior, a robot must first correctly sense and predict the world around it within some sufficiently large sensor horizon (the prediction problem), then correctly control relative to the predictions (the control problem). This paper addresses the control problem by proposing Reachability-based Trajectory Design for Dynamic environments (RTD-D), which guarantees that a robot with an arbitrary nonlinear dynamic model correctly responds to predictions in arbitrary dynamic environments. RTD-D first computes a Forward Reachable Set (FRS) offline of the robot tracking parameterized desired trajectories that include fail-safe maneuvers. Then, for online receding-horizon planning, the method provides a way to discretize predictions of an arbitrary dynamic environment to enable real-time collision checking. The FRS is used to map these discretized predictions to trajectories that the robot can track while provably not-at-fault. One such trajectory is chosen at each iteration, or the robot executes the fail-safe maneuver from its previous trajectory which is guaranteed to be not at fault. RTD-D is shown to produce not-at-fault behavior over thousands of simulations and several real-world hardware demonstrations on two robots: a Segway, and a small electric vehicle.

show abstract

“…This approach uses semi-definite programming to identify the limits of safety in the state space of a system as well as associated controllers for a broad class of nonlinear [5], [6], [7] and hybrid systems [8], [9]. These safe sets can take the form of reachable sets (sets that can reach a known safe state) [10], [9], [5] or invariant sets (sets whose members can be controlled to remain in the set indefinitely) in state space [11], [8], [12]. However, the representation of each of these sets in state space severely restricts the size of the problem that can be tackled by these approaches.…”

Section: Introductionmentioning

confidence: 99%

Walking With Confidence: Safety Regulation for Full Order Biped Models

Smit-Anseeuw

Remy

Vasudevan

2019

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

Safety guarantees are valuable in the control of walking robots, as falling can be both dangerous and costly. Unfortunately, set-based tools for generating safety guarantees (such as sums-of-squares optimization) are typically restricted to simplified, low-dimensional models of walking robots. For more complex models, methods based on hybrid zero dynamics can ensure the local stability of a pre-specified limit cycle, but provide limited guarantees. This paper combines the benefits of both approaches by using sums-of-squares optimization on a hybrid zero dynamics manifold to generate a guaranteed safe set for a 10-dimensional walking robot model. Along with this set, this paper describes how to generate a controller that maintains safety by modifying the manifold parameters when on the edge of the safe set. The proposed approach, which is applied to a bipedal Rabbit model, provides a roadmap for applying sums-of-squares techniques to high dimensional systems. This opens the door for a broad set of tools that can generate flexible and safe controllers for complex walking robot models.

show abstract

Convex computation of the reachable set for controlled polynomial hybrid systems

Cited by 38 publications

References 15 publications

Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction

Stability Analysis and Control of Rigid-Body Systems With Impacts and Friction

Towards Provably Not-At-Fault Control of Autonomous Robots in Arbitrary Dynamic Environments

Walking With Confidence: Safety Regulation for Full Order Biped Models

Contact Info

Product

Resources

About