@param mass The mass of the system. @param l0 The springy leg has rest length of l0 @param k The spring constant @par

Generates state transitions using pybullet. The transitions are returned both in image and state space @param load_world_cb a

@param system A dynamical system.

@param dtype The torch datatype @param x_lo, x_up torch tensor that lower and upper bound the state @param dynamics_relu torc

@param dtype The torch datatype @param x_lo, x_up torch tensor that lower and upper bound the state @param dynamics_relu torc

@param dtype The torch datatype @param x_lo, x_up torch tensor that lower and upper bound the state @param dynamics_relu torc

@param x_lo The lower bound of x[n] and x[n+1]. This is only used in forming the mixed-integer linear constraints. @param x_u

@param x_lo The lower bound of state x = [q; v]. @param x_up The upper bound of state x = [q; v]. @param u_lo The lower bound

@param dynamics_relu A fully connected network that takes the input as a partial state and the control, and outputs the change of vel

This stores the (possibly relaxed) constraints on the controller that maps x to u.

Container for training options. Gets passed to DynamicsLearning constructor

We want R to be a full column rank matrix, with size m x n and m >= n. The first n rows of R (The square matrix on top of R) is param

R = U * Σ * V, where U and V are given orthornomral matrices. Σ is a diagonal matrix such that Σ[i, i] = a(i) + v(i)²

@param forward_system. The forward dynamical system representing x[n+1] = f(x[n], u[n]). This system must implements functions like

@param figsize The size of the fig @param subplot The argument in add_subplot(subplot) when adding the axis for pendulum.

Args: m_sphere: The mass of the sphere. m_ee: The mass of the end-effector. length: The length of the pole

Args: u_z_equilibrium: The equilibrium input force in the z direction (which is the total gravitational force of the pole

The parameter of this quadrotor is obtained from Attitude stabilization of a VTOL quadrotor aircraft by Abdelhamid Tayebi and

@param dynamics_relu Then network ϕ in the documentation above. @param hover_thrust The thrust command to maintain equilibrium.

@param u_lo The lower limit of the input. Note that the system input is the thrust, so this lower limit should be non-negative.

@param x_lo The lower bound of the state. @param x_up The upper bound of the state. @param u_lo The lower input limits.

@param x_lo The lower bound of the state. @param x_up The upper bound of the state. @param u_lo The lower input limits.

@param x_lo The lower bound of the state. @param x_up The upper bound of the state. @param u_lo The lower input limits.

This function will be called inside output_constraint(). We group the network layers by a linear layer followed by a (leaky) ReLU layer,

Add the constraint on output = relu(W * input + b). @param linear_layer @param binary_var_type The variable type for the binary variable.

Adds the constraints to @p mip on the forward dynamics. Args: u_input_prog: Set to None don't plan to compute the ReLU input bounds

This function is intended for internal usage only (but I expose it as a public function for unit test). Add the constraint and variables

For the constraint c(w'*x_hat+b) <= y w'*x_hat+b <= y y <= x_coeffs * x_hat + beta_coeffs * beta + constants 0 <= beta <= 1 F

For a variable x in the interval [x_lo, x_up], we denote the absolute value |x| as s, and returns the mixed-integer constraints on x, s and t

Add the dynamic constraint pos[n+1] = pos[n] + (v[n] + v[n+1]) * dt / 2 [vel[n+1], rpy[n+1]] = [vel[n], rpy[n]] + ϕ(rpy[n], u

Add the dynamic constraints a mixed-integer linear constraints. Refer to relu_system.py for the common API. The constraints a

Add the dynamic constraints a mixed-integer linear constraints. Refer to relu_system.py for the common API. The constraints a

Adds normal noise to a dataset @param noise_std_percent tensor with standard deviation of the noise, as percent of the mean of the magnit

For a saturation block y = upper_limit if x >= upper_limit y = x if lower_limit <= x <= upper_limit y = lower_limit if x <= lower_lim

moves all the relevant parameters to device (e.g. 'cpu', 'cuda')

Given the state of the SLIP at apex (ż = 0) during the flight phase, compute the state at the next apex. @param pos_x The ho

Determine the type for the binary variables based on the bound propagation method.

Given a box region x_lo <= x <= x_up, return the mixed-integer constraint that x is on the boundary of this box region. For each x[i], we

For some apex state, the robot can not reach the next apex.