59,967 research outputs found
Real-Time Motion Planning of Legged Robots: A Model Predictive Control Approach
We introduce a real-time, constrained, nonlinear Model Predictive Control for
the motion planning of legged robots. The proposed approach uses a constrained
optimal control algorithm known as SLQ. We improve the efficiency of this
algorithm by introducing a multi-processing scheme for estimating value
function in its backward pass. This pass has been often calculated as a single
process. This parallel SLQ algorithm can optimize longer time horizons without
proportional increase in its computation time. Thus, our MPC algorithm can
generate optimized trajectories for the next few phases of the motion within
only a few milliseconds. This outperforms the state of the art by at least one
order of magnitude. The performance of the approach is validated on a quadruped
robot for generating dynamic gaits such as trotting.Comment: 8 page
Computationally Efficient Trajectory Optimization for Linear Control Systems with Input and State Constraints
This paper presents a trajectory generation method that optimizes a quadratic
cost functional with respect to linear system dynamics and to linear input and
state constraints. The method is based on continuous-time flatness-based
trajectory generation, and the outputs are parameterized using a polynomial
basis. A method to parameterize the constraints is introduced using a result on
polynomial nonpositivity. The resulting parameterized problem remains
linear-quadratic and can be solved using quadratic programming. The problem can
be further simplified to a linear programming problem by linearization around
the unconstrained optimum. The method promises to be computationally efficient
for constrained systems with a high optimization horizon. As application, a
predictive torque controller for a permanent magnet synchronous motor which is
based on real-time optimization is presented.Comment: Proceedings of the American Control Conference (ACC), pp. 1904-1909,
San Francisco, USA, June 29 - July 1, 201
Stochastic Optimal Power Flow Based on Data-Driven Distributionally Robust Optimization
We propose a data-driven method to solve a stochastic optimal power flow
(OPF) problem based on limited information about forecast error distributions.
The objective is to determine power schedules for controllable devices in a
power network to balance operation cost and conditional value-at-risk (CVaR) of
device and network constraint violations. These decisions include scheduled
power output adjustments and reserve policies, which specify planned reactions
to forecast errors in order to accommodate fluctuating renewable energy
sources. Instead of assuming the uncertainties across the networks follow
prescribed probability distributions, we assume the distributions are only
observable through a finite training dataset. By utilizing the Wasserstein
metric to quantify differences between the empirical data-based distribution
and the real data-generating distribution, we formulate a distributionally
robust optimization OPF problem to search for power schedules and reserve
policies that are robust to sampling errors inherent in the dataset. A simple
numerical example illustrates inherent tradeoffs between operation cost and
risk of constraint violation, and we show how our proposed method offers a
data-driven framework to balance these objectives
Constrained nonlinear optimal control: a converse HJB approach
Extending the concept of solving the Hamilton-Jacobi-Bellman (HJB) optimization equation backwards [2], the so called converse constrained optimal control problem is introduced, and used to create various classes of nonlinear systems for which the optimal controller subject to constraints is known. In this way a systematic method for the testing, validation and comparison of different control techniques
with the optimal is established. Because it naturally and explicitly handles constraints, particularly control input saturation, model predictive control (MPC) is a potentially powerful approach for nonlinear control design. However, nonconvexity of the nonlinear programs (NLP) involved in the MPC optimization makes the solution problematic. In order to explore properties of MPC-based constrained control schemes, and to point out the potential issues in implementing MPC, challenging benchmark examples are generated and analyzed. Properties of MPC-based constrained techniques are then evaluated and implementation issues are explored by applying both nonlinear MPC and MPC with feedback linearization
Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
Many algorithms for control, optimization and estimation in robotics depend
on derivatives of the underlying system dynamics, e.g. to compute
linearizations, sensitivities or gradient directions. However, we show that
when dealing with Rigid Body Dynamics, these derivatives are difficult to
derive analytically and to implement efficiently. To overcome this issue, we
extend the modelling tool `RobCoGen' to be compatible with Automatic
Differentiation. Additionally, we propose how to automatically obtain the
derivatives and generate highly efficient source code. We highlight the
flexibility and performance of the approach in two application examples. First,
we show a Trajectory Optimization example for the quadrupedal robot HyQ, which
employs auto-differentiation on the dynamics including a contact model. Second,
we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly
moving obstacle in a go-to task by fast, dynamic replanning
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