Nonlinear Model Predictive Control of Robotic Systems with Control Lyapunov Functions

Abstract

The theoretical unification of Nonlinear Model Predictive Control (NMPC) with Control Lyapunov Functions (CLFs) provides a framework for achieving optimal control performance while ensuring stability guarantees. In this paper we present the first real-time realization of a unified NMPC and CLF controller on a robotic system with limited computational resources. These limitations motivate a set of approaches for efficiently incorporating CLF stability constraints into a general NMPC formulation. We evaluate the performance of the proposed methods compared to baseline CLF and NMPC controllers with a robotic Segway platform both in simulation and on hardware. The addition of a prediction horizon provides a performance advantage over CLF based controllers, which operate optimally point-wise in time. Moreover, the explicitly imposed stability constraints remove the need for difficult cost function and parameter tuning required by NMPC. Therefore the unified controller improves the performance of each isolated controller and simplifies the overall design process.

Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control

“…In this work, we build upon a kino-dynamic MPC formulation [22] where joint velocities and contact forces are decision variables in a low frequency MPC controller. This removes the need for heuristic coordination of separate leg and torso controllers and allows direct integration of CBF safety constraints into the MPC formulation similar to [25]. A higher rate tracking controller is implemented that fuses inverse dynamics with the CBF safety constraints to offer guarantees of safety with the whole-body dynamics in consideration [26].…”

A Review of Safe Online Learning for Nonlinear Control Systems

“…Offline techniques to determine a library of safe states and actions include explicit Hamilton Jacobi Isaacs (HJI), [25], [52], [53], calcualtions over a discretised state space or precomputed robust trajectories in the form of funnel libraries, [54] or linearised CPA techniques that adopt linear quadratic regulator (LQR) parameter varying controllers, [55]. Online techniques adopt some form of MPC over a time horizon either directly via a nonlinear model and sequential quadratic programming (SQP), [56], [57] or as in the case of the control contraction metric (CCM) technique via optimisation of a stabilizing control trajectory using a Riemannian metric, [1], [11], [58]. Uncertainty aware (UA) techniques define algorithms that employ BO for exploration, [2], [25], [59].…”

“…Nonlinear model predictive control (NMPC) has recently been employed for both trajectory optimisation in learning algorithms [56], and for safety certification in combination with stochastic uncertainty, [7], [59]. A recent review of MPC techniques is detailed in [60].…”

“…Stochastic techniques are a significant challenge for control theory proofs however, due to the nonlinear propagation of Gaussian distributions, [60]. Recently Grandia et al [56] have integrated CLFs with MPC for a 4D Segway robot by either enforcing exponential convergence of the Lyapunov cost function at every MPC iteration or by restricting each iteration to a Lyapunov level set. The algorithm uses SQP with a modified Hessian.…”

Iterative Model Predictive Control for Piecewise Systems

“…Yet the presence of discrete variables make planning and control problems challenging, as it is required to reason about all possible combinations of discrete events. This challenge can be mitigated by designing hierarchical strategies, where a high-level planner computes the discrete variables and a low-level controller optimizes the system trajectory described by continuous variables [1]- [4].…”